From 82084d8210bd0e3dda2219fbdee389aef9a03b52 Mon Sep 17 00:00:00 2001
From: Reidmen
Date: Fri, 11 Dec 2020 16:03:48 +0100
Subject: [PATCH] First commit, included main, solvers, and ipynb
---
.gitignore | 41 +
ALE Testing - Article.ipynb | 12176 ++++++++++++++++++++++++++++++++++
README.rst | 63 +
common.py | 54 +
main.py | 144 +
solvers.py | 1005 +++
6 files changed, 13483 insertions(+)
create mode 100644 .gitignore
create mode 100644 ALE Testing - Article.ipynb
create mode 100644 README.rst
create mode 100644 common.py
create mode 100644 main.py
create mode 100644 solvers.py
diff --git a/.gitignore b/.gitignore
new file mode 100644
index 0000000..f0e3716
--- /dev/null
+++ b/.gitignore
@@ -0,0 +1,41 @@
+# Byte-compiled / optimized / DLL files
+__pycache__/
+
+# PEP 582; used by e.g. github.com/David-OConnor/pyflow
+__pypackages__/
+
+# Distribution / packaging
+.Python
+build/
+develop-eggs/
+dist/
+downloads/
+eggs/
+.eggs/
+lib/
+lib64/
+parts/
+sdist/
+var/
+wheels/
+share/python-wheels/
+*.egg-info/
+.installed.cfg
+*.egg
+MANIFEST
+
+# Generated results from FEniCS/Python plots, etc...
+*.xdmf
+*.h5
+*.pyc
+*.png
+
+# Jupyter checkpoints
+#*.ipynb
+.ipynb_checkpoints/
+
+# Numerical results
+tests/
+
+# Paraview state files
+*.pvsm
diff --git a/ALE Testing - Article.ipynb b/ALE Testing - Article.ipynb
new file mode 100644
index 0000000..3a73cc8
--- /dev/null
+++ b/ALE Testing - Article.ipynb
@@ -0,0 +1,12176 @@
+{
+ "cells": [
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {
+ "scrolled": true
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "DOLFIN VERSION: 2019.1.0\n",
+ "SOLVER VERSION: 0.2\n",
+ "__author__: Reidmen Arostica\n",
+ "The solution of the linear system is done with built-in PETS Krylov solver.\n",
+ "Initializing testing of two deformation cases with input parameters:\n",
+ " Solver to use -solver_to_use- : LU\n",
+ " GCL-stabilization term -gcl_stab- : True\n",
+ " Evaluation of jacobian at n in time-derivate term -jac_at_n- : False\n",
+ " \n",
+ "\n",
+ "Initializing iNSE problem with Deformation type: High_Osc_exp\n",
+ "\n",
+ "\n",
+ "Setup with initial condition: True\n",
+ "Using a non-zero initial condition (2D-Gaussian) for the velocity field!\n",
+ "Using time-derivative term approximated with Jacobian at n+1...\n",
+ "Using LU Solver...\n",
+ "Starting iteration over time...\n",
+ "E (Energy) of initial velocity field: 0.01659 at time 0.000\n",
+ "\n",
+ "J integrated over the domain: 14.686 at time: 0.010\n",
+ "J_n integrated over the domain: 12.000 at time: 0.010\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.010\n",
+ "d (def. map) integrated over the domain: 219.674 at time: 0.010\n",
+ "Strain energy E( eps(|u|^2) ): 0.00015 at time 0.010\n",
+ "Residual of scheme -> 'delta' value: 0.00330 at time 0.010\n",
+ "\n",
+ "J integrated over the domain: 17.203 at time: 0.020\n",
+ "J_n integrated over the domain: 14.686 at time: 0.020\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.020\n",
+ "d (def. map) integrated over the domain: 299.941 at time: 0.020\n",
+ "Strain energy E( eps(|u|^2) ): 0.00011 at time 0.020\n",
+ "Residual of scheme -> 'delta' value: 0.00008 at time 0.020\n",
+ "\n",
+ "J integrated over the domain: 19.393 at time: 0.030\n",
+ "J_n integrated over the domain: 17.203 at time: 0.030\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.030\n",
+ "d (def. map) integrated over the domain: 380.093 at time: 0.030\n",
+ "Strain energy E( eps(|u|^2) ): 0.00009 at time 0.030\n",
+ "Residual of scheme -> 'delta' value: 0.00004 at time 0.030\n",
+ "\n",
+ "J integrated over the domain: 21.119 at time: 0.040\n",
+ "J_n integrated over the domain: 19.393 at time: 0.040\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.040\n",
+ "d (def. map) integrated over the domain: 450.001 at time: 0.040\n",
+ "Strain energy E( eps(|u|^2) ): 0.00008 at time 0.040\n",
+ "Residual of scheme -> 'delta' value: 0.00002 at time 0.040\n",
+ "\n",
+ "J integrated over the domain: 22.271 at time: 0.050\n",
+ "J_n integrated over the domain: 21.119 at time: 0.050\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.050\n",
+ "d (def. map) integrated over the domain: 500.016 at time: 0.050\n",
+ "Strain energy E( eps(|u|^2) ): 0.00007 at time 0.050\n",
+ "Residual of scheme -> 'delta' value: 0.00001 at time 0.050\n",
+ "\n",
+ "J integrated over the domain: 22.779 at time: 0.060\n",
+ "J_n integrated over the domain: 22.271 at time: 0.060\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.060\n",
+ "d (def. map) integrated over the domain: 522.869 at time: 0.060\n",
+ "Strain energy E( eps(|u|^2) ): 0.00006 at time 0.060\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.060\n",
+ "\n",
+ "J integrated over the domain: 22.609 at time: 0.070\n",
+ "J_n integrated over the domain: 22.779 at time: 0.070\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.070\n",
+ "d (def. map) integrated over the domain: 515.153 at time: 0.070\n",
+ "Strain energy E( eps(|u|^2) ): 0.00005 at time 0.070\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.070\n",
+ "\n",
+ "J integrated over the domain: 21.772 at time: 0.080\n",
+ "J_n integrated over the domain: 22.609 at time: 0.080\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.080\n",
+ "d (def. map) integrated over the domain: 478.026 at time: 0.080\n",
+ "Strain energy E( eps(|u|^2) ): 0.00005 at time 0.080\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.080\n",
+ "\n",
+ "J integrated over the domain: 20.322 at time: 0.090\n",
+ "J_n integrated over the domain: 21.772 at time: 0.090\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.090\n",
+ "d (def. map) integrated over the domain: 416.965 at time: 0.090\n",
+ "Strain energy E( eps(|u|^2) ): 0.00005 at time 0.090\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.090\n",
+ "\n",
+ "J integrated over the domain: 18.348 at time: 0.100\n",
+ "J_n integrated over the domain: 20.322 at time: 0.100\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.100\n",
+ "d (def. map) integrated over the domain: 340.652 at time: 0.100\n",
+ "Strain energy E( eps(|u|^2) ): 0.00004 at time 0.100\n",
+ "Residual of scheme -> 'delta' value: 0.00001 at time 0.100\n",
+ "\n",
+ "J integrated over the domain: 15.976 at time: 0.110\n",
+ "J_n integrated over the domain: 18.348 at time: 0.110\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.110\n",
+ "d (def. map) integrated over the domain: 259.224 at time: 0.110\n",
+ "Strain energy E( eps(|u|^2) ): 0.00005 at time 0.110\n",
+ "Residual of scheme -> 'delta' value: 0.00002 at time 0.110\n",
+ "\n",
+ "J integrated over the domain: 13.354 at time: 0.120\n",
+ "J_n integrated over the domain: 15.976 at time: 0.120\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.120\n",
+ "d (def. map) integrated over the domain: 182.319 at time: 0.120\n",
+ "Strain energy E( eps(|u|^2) ): 0.00009 at time 0.120\n",
+ "Residual of scheme -> 'delta' value: 0.00002 at time 0.120\n",
+ "\n",
+ "J integrated over the domain: 10.646 at time: 0.130\n",
+ "J_n integrated over the domain: 13.354 at time: 0.130\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.130\n",
+ "d (def. map) integrated over the domain: 117.346 at time: 0.130\n",
+ "Strain energy E( eps(|u|^2) ): 0.00021 at time 0.130\n",
+ "Residual of scheme -> 'delta' value: 0.00001 at time 0.130\n",
+ "\n",
+ "J integrated over the domain: 8.024 at time: 0.140\n",
+ "J_n integrated over the domain: 10.646 at time: 0.140\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.140\n",
+ "d (def. map) integrated over the domain: 68.389 at time: 0.140\n",
+ "Strain energy E( eps(|u|^2) ): 0.00033 at time 0.140\n",
+ "Residual of scheme -> 'delta' value: -0.00003 at time 0.140\n",
+ "\n",
+ "J integrated over the domain: 5.652 at time: 0.150\n",
+ "J_n integrated over the domain: 8.024 at time: 0.150\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.150\n",
+ "d (def. map) integrated over the domain: 35.944 at time: 0.150\n",
+ "Strain energy E( eps(|u|^2) ): 0.00030 at time 0.150\n",
+ "Residual of scheme -> 'delta' value: -0.00007 at time 0.150\n",
+ "\n",
+ "J integrated over the domain: 3.678 at time: 0.160\n",
+ "J_n integrated over the domain: 5.652 at time: 0.160\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.160\n",
+ "d (def. map) integrated over the domain: 17.531 at time: 0.160\n",
+ "Strain energy E( eps(|u|^2) ): 0.00016 at time 0.160\n",
+ "Residual of scheme -> 'delta' value: -0.00007 at time 0.160\n",
+ "\n",
+ "J integrated over the domain: 2.228 at time: 0.170\n",
+ "J_n integrated over the domain: 3.678 at time: 0.170\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.170\n",
+ "d (def. map) integrated over the domain: 8.963 at time: 0.170\n",
+ "Strain energy E( eps(|u|^2) ): 0.00004 at time 0.170\n",
+ "Residual of scheme -> 'delta' value: -0.00003 at time 0.170\n",
+ "\n",
+ "J integrated over the domain: 1.391 at time: 0.180\n",
+ "J_n integrated over the domain: 2.228 at time: 0.180\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.180\n",
+ "d (def. map) integrated over the domain: 5.936 at time: 0.180\n",
+ "Strain energy E( eps(|u|^2) ): 0.00001 at time 0.180\n",
+ "Residual of scheme -> 'delta' value: -0.00001 at time 0.180\n",
+ "\n",
+ "J integrated over the domain: 1.221 at time: 0.190\n",
+ "J_n integrated over the domain: 1.391 at time: 0.190\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.190\n",
+ "d (def. map) integrated over the domain: 5.492 at time: 0.190\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.190\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.190\n",
+ "\n",
+ "J integrated over the domain: 1.729 at time: 0.200\n",
+ "J_n integrated over the domain: 1.221 at time: 0.200\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.200\n",
+ "d (def. map) integrated over the domain: 6.988 at time: 0.200\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.200\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.200\n",
+ "\n",
+ "J integrated over the domain: 2.881 at time: 0.210\n",
+ "J_n integrated over the domain: 1.729 at time: 0.210\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.210\n",
+ "d (def. map) integrated over the domain: 12.302 at time: 0.210\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.210\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.210\n",
+ "\n",
+ "J integrated over the domain: 4.607 at time: 0.220\n",
+ "J_n integrated over the domain: 2.881 at time: 0.220\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.220\n",
+ "d (def. map) integrated over the domain: 25.223 at time: 0.220\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.220\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.220\n",
+ "\n"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "J integrated over the domain: 6.797 at time: 0.230\n",
+ "J_n integrated over the domain: 4.607 at time: 0.230\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.230\n",
+ "d (def. map) integrated over the domain: 50.200 at time: 0.230\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.230\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.230\n",
+ "\n",
+ "J integrated over the domain: 9.314 at time: 0.240\n",
+ "J_n integrated over the domain: 6.797 at time: 0.240\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.240\n",
+ "d (def. map) integrated over the domain: 90.753 at time: 0.240\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.240\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.240\n",
+ "\n",
+ "J integrated over the domain: 12.000 at time: 0.250\n",
+ "J_n integrated over the domain: 9.314 at time: 0.250\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.250\n",
+ "d (def. map) integrated over the domain: 148.000 at time: 0.250\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.250\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.250\n",
+ "\n",
+ "J integrated over the domain: 14.686 at time: 0.260\n",
+ "J_n integrated over the domain: 12.000 at time: 0.260\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.260\n",
+ "d (def. map) integrated over the domain: 219.674 at time: 0.260\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.260\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.260\n",
+ "\n",
+ "J integrated over the domain: 17.203 at time: 0.270\n",
+ "J_n integrated over the domain: 14.686 at time: 0.270\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.270\n",
+ "d (def. map) integrated over the domain: 299.941 at time: 0.270\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.270\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.270\n",
+ "\n",
+ "J integrated over the domain: 19.393 at time: 0.280\n",
+ "J_n integrated over the domain: 17.203 at time: 0.280\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.280\n",
+ "d (def. map) integrated over the domain: 380.093 at time: 0.280\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.280\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.280\n",
+ "\n",
+ "J integrated over the domain: 21.119 at time: 0.290\n",
+ "J_n integrated over the domain: 19.393 at time: 0.290\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.290\n",
+ "d (def. map) integrated over the domain: 450.001 at time: 0.290\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.290\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.290\n",
+ "\n",
+ "J integrated over the domain: 22.271 at time: 0.300\n",
+ "J_n integrated over the domain: 21.119 at time: 0.300\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.300\n",
+ "d (def. map) integrated over the domain: 500.016 at time: 0.300\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.300\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.300\n",
+ "\n",
+ "J integrated over the domain: 22.779 at time: 0.310\n",
+ "J_n integrated over the domain: 22.271 at time: 0.310\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.310\n",
+ "d (def. map) integrated over the domain: 522.869 at time: 0.310\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.310\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.310\n",
+ "\n",
+ "J integrated over the domain: 22.609 at time: 0.320\n",
+ "J_n integrated over the domain: 22.779 at time: 0.320\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.320\n",
+ "d (def. map) integrated over the domain: 515.153 at time: 0.320\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.320\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.320\n",
+ "\n",
+ "J integrated over the domain: 21.772 at time: 0.330\n",
+ "J_n integrated over the domain: 22.609 at time: 0.330\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.330\n",
+ "d (def. map) integrated over the domain: 478.026 at time: 0.330\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.330\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.330\n",
+ "\n",
+ "J integrated over the domain: 20.322 at time: 0.340\n",
+ "J_n integrated over the domain: 21.772 at time: 0.340\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.340\n",
+ "d (def. map) integrated over the domain: 416.965 at time: 0.340\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.340\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.340\n",
+ "\n",
+ "J integrated over the domain: 18.348 at time: 0.350\n",
+ "J_n integrated over the domain: 20.322 at time: 0.350\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.350\n",
+ "d (def. map) integrated over the domain: 340.652 at time: 0.350\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.350\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.350\n",
+ "\n",
+ "J integrated over the domain: 15.976 at time: 0.360\n",
+ "J_n integrated over the domain: 18.348 at time: 0.360\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.360\n",
+ "d (def. map) integrated over the domain: 259.224 at time: 0.360\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.360\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.360\n",
+ "\n",
+ "J integrated over the domain: 13.354 at time: 0.370\n",
+ "J_n integrated over the domain: 15.976 at time: 0.370\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.370\n",
+ "d (def. map) integrated over the domain: 182.319 at time: 0.370\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.370\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.370\n",
+ "\n",
+ "J integrated over the domain: 10.646 at time: 0.380\n",
+ "J_n integrated over the domain: 13.354 at time: 0.380\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.380\n",
+ "d (def. map) integrated over the domain: 117.346 at time: 0.380\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.380\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.380\n",
+ "\n",
+ "J integrated over the domain: 8.024 at time: 0.390\n",
+ "J_n integrated over the domain: 10.646 at time: 0.390\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.390\n",
+ "d (def. map) integrated over the domain: 68.389 at time: 0.390\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.390\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.390\n",
+ "\n",
+ "J integrated over the domain: 5.652 at time: 0.400\n",
+ "J_n integrated over the domain: 8.024 at time: 0.400\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.400\n",
+ "d (def. map) integrated over the domain: 35.944 at time: 0.400\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.400\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.400\n",
+ "\n",
+ "J integrated over the domain: 3.678 at time: 0.410\n",
+ "J_n integrated over the domain: 5.652 at time: 0.410\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.410\n",
+ "d (def. map) integrated over the domain: 17.531 at time: 0.410\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.410\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.410\n",
+ "\n",
+ "J integrated over the domain: 2.228 at time: 0.420\n",
+ "J_n integrated over the domain: 3.678 at time: 0.420\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.420\n",
+ "d (def. map) integrated over the domain: 8.963 at time: 0.420\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.420\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.420\n",
+ "\n",
+ "J integrated over the domain: 1.391 at time: 0.430\n",
+ "J_n integrated over the domain: 2.228 at time: 0.430\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.430\n",
+ "d (def. map) integrated over the domain: 5.936 at time: 0.430\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.430\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.430\n",
+ "\n",
+ "J integrated over the domain: 1.221 at time: 0.440\n",
+ "J_n integrated over the domain: 1.391 at time: 0.440\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.440\n",
+ "d (def. map) integrated over the domain: 5.492 at time: 0.440\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.440\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.440\n",
+ "\n",
+ "J integrated over the domain: 1.729 at time: 0.450\n",
+ "J_n integrated over the domain: 1.221 at time: 0.450\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.450\n",
+ "d (def. map) integrated over the domain: 6.988 at time: 0.450\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.450\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.450\n",
+ "\n",
+ "J integrated over the domain: 2.881 at time: 0.460\n",
+ "J_n integrated over the domain: 1.729 at time: 0.460\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.460\n",
+ "d (def. map) integrated over the domain: 12.302 at time: 0.460\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.460\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.460\n",
+ "\n"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "J integrated over the domain: 4.607 at time: 0.470\n",
+ "J_n integrated over the domain: 2.881 at time: 0.470\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.470\n",
+ "d (def. map) integrated over the domain: 25.223 at time: 0.470\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.470\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.470\n",
+ "\n",
+ "J integrated over the domain: 6.797 at time: 0.480\n",
+ "J_n integrated over the domain: 4.607 at time: 0.480\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.480\n",
+ "d (def. map) integrated over the domain: 50.200 at time: 0.480\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.480\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.480\n",
+ "\n",
+ "J integrated over the domain: 9.314 at time: 0.490\n",
+ "J_n integrated over the domain: 6.797 at time: 0.490\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.490\n",
+ "d (def. map) integrated over the domain: 90.753 at time: 0.490\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.490\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.490\n",
+ "\n",
+ "J integrated over the domain: 12.000 at time: 0.500\n",
+ "J_n integrated over the domain: 9.314 at time: 0.500\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.500\n",
+ "d (def. map) integrated over the domain: 148.000 at time: 0.500\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.500\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.500\n",
+ "\n",
+ "J integrated over the domain: 14.686 at time: 0.510\n",
+ "J_n integrated over the domain: 12.000 at time: 0.510\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.510\n",
+ "d (def. map) integrated over the domain: 219.674 at time: 0.510\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.510\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.510\n",
+ "\n",
+ "J integrated over the domain: 17.203 at time: 0.520\n",
+ "J_n integrated over the domain: 14.686 at time: 0.520\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.520\n",
+ "d (def. map) integrated over the domain: 299.941 at time: 0.520\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.520\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.520\n",
+ "\n",
+ "J integrated over the domain: 19.393 at time: 0.530\n",
+ "J_n integrated over the domain: 17.203 at time: 0.530\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.530\n",
+ "d (def. map) integrated over the domain: 380.093 at time: 0.530\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.530\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.530\n",
+ "\n",
+ "J integrated over the domain: 21.119 at time: 0.540\n",
+ "J_n integrated over the domain: 19.393 at time: 0.540\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.540\n",
+ "d (def. map) integrated over the domain: 450.001 at time: 0.540\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.540\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.540\n",
+ "\n",
+ "J integrated over the domain: 22.271 at time: 0.550\n",
+ "J_n integrated over the domain: 21.119 at time: 0.550\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.550\n",
+ "d (def. map) integrated over the domain: 500.016 at time: 0.550\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.550\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.550\n",
+ "\n",
+ "J integrated over the domain: 22.779 at time: 0.560\n",
+ "J_n integrated over the domain: 22.271 at time: 0.560\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.560\n",
+ "d (def. map) integrated over the domain: 522.869 at time: 0.560\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.560\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.560\n",
+ "\n",
+ "J integrated over the domain: 22.609 at time: 0.570\n",
+ "J_n integrated over the domain: 22.779 at time: 0.570\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.570\n",
+ "d (def. map) integrated over the domain: 515.153 at time: 0.570\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.570\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.570\n",
+ "\n",
+ "J integrated over the domain: 21.772 at time: 0.580\n",
+ "J_n integrated over the domain: 22.609 at time: 0.580\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.580\n",
+ "d (def. map) integrated over the domain: 478.026 at time: 0.580\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.580\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.580\n",
+ "\n",
+ "J integrated over the domain: 20.322 at time: 0.590\n",
+ "J_n integrated over the domain: 21.772 at time: 0.590\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.590\n",
+ "d (def. map) integrated over the domain: 416.965 at time: 0.590\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.590\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.590\n",
+ "\n",
+ "J integrated over the domain: 18.348 at time: 0.600\n",
+ "J_n integrated over the domain: 20.322 at time: 0.600\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.600\n",
+ "d (def. map) integrated over the domain: 340.652 at time: 0.600\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.600\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.600\n",
+ "\n",
+ "J integrated over the domain: 15.976 at time: 0.610\n",
+ "J_n integrated over the domain: 18.348 at time: 0.610\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.610\n",
+ "d (def. map) integrated over the domain: 259.224 at time: 0.610\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.610\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.610\n",
+ "\n",
+ "J integrated over the domain: 13.354 at time: 0.620\n",
+ "J_n integrated over the domain: 15.976 at time: 0.620\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.620\n",
+ "d (def. map) integrated over the domain: 182.319 at time: 0.620\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.620\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.620\n",
+ "\n",
+ "J integrated over the domain: 10.646 at time: 0.630\n",
+ "J_n integrated over the domain: 13.354 at time: 0.630\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.630\n",
+ "d (def. map) integrated over the domain: 117.346 at time: 0.630\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.630\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.630\n",
+ "\n",
+ "J integrated over the domain: 8.024 at time: 0.640\n",
+ "J_n integrated over the domain: 10.646 at time: 0.640\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.640\n",
+ "d (def. map) integrated over the domain: 68.389 at time: 0.640\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.640\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.640\n",
+ "\n",
+ "J integrated over the domain: 5.652 at time: 0.650\n",
+ "J_n integrated over the domain: 8.024 at time: 0.650\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.650\n",
+ "d (def. map) integrated over the domain: 35.944 at time: 0.650\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.650\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.650\n",
+ "\n",
+ "J integrated over the domain: 3.678 at time: 0.660\n",
+ "J_n integrated over the domain: 5.652 at time: 0.660\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.660\n",
+ "d (def. map) integrated over the domain: 17.531 at time: 0.660\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.660\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.660\n",
+ "\n",
+ "J integrated over the domain: 2.228 at time: 0.670\n",
+ "J_n integrated over the domain: 3.678 at time: 0.670\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.670\n",
+ "d (def. map) integrated over the domain: 8.963 at time: 0.670\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.670\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.670\n",
+ "\n",
+ "J integrated over the domain: 1.391 at time: 0.680\n",
+ "J_n integrated over the domain: 2.228 at time: 0.680\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.680\n",
+ "d (def. map) integrated over the domain: 5.936 at time: 0.680\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.680\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.680\n",
+ "\n",
+ "J integrated over the domain: 1.221 at time: 0.690\n",
+ "J_n integrated over the domain: 1.391 at time: 0.690\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.690\n",
+ "d (def. map) integrated over the domain: 5.492 at time: 0.690\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.690\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.690\n",
+ "\n",
+ "J integrated over the domain: 1.729 at time: 0.700\n",
+ "J_n integrated over the domain: 1.221 at time: 0.700\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.700\n",
+ "d (def. map) integrated over the domain: 6.988 at time: 0.700\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.700\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.700\n",
+ "\n"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "J integrated over the domain: 2.881 at time: 0.710\n",
+ "J_n integrated over the domain: 1.729 at time: 0.710\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.710\n",
+ "d (def. map) integrated over the domain: 12.302 at time: 0.710\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.710\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.710\n",
+ "\n",
+ "J integrated over the domain: 4.607 at time: 0.720\n",
+ "J_n integrated over the domain: 2.881 at time: 0.720\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.720\n",
+ "d (def. map) integrated over the domain: 25.223 at time: 0.720\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.720\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.720\n",
+ "\n",
+ "J integrated over the domain: 6.797 at time: 0.730\n",
+ "J_n integrated over the domain: 4.607 at time: 0.730\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.730\n",
+ "d (def. map) integrated over the domain: 50.200 at time: 0.730\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.730\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.730\n",
+ "\n",
+ "J integrated over the domain: 9.314 at time: 0.740\n",
+ "J_n integrated over the domain: 6.797 at time: 0.740\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.740\n",
+ "d (def. map) integrated over the domain: 90.753 at time: 0.740\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.740\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.740\n",
+ "\n",
+ "J integrated over the domain: 12.000 at time: 0.750\n",
+ "J_n integrated over the domain: 9.314 at time: 0.750\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.750\n",
+ "d (def. map) integrated over the domain: 148.000 at time: 0.750\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.750\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.750\n",
+ "\n",
+ "J integrated over the domain: 14.686 at time: 0.760\n",
+ "J_n integrated over the domain: 12.000 at time: 0.760\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.760\n",
+ "d (def. map) integrated over the domain: 219.674 at time: 0.760\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.760\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.760\n",
+ "\n",
+ "J integrated over the domain: 17.203 at time: 0.770\n",
+ "J_n integrated over the domain: 14.686 at time: 0.770\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.770\n",
+ "d (def. map) integrated over the domain: 299.941 at time: 0.770\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.770\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.770\n",
+ "\n",
+ "J integrated over the domain: 19.393 at time: 0.780\n",
+ "J_n integrated over the domain: 17.203 at time: 0.780\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.780\n",
+ "d (def. map) integrated over the domain: 380.093 at time: 0.780\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.780\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.780\n",
+ "\n",
+ "J integrated over the domain: 21.119 at time: 0.790\n",
+ "J_n integrated over the domain: 19.393 at time: 0.790\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.790\n",
+ "d (def. map) integrated over the domain: 450.001 at time: 0.790\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.790\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.790\n",
+ "\n",
+ "J integrated over the domain: 22.271 at time: 0.800\n",
+ "J_n integrated over the domain: 21.119 at time: 0.800\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.800\n",
+ "d (def. map) integrated over the domain: 500.016 at time: 0.800\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.800\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.800\n",
+ "\n",
+ "J integrated over the domain: 22.779 at time: 0.810\n",
+ "J_n integrated over the domain: 22.271 at time: 0.810\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.810\n",
+ "d (def. map) integrated over the domain: 522.869 at time: 0.810\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.810\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.810\n",
+ "\n",
+ "J integrated over the domain: 22.609 at time: 0.820\n",
+ "J_n integrated over the domain: 22.779 at time: 0.820\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.820\n",
+ "d (def. map) integrated over the domain: 515.153 at time: 0.820\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.820\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.820\n",
+ "\n",
+ "J integrated over the domain: 21.772 at time: 0.830\n",
+ "J_n integrated over the domain: 22.609 at time: 0.830\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.830\n",
+ "d (def. map) integrated over the domain: 478.026 at time: 0.830\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.830\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.830\n",
+ "\n",
+ "J integrated over the domain: 20.322 at time: 0.840\n",
+ "J_n integrated over the domain: 21.772 at time: 0.840\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.840\n",
+ "d (def. map) integrated over the domain: 416.965 at time: 0.840\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.840\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.840\n",
+ "\n",
+ "J integrated over the domain: 18.348 at time: 0.850\n",
+ "J_n integrated over the domain: 20.322 at time: 0.850\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.850\n",
+ "d (def. map) integrated over the domain: 340.652 at time: 0.850\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.850\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.850\n",
+ "\n",
+ "J integrated over the domain: 15.976 at time: 0.860\n",
+ "J_n integrated over the domain: 18.348 at time: 0.860\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.860\n",
+ "d (def. map) integrated over the domain: 259.224 at time: 0.860\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.860\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.860\n",
+ "\n",
+ "J integrated over the domain: 13.354 at time: 0.870\n",
+ "J_n integrated over the domain: 15.976 at time: 0.870\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.870\n",
+ "d (def. map) integrated over the domain: 182.319 at time: 0.870\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.870\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.870\n",
+ "\n",
+ "J integrated over the domain: 10.646 at time: 0.880\n",
+ "J_n integrated over the domain: 13.354 at time: 0.880\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.880\n",
+ "d (def. map) integrated over the domain: 117.346 at time: 0.880\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.880\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.880\n",
+ "\n",
+ "J integrated over the domain: 8.024 at time: 0.890\n",
+ "J_n integrated over the domain: 10.646 at time: 0.890\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.890\n",
+ "d (def. map) integrated over the domain: 68.389 at time: 0.890\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.890\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.890\n",
+ "\n",
+ "J integrated over the domain: 5.652 at time: 0.900\n",
+ "J_n integrated over the domain: 8.024 at time: 0.900\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.900\n",
+ "d (def. map) integrated over the domain: 35.944 at time: 0.900\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.900\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.900\n",
+ "\n",
+ "J integrated over the domain: 3.678 at time: 0.910\n",
+ "J_n integrated over the domain: 5.652 at time: 0.910\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.910\n",
+ "d (def. map) integrated over the domain: 17.531 at time: 0.910\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.910\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.910\n",
+ "\n",
+ "J integrated over the domain: 2.228 at time: 0.920\n",
+ "J_n integrated over the domain: 3.678 at time: 0.920\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.920\n",
+ "d (def. map) integrated over the domain: 8.963 at time: 0.920\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.920\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.920\n",
+ "\n",
+ "J integrated over the domain: 1.391 at time: 0.930\n",
+ "J_n integrated over the domain: 2.228 at time: 0.930\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.930\n",
+ "d (def. map) integrated over the domain: 5.936 at time: 0.930\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.930\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.930\n",
+ "\n",
+ "J integrated over the domain: 1.221 at time: 0.940\n",
+ "J_n integrated over the domain: 1.391 at time: 0.940\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.940\n",
+ "d (def. map) integrated over the domain: 5.492 at time: 0.940\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.940\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.940\n",
+ "\n"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "J integrated over the domain: 1.729 at time: 0.950\n",
+ "J_n integrated over the domain: 1.221 at time: 0.950\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.950\n",
+ "d (def. map) integrated over the domain: 6.988 at time: 0.950\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.950\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.950\n",
+ "\n",
+ "J integrated over the domain: 2.881 at time: 0.960\n",
+ "J_n integrated over the domain: 1.729 at time: 0.960\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.960\n",
+ "d (def. map) integrated over the domain: 12.302 at time: 0.960\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.960\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.960\n",
+ "\n",
+ "J integrated over the domain: 4.607 at time: 0.970\n",
+ "J_n integrated over the domain: 2.881 at time: 0.970\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.970\n",
+ "d (def. map) integrated over the domain: 25.223 at time: 0.970\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.970\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.970\n",
+ "\n",
+ "J integrated over the domain: 6.797 at time: 0.980\n",
+ "J_n integrated over the domain: 4.607 at time: 0.980\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.980\n",
+ "d (def. map) integrated over the domain: 50.200 at time: 0.980\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.980\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.980\n",
+ "\n",
+ "J integrated over the domain: 9.314 at time: 0.990\n",
+ "J_n integrated over the domain: 6.797 at time: 0.990\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.990\n",
+ "d (def. map) integrated over the domain: 90.753 at time: 0.990\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.990\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.990\n",
+ "\n",
+ "J integrated over the domain: 12.000 at time: 1.000\n",
+ "J_n integrated over the domain: 9.314 at time: 1.000\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.000\n",
+ "d (def. map) integrated over the domain: 148.000 at time: 1.000\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.000\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.000\n",
+ "\n",
+ "J integrated over the domain: 14.686 at time: 1.010\n",
+ "J_n integrated over the domain: 12.000 at time: 1.010\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.010\n",
+ "d (def. map) integrated over the domain: 219.674 at time: 1.010\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.010\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.010\n",
+ "\n",
+ "J integrated over the domain: 17.203 at time: 1.020\n",
+ "J_n integrated over the domain: 14.686 at time: 1.020\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.020\n",
+ "d (def. map) integrated over the domain: 299.941 at time: 1.020\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.020\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.020\n",
+ "\n",
+ "J integrated over the domain: 19.393 at time: 1.030\n",
+ "J_n integrated over the domain: 17.203 at time: 1.030\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.030\n",
+ "d (def. map) integrated over the domain: 380.093 at time: 1.030\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.030\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.030\n",
+ "\n",
+ "J integrated over the domain: 21.119 at time: 1.040\n",
+ "J_n integrated over the domain: 19.393 at time: 1.040\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.040\n",
+ "d (def. map) integrated over the domain: 450.001 at time: 1.040\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.040\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.040\n",
+ "\n",
+ "J integrated over the domain: 22.271 at time: 1.050\n",
+ "J_n integrated over the domain: 21.119 at time: 1.050\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.050\n",
+ "d (def. map) integrated over the domain: 500.016 at time: 1.050\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.050\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.050\n",
+ "\n",
+ "J integrated over the domain: 22.779 at time: 1.060\n",
+ "J_n integrated over the domain: 22.271 at time: 1.060\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.060\n",
+ "d (def. map) integrated over the domain: 522.869 at time: 1.060\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.060\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.060\n",
+ "\n",
+ "J integrated over the domain: 22.609 at time: 1.070\n",
+ "J_n integrated over the domain: 22.779 at time: 1.070\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.070\n",
+ "d (def. map) integrated over the domain: 515.153 at time: 1.070\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.070\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.070\n",
+ "\n",
+ "J integrated over the domain: 21.772 at time: 1.080\n",
+ "J_n integrated over the domain: 22.609 at time: 1.080\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.080\n",
+ "d (def. map) integrated over the domain: 478.026 at time: 1.080\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.080\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.080\n",
+ "\n",
+ "J integrated over the domain: 20.322 at time: 1.090\n",
+ "J_n integrated over the domain: 21.772 at time: 1.090\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.090\n",
+ "d (def. map) integrated over the domain: 416.965 at time: 1.090\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.090\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.090\n",
+ "\n",
+ "J integrated over the domain: 18.348 at time: 1.100\n",
+ "J_n integrated over the domain: 20.322 at time: 1.100\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.100\n",
+ "d (def. map) integrated over the domain: 340.652 at time: 1.100\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.100\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.100\n",
+ "\n",
+ "J integrated over the domain: 15.976 at time: 1.110\n",
+ "J_n integrated over the domain: 18.348 at time: 1.110\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.110\n",
+ "d (def. map) integrated over the domain: 259.224 at time: 1.110\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.110\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.110\n",
+ "\n",
+ "J integrated over the domain: 13.354 at time: 1.120\n",
+ "J_n integrated over the domain: 15.976 at time: 1.120\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.120\n",
+ "d (def. map) integrated over the domain: 182.319 at time: 1.120\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.120\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.120\n",
+ "\n",
+ "J integrated over the domain: 10.646 at time: 1.130\n",
+ "J_n integrated over the domain: 13.354 at time: 1.130\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.130\n",
+ "d (def. map) integrated over the domain: 117.346 at time: 1.130\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.130\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.130\n",
+ "\n",
+ "J integrated over the domain: 8.024 at time: 1.140\n",
+ "J_n integrated over the domain: 10.646 at time: 1.140\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.140\n",
+ "d (def. map) integrated over the domain: 68.389 at time: 1.140\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.140\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.140\n",
+ "\n",
+ "J integrated over the domain: 5.652 at time: 1.150\n",
+ "J_n integrated over the domain: 8.024 at time: 1.150\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.150\n",
+ "d (def. map) integrated over the domain: 35.944 at time: 1.150\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.150\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.150\n",
+ "\n",
+ "J integrated over the domain: 3.678 at time: 1.160\n",
+ "J_n integrated over the domain: 5.652 at time: 1.160\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.160\n",
+ "d (def. map) integrated over the domain: 17.531 at time: 1.160\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.160\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.160\n",
+ "\n",
+ "J integrated over the domain: 2.228 at time: 1.170\n",
+ "J_n integrated over the domain: 3.678 at time: 1.170\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.170\n",
+ "d (def. map) integrated over the domain: 8.963 at time: 1.170\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.170\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.170\n",
+ "\n",
+ "J integrated over the domain: 1.391 at time: 1.180\n",
+ "J_n integrated over the domain: 2.228 at time: 1.180\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.180\n",
+ "d (def. map) integrated over the domain: 5.936 at time: 1.180\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.180\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.180\n",
+ "\n"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "J integrated over the domain: 1.221 at time: 1.190\n",
+ "J_n integrated over the domain: 1.391 at time: 1.190\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.190\n",
+ "d (def. map) integrated over the domain: 5.492 at time: 1.190\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.190\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.190\n",
+ "\n",
+ "J integrated over the domain: 1.729 at time: 1.200\n",
+ "J_n integrated over the domain: 1.221 at time: 1.200\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.200\n",
+ "d (def. map) integrated over the domain: 6.988 at time: 1.200\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.200\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.200\n",
+ "\n",
+ "J integrated over the domain: 2.881 at time: 1.210\n",
+ "J_n integrated over the domain: 1.729 at time: 1.210\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.210\n",
+ "d (def. map) integrated over the domain: 12.302 at time: 1.210\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.210\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.210\n",
+ "\n",
+ "J integrated over the domain: 4.607 at time: 1.220\n",
+ "J_n integrated over the domain: 2.881 at time: 1.220\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.220\n",
+ "d (def. map) integrated over the domain: 25.223 at time: 1.220\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.220\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.220\n",
+ "\n",
+ "J integrated over the domain: 6.797 at time: 1.230\n",
+ "J_n integrated over the domain: 4.607 at time: 1.230\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.230\n",
+ "d (def. map) integrated over the domain: 50.200 at time: 1.230\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.230\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.230\n",
+ "\n",
+ "J integrated over the domain: 9.314 at time: 1.240\n",
+ "J_n integrated over the domain: 6.797 at time: 1.240\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.240\n",
+ "d (def. map) integrated over the domain: 90.753 at time: 1.240\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.240\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.240\n",
+ "\n",
+ "J integrated over the domain: 12.000 at time: 1.250\n",
+ "J_n integrated over the domain: 9.314 at time: 1.250\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.250\n",
+ "d (def. map) integrated over the domain: 148.000 at time: 1.250\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.250\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.250\n",
+ "\n",
+ "J integrated over the domain: 14.686 at time: 1.260\n",
+ "J_n integrated over the domain: 12.000 at time: 1.260\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.260\n",
+ "d (def. map) integrated over the domain: 219.674 at time: 1.260\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.260\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.260\n",
+ "\n",
+ "J integrated over the domain: 17.203 at time: 1.270\n",
+ "J_n integrated over the domain: 14.686 at time: 1.270\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.270\n",
+ "d (def. map) integrated over the domain: 299.941 at time: 1.270\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.270\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.270\n",
+ "\n",
+ "J integrated over the domain: 19.393 at time: 1.280\n",
+ "J_n integrated over the domain: 17.203 at time: 1.280\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.280\n",
+ "d (def. map) integrated over the domain: 380.093 at time: 1.280\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.280\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.280\n",
+ "\n",
+ "J integrated over the domain: 21.119 at time: 1.290\n",
+ "J_n integrated over the domain: 19.393 at time: 1.290\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.290\n",
+ "d (def. map) integrated over the domain: 450.001 at time: 1.290\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.290\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.290\n",
+ "\n",
+ "J integrated over the domain: 22.271 at time: 1.300\n",
+ "J_n integrated over the domain: 21.119 at time: 1.300\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.300\n",
+ "d (def. map) integrated over the domain: 500.016 at time: 1.300\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.300\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.300\n",
+ "\n",
+ "J integrated over the domain: 22.779 at time: 1.310\n",
+ "J_n integrated over the domain: 22.271 at time: 1.310\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.310\n",
+ "d (def. map) integrated over the domain: 522.869 at time: 1.310\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.310\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.310\n",
+ "\n",
+ "J integrated over the domain: 22.609 at time: 1.320\n",
+ "J_n integrated over the domain: 22.779 at time: 1.320\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.320\n",
+ "d (def. map) integrated over the domain: 515.153 at time: 1.320\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.320\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.320\n",
+ "\n",
+ "J integrated over the domain: 21.772 at time: 1.330\n",
+ "J_n integrated over the domain: 22.609 at time: 1.330\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.330\n",
+ "d (def. map) integrated over the domain: 478.026 at time: 1.330\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.330\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.330\n",
+ "\n",
+ "J integrated over the domain: 20.322 at time: 1.340\n",
+ "J_n integrated over the domain: 21.772 at time: 1.340\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.340\n",
+ "d (def. map) integrated over the domain: 416.965 at time: 1.340\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.340\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.340\n",
+ "\n",
+ "J integrated over the domain: 18.348 at time: 1.350\n",
+ "J_n integrated over the domain: 20.322 at time: 1.350\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.350\n",
+ "d (def. map) integrated over the domain: 340.652 at time: 1.350\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.350\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.350\n",
+ "\n",
+ "J integrated over the domain: 15.976 at time: 1.360\n",
+ "J_n integrated over the domain: 18.348 at time: 1.360\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.360\n",
+ "d (def. map) integrated over the domain: 259.224 at time: 1.360\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.360\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.360\n",
+ "\n",
+ "J integrated over the domain: 13.354 at time: 1.370\n",
+ "J_n integrated over the domain: 15.976 at time: 1.370\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.370\n",
+ "d (def. map) integrated over the domain: 182.319 at time: 1.370\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.370\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.370\n",
+ "\n",
+ "J integrated over the domain: 10.646 at time: 1.380\n",
+ "J_n integrated over the domain: 13.354 at time: 1.380\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.380\n",
+ "d (def. map) integrated over the domain: 117.346 at time: 1.380\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.380\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.380\n",
+ "\n",
+ "J integrated over the domain: 8.024 at time: 1.390\n",
+ "J_n integrated over the domain: 10.646 at time: 1.390\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.390\n",
+ "d (def. map) integrated over the domain: 68.389 at time: 1.390\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.390\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.390\n",
+ "\n",
+ "J integrated over the domain: 5.652 at time: 1.400\n",
+ "J_n integrated over the domain: 8.024 at time: 1.400\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.400\n",
+ "d (def. map) integrated over the domain: 35.944 at time: 1.400\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.400\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.400\n",
+ "\n",
+ "J integrated over the domain: 3.678 at time: 1.410\n",
+ "J_n integrated over the domain: 5.652 at time: 1.410\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.410\n",
+ "d (def. map) integrated over the domain: 17.531 at time: 1.410\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.410\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.410\n",
+ "\n",
+ "J integrated over the domain: 2.228 at time: 1.420\n",
+ "J_n integrated over the domain: 3.678 at time: 1.420\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.420\n",
+ "d (def. map) integrated over the domain: 8.963 at time: 1.420\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.420\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.420\n",
+ "\n"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "J integrated over the domain: 1.391 at time: 1.430\n",
+ "J_n integrated over the domain: 2.228 at time: 1.430\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.430\n",
+ "d (def. map) integrated over the domain: 5.936 at time: 1.430\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.430\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.430\n",
+ "\n",
+ "J integrated over the domain: 1.221 at time: 1.440\n",
+ "J_n integrated over the domain: 1.391 at time: 1.440\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.440\n",
+ "d (def. map) integrated over the domain: 5.492 at time: 1.440\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.440\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.440\n",
+ "\n",
+ "J integrated over the domain: 1.729 at time: 1.450\n",
+ "J_n integrated over the domain: 1.221 at time: 1.450\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.450\n",
+ "d (def. map) integrated over the domain: 6.988 at time: 1.450\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.450\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.450\n",
+ "\n",
+ "J integrated over the domain: 2.881 at time: 1.460\n",
+ "J_n integrated over the domain: 1.729 at time: 1.460\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.460\n",
+ "d (def. map) integrated over the domain: 12.302 at time: 1.460\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.460\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.460\n",
+ "\n",
+ "J integrated over the domain: 4.607 at time: 1.470\n",
+ "J_n integrated over the domain: 2.881 at time: 1.470\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.470\n",
+ "d (def. map) integrated over the domain: 25.223 at time: 1.470\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.470\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.470\n",
+ "\n",
+ "J integrated over the domain: 6.797 at time: 1.480\n",
+ "J_n integrated over the domain: 4.607 at time: 1.480\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.480\n",
+ "d (def. map) integrated over the domain: 50.200 at time: 1.480\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.480\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.480\n",
+ "\n",
+ "J integrated over the domain: 9.314 at time: 1.490\n",
+ "J_n integrated over the domain: 6.797 at time: 1.490\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.490\n",
+ "d (def. map) integrated over the domain: 90.753 at time: 1.490\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.490\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.490\n",
+ "\n",
+ "J integrated over the domain: 12.000 at time: 1.500\n",
+ "J_n integrated over the domain: 9.314 at time: 1.500\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.500\n",
+ "d (def. map) integrated over the domain: 148.000 at time: 1.500\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.500\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.500\n",
+ "\n",
+ "J integrated over the domain: 14.686 at time: 1.510\n",
+ "J_n integrated over the domain: 12.000 at time: 1.510\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.510\n",
+ "d (def. map) integrated over the domain: 219.674 at time: 1.510\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.510\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.510\n",
+ "\n",
+ "J integrated over the domain: 17.203 at time: 1.520\n",
+ "J_n integrated over the domain: 14.686 at time: 1.520\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.520\n",
+ "d (def. map) integrated over the domain: 299.941 at time: 1.520\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.520\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.520\n",
+ "\n",
+ "J integrated over the domain: 19.393 at time: 1.530\n",
+ "J_n integrated over the domain: 17.203 at time: 1.530\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.530\n",
+ "d (def. map) integrated over the domain: 380.093 at time: 1.530\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.530\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.530\n",
+ "\n",
+ "J integrated over the domain: 21.119 at time: 1.540\n",
+ "J_n integrated over the domain: 19.393 at time: 1.540\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.540\n",
+ "d (def. map) integrated over the domain: 450.001 at time: 1.540\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.540\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.540\n",
+ "\n",
+ "J integrated over the domain: 22.271 at time: 1.550\n",
+ "J_n integrated over the domain: 21.119 at time: 1.550\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.550\n",
+ "d (def. map) integrated over the domain: 500.016 at time: 1.550\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.550\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.550\n",
+ "\n",
+ "J integrated over the domain: 22.779 at time: 1.560\n",
+ "J_n integrated over the domain: 22.271 at time: 1.560\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.560\n",
+ "d (def. map) integrated over the domain: 522.869 at time: 1.560\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.560\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.560\n",
+ "\n",
+ "J integrated over the domain: 22.609 at time: 1.570\n",
+ "J_n integrated over the domain: 22.779 at time: 1.570\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.570\n",
+ "d (def. map) integrated over the domain: 515.153 at time: 1.570\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.570\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.570\n",
+ "\n",
+ "J integrated over the domain: 21.772 at time: 1.580\n",
+ "J_n integrated over the domain: 22.609 at time: 1.580\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.580\n",
+ "d (def. map) integrated over the domain: 478.026 at time: 1.580\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.580\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.580\n",
+ "\n",
+ "J integrated over the domain: 20.322 at time: 1.590\n",
+ "J_n integrated over the domain: 21.772 at time: 1.590\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.590\n",
+ "d (def. map) integrated over the domain: 416.965 at time: 1.590\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.590\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.590\n",
+ "\n",
+ "J integrated over the domain: 18.348 at time: 1.600\n",
+ "J_n integrated over the domain: 20.322 at time: 1.600\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.600\n",
+ "d (def. map) integrated over the domain: 340.652 at time: 1.600\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.600\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.600\n",
+ "\n",
+ "J integrated over the domain: 15.976 at time: 1.610\n",
+ "J_n integrated over the domain: 18.348 at time: 1.610\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.610\n",
+ "d (def. map) integrated over the domain: 259.224 at time: 1.610\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.610\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.610\n",
+ "\n",
+ "J integrated over the domain: 13.354 at time: 1.620\n",
+ "J_n integrated over the domain: 15.976 at time: 1.620\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.620\n",
+ "d (def. map) integrated over the domain: 182.319 at time: 1.620\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.620\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.620\n",
+ "\n",
+ "J integrated over the domain: 10.646 at time: 1.630\n",
+ "J_n integrated over the domain: 13.354 at time: 1.630\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.630\n",
+ "d (def. map) integrated over the domain: 117.346 at time: 1.630\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.630\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.630\n",
+ "\n",
+ "J integrated over the domain: 8.024 at time: 1.640\n",
+ "J_n integrated over the domain: 10.646 at time: 1.640\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.640\n",
+ "d (def. map) integrated over the domain: 68.389 at time: 1.640\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.640\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.640\n",
+ "\n",
+ "J integrated over the domain: 5.652 at time: 1.650\n",
+ "J_n integrated over the domain: 8.024 at time: 1.650\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.650\n",
+ "d (def. map) integrated over the domain: 35.944 at time: 1.650\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.650\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.650\n",
+ "\n",
+ "J integrated over the domain: 3.678 at time: 1.660\n",
+ "J_n integrated over the domain: 5.652 at time: 1.660\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.660\n",
+ "d (def. map) integrated over the domain: 17.531 at time: 1.660\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.660\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.660\n",
+ "\n"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "J integrated over the domain: 2.228 at time: 1.670\n",
+ "J_n integrated over the domain: 3.678 at time: 1.670\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.670\n",
+ "d (def. map) integrated over the domain: 8.963 at time: 1.670\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.670\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.670\n",
+ "\n",
+ "J integrated over the domain: 1.391 at time: 1.680\n",
+ "J_n integrated over the domain: 2.228 at time: 1.680\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.680\n",
+ "d (def. map) integrated over the domain: 5.936 at time: 1.680\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.680\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.680\n",
+ "\n",
+ "J integrated over the domain: 1.221 at time: 1.690\n",
+ "J_n integrated over the domain: 1.391 at time: 1.690\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.690\n",
+ "d (def. map) integrated over the domain: 5.492 at time: 1.690\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.690\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.690\n",
+ "\n",
+ "J integrated over the domain: 1.729 at time: 1.700\n",
+ "J_n integrated over the domain: 1.221 at time: 1.700\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.700\n",
+ "d (def. map) integrated over the domain: 6.988 at time: 1.700\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.700\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.700\n",
+ "\n",
+ "J integrated over the domain: 2.881 at time: 1.710\n",
+ "J_n integrated over the domain: 1.729 at time: 1.710\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.710\n",
+ "d (def. map) integrated over the domain: 12.302 at time: 1.710\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.710\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.710\n",
+ "\n",
+ "J integrated over the domain: 4.607 at time: 1.720\n",
+ "J_n integrated over the domain: 2.881 at time: 1.720\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.720\n",
+ "d (def. map) integrated over the domain: 25.223 at time: 1.720\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.720\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.720\n",
+ "\n",
+ "J integrated over the domain: 6.797 at time: 1.730\n",
+ "J_n integrated over the domain: 4.607 at time: 1.730\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.730\n",
+ "d (def. map) integrated over the domain: 50.200 at time: 1.730\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.730\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.730\n",
+ "\n",
+ "J integrated over the domain: 9.314 at time: 1.740\n",
+ "J_n integrated over the domain: 6.797 at time: 1.740\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.740\n",
+ "d (def. map) integrated over the domain: 90.753 at time: 1.740\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.740\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.740\n",
+ "\n",
+ "J integrated over the domain: 12.000 at time: 1.750\n",
+ "J_n integrated over the domain: 9.314 at time: 1.750\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.750\n",
+ "d (def. map) integrated over the domain: 148.000 at time: 1.750\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.750\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.750\n",
+ "\n",
+ "J integrated over the domain: 14.686 at time: 1.760\n",
+ "J_n integrated over the domain: 12.000 at time: 1.760\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.760\n",
+ "d (def. map) integrated over the domain: 219.674 at time: 1.760\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.760\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.760\n",
+ "\n",
+ "J integrated over the domain: 17.203 at time: 1.770\n",
+ "J_n integrated over the domain: 14.686 at time: 1.770\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.770\n",
+ "d (def. map) integrated over the domain: 299.941 at time: 1.770\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.770\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.770\n",
+ "\n",
+ "J integrated over the domain: 19.393 at time: 1.780\n",
+ "J_n integrated over the domain: 17.203 at time: 1.780\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.780\n",
+ "d (def. map) integrated over the domain: 380.093 at time: 1.780\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.780\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.780\n",
+ "\n",
+ "J integrated over the domain: 21.119 at time: 1.790\n",
+ "J_n integrated over the domain: 19.393 at time: 1.790\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.790\n",
+ "d (def. map) integrated over the domain: 450.001 at time: 1.790\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.790\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.790\n",
+ "\n",
+ "J integrated over the domain: 22.271 at time: 1.800\n",
+ "J_n integrated over the domain: 21.119 at time: 1.800\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.800\n",
+ "d (def. map) integrated over the domain: 500.016 at time: 1.800\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.800\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.800\n",
+ "\n",
+ "J integrated over the domain: 22.779 at time: 1.810\n",
+ "J_n integrated over the domain: 22.271 at time: 1.810\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.810\n",
+ "d (def. map) integrated over the domain: 522.869 at time: 1.810\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.810\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.810\n",
+ "\n",
+ "J integrated over the domain: 22.609 at time: 1.820\n",
+ "J_n integrated over the domain: 22.779 at time: 1.820\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.820\n",
+ "d (def. map) integrated over the domain: 515.153 at time: 1.820\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.820\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.820\n",
+ "\n",
+ "J integrated over the domain: 21.772 at time: 1.830\n",
+ "J_n integrated over the domain: 22.609 at time: 1.830\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.830\n",
+ "d (def. map) integrated over the domain: 478.026 at time: 1.830\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.830\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.830\n",
+ "\n",
+ "J integrated over the domain: 20.322 at time: 1.840\n",
+ "J_n integrated over the domain: 21.772 at time: 1.840\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.840\n",
+ "d (def. map) integrated over the domain: 416.965 at time: 1.840\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.840\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.840\n",
+ "\n",
+ "J integrated over the domain: 18.348 at time: 1.850\n",
+ "J_n integrated over the domain: 20.322 at time: 1.850\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.850\n",
+ "d (def. map) integrated over the domain: 340.652 at time: 1.850\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.850\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.850\n",
+ "\n",
+ "J integrated over the domain: 15.976 at time: 1.860\n",
+ "J_n integrated over the domain: 18.348 at time: 1.860\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.860\n",
+ "d (def. map) integrated over the domain: 259.224 at time: 1.860\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.860\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.860\n",
+ "\n",
+ "J integrated over the domain: 13.354 at time: 1.870\n",
+ "J_n integrated over the domain: 15.976 at time: 1.870\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.870\n",
+ "d (def. map) integrated over the domain: 182.319 at time: 1.870\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.870\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.870\n",
+ "\n",
+ "J integrated over the domain: 10.646 at time: 1.880\n",
+ "J_n integrated over the domain: 13.354 at time: 1.880\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.880\n",
+ "d (def. map) integrated over the domain: 117.346 at time: 1.880\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.880\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.880\n",
+ "\n",
+ "J integrated over the domain: 8.024 at time: 1.890\n",
+ "J_n integrated over the domain: 10.646 at time: 1.890\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.890\n",
+ "d (def. map) integrated over the domain: 68.389 at time: 1.890\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.890\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.890\n",
+ "\n",
+ "J integrated over the domain: 5.652 at time: 1.900\n",
+ "J_n integrated over the domain: 8.024 at time: 1.900\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.900\n",
+ "d (def. map) integrated over the domain: 35.944 at time: 1.900\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.900\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.900\n",
+ "\n"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "J integrated over the domain: 3.678 at time: 1.910\n",
+ "J_n integrated over the domain: 5.652 at time: 1.910\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.910\n",
+ "d (def. map) integrated over the domain: 17.531 at time: 1.910\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.910\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.910\n",
+ "\n",
+ "J integrated over the domain: 2.228 at time: 1.920\n",
+ "J_n integrated over the domain: 3.678 at time: 1.920\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.920\n",
+ "d (def. map) integrated over the domain: 8.963 at time: 1.920\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.920\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.920\n",
+ "\n",
+ "J integrated over the domain: 1.391 at time: 1.930\n",
+ "J_n integrated over the domain: 2.228 at time: 1.930\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.930\n",
+ "d (def. map) integrated over the domain: 5.936 at time: 1.930\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.930\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.930\n",
+ "\n",
+ "J integrated over the domain: 1.221 at time: 1.940\n",
+ "J_n integrated over the domain: 1.391 at time: 1.940\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.940\n",
+ "d (def. map) integrated over the domain: 5.492 at time: 1.940\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.940\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.940\n",
+ "\n",
+ "J integrated over the domain: 1.729 at time: 1.950\n",
+ "J_n integrated over the domain: 1.221 at time: 1.950\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.950\n",
+ "d (def. map) integrated over the domain: 6.988 at time: 1.950\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.950\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.950\n",
+ "\n",
+ "J integrated over the domain: 2.881 at time: 1.960\n",
+ "J_n integrated over the domain: 1.729 at time: 1.960\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.960\n",
+ "d (def. map) integrated over the domain: 12.302 at time: 1.960\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.960\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.960\n",
+ "\n",
+ "J integrated over the domain: 4.607 at time: 1.970\n",
+ "J_n integrated over the domain: 2.881 at time: 1.970\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.970\n",
+ "d (def. map) integrated over the domain: 25.223 at time: 1.970\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.970\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.970\n",
+ "\n",
+ "J integrated over the domain: 6.797 at time: 1.980\n",
+ "J_n integrated over the domain: 4.607 at time: 1.980\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.980\n",
+ "d (def. map) integrated over the domain: 50.200 at time: 1.980\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.980\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.980\n",
+ "\n",
+ "J integrated over the domain: 9.314 at time: 1.990\n",
+ "J_n integrated over the domain: 6.797 at time: 1.990\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.990\n",
+ "d (def. map) integrated over the domain: 90.753 at time: 1.990\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.990\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.990\n",
+ "\n",
+ "J integrated over the domain: 12.000 at time: 2.000\n",
+ "J_n integrated over the domain: 9.314 at time: 2.000\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 2.000\n",
+ "d (def. map) integrated over the domain: 148.000 at time: 2.000\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 2.000\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 2.000\n",
+ "\n",
+ "Number of degrees of freedom: 14387\n",
+ "Solution Computed in 105.4 seconds\n",
+ "\n",
+ "----------------Computation Completed!----------------\n",
+ "\n",
+ "\n",
+ "Initializing iNSE problem with Deformation type: High_Osc_con\n",
+ "\n",
+ "\n",
+ "Setup with initial condition: True\n",
+ "Using a non-zero initial condition (2D-Gaussian) for the velocity field!\n",
+ "Using time-derivative term approximated with Jacobian at n+1...\n",
+ "Using LU Solver...\n",
+ "Starting iteration over time...\n",
+ "E (Energy) of initial velocity field: 0.01659 at time 0.000\n",
+ "\n",
+ "J integrated over the domain: 9.314 at time: 0.010\n",
+ "J_n integrated over the domain: 12.000 at time: 0.010\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.010\n",
+ "d (def. map) integrated over the domain: 90.753 at time: 0.010\n",
+ "Strain energy E( eps(|u|^2) ): 0.00049 at time 0.010\n",
+ "Residual of scheme -> 'delta' value: -0.00319 at time 0.010\n",
+ "\n",
+ "J integrated over the domain: 6.797 at time: 0.020\n",
+ "J_n integrated over the domain: 9.314 at time: 0.020\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.020\n",
+ "d (def. map) integrated over the domain: 50.200 at time: 0.020\n",
+ "Strain energy E( eps(|u|^2) ): 0.00065 at time 0.020\n",
+ "Residual of scheme -> 'delta' value: -0.00012 at time 0.020\n",
+ "\n",
+ "J integrated over the domain: 4.607 at time: 0.030\n",
+ "J_n integrated over the domain: 6.797 at time: 0.030\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.030\n",
+ "d (def. map) integrated over the domain: 25.223 at time: 0.030\n",
+ "Strain energy E( eps(|u|^2) ): 0.00043 at time 0.030\n",
+ "Residual of scheme -> 'delta' value: -0.00015 at time 0.030\n",
+ "\n",
+ "J integrated over the domain: 2.881 at time: 0.040\n",
+ "J_n integrated over the domain: 4.607 at time: 0.040\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.040\n",
+ "d (def. map) integrated over the domain: 12.302 at time: 0.040\n",
+ "Strain energy E( eps(|u|^2) ): 0.00015 at time 0.040\n",
+ "Residual of scheme -> 'delta' value: -0.00009 at time 0.040\n",
+ "\n",
+ "J integrated over the domain: 1.729 at time: 0.050\n",
+ "J_n integrated over the domain: 2.881 at time: 0.050\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.050\n",
+ "d (def. map) integrated over the domain: 6.988 at time: 0.050\n",
+ "Strain energy E( eps(|u|^2) ): 0.00003 at time 0.050\n",
+ "Residual of scheme -> 'delta' value: -0.00002 at time 0.050\n",
+ "\n",
+ "J integrated over the domain: 1.221 at time: 0.060\n",
+ "J_n integrated over the domain: 1.729 at time: 0.060\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.060\n",
+ "d (def. map) integrated over the domain: 5.492 at time: 0.060\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.060\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.060\n",
+ "\n",
+ "J integrated over the domain: 1.391 at time: 0.070\n",
+ "J_n integrated over the domain: 1.221 at time: 0.070\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.070\n",
+ "d (def. map) integrated over the domain: 5.936 at time: 0.070\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.070\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.070\n",
+ "\n",
+ "J integrated over the domain: 2.228 at time: 0.080\n",
+ "J_n integrated over the domain: 1.391 at time: 0.080\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.080\n",
+ "d (def. map) integrated over the domain: 8.963 at time: 0.080\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.080\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.080\n",
+ "\n",
+ "J integrated over the domain: 3.678 at time: 0.090\n",
+ "J_n integrated over the domain: 2.228 at time: 0.090\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.090\n",
+ "d (def. map) integrated over the domain: 17.531 at time: 0.090\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.090\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.090\n",
+ "\n",
+ "J integrated over the domain: 5.652 at time: 0.100\n",
+ "J_n integrated over the domain: 3.678 at time: 0.100\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.100\n",
+ "d (def. map) integrated over the domain: 35.944 at time: 0.100\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.100\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.100\n",
+ "\n",
+ "J integrated over the domain: 8.024 at time: 0.110\n",
+ "J_n integrated over the domain: 5.652 at time: 0.110\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.110\n",
+ "d (def. map) integrated over the domain: 68.389 at time: 0.110\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.110\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.110\n",
+ "\n",
+ "J integrated over the domain: 10.646 at time: 0.120\n",
+ "J_n integrated over the domain: 8.024 at time: 0.120\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.120\n",
+ "d (def. map) integrated over the domain: 117.346 at time: 0.120\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.120\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.120\n",
+ "\n",
+ "J integrated over the domain: 13.354 at time: 0.130\n",
+ "J_n integrated over the domain: 10.646 at time: 0.130\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.130\n",
+ "d (def. map) integrated over the domain: 182.319 at time: 0.130\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.130\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.130\n",
+ "\n"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "J integrated over the domain: 15.976 at time: 0.140\n",
+ "J_n integrated over the domain: 13.354 at time: 0.140\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.140\n",
+ "d (def. map) integrated over the domain: 259.224 at time: 0.140\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.140\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.140\n",
+ "\n",
+ "J integrated over the domain: 18.348 at time: 0.150\n",
+ "J_n integrated over the domain: 15.976 at time: 0.150\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.150\n",
+ "d (def. map) integrated over the domain: 340.652 at time: 0.150\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.150\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.150\n",
+ "\n",
+ "J integrated over the domain: 20.322 at time: 0.160\n",
+ "J_n integrated over the domain: 18.348 at time: 0.160\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.160\n",
+ "d (def. map) integrated over the domain: 416.965 at time: 0.160\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.160\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.160\n",
+ "\n",
+ "J integrated over the domain: 21.772 at time: 0.170\n",
+ "J_n integrated over the domain: 20.322 at time: 0.170\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.170\n",
+ "d (def. map) integrated over the domain: 478.026 at time: 0.170\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.170\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.170\n",
+ "\n",
+ "J integrated over the domain: 22.609 at time: 0.180\n",
+ "J_n integrated over the domain: 21.772 at time: 0.180\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.180\n",
+ "d (def. map) integrated over the domain: 515.153 at time: 0.180\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.180\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.180\n",
+ "\n",
+ "J integrated over the domain: 22.779 at time: 0.190\n",
+ "J_n integrated over the domain: 22.609 at time: 0.190\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.190\n",
+ "d (def. map) integrated over the domain: 522.869 at time: 0.190\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.190\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.190\n",
+ "\n",
+ "J integrated over the domain: 22.271 at time: 0.200\n",
+ "J_n integrated over the domain: 22.779 at time: 0.200\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.200\n",
+ "d (def. map) integrated over the domain: 500.016 at time: 0.200\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.200\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.200\n",
+ "\n",
+ "J integrated over the domain: 21.119 at time: 0.210\n",
+ "J_n integrated over the domain: 22.271 at time: 0.210\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.210\n",
+ "d (def. map) integrated over the domain: 450.001 at time: 0.210\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.210\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.210\n",
+ "\n",
+ "J integrated over the domain: 19.393 at time: 0.220\n",
+ "J_n integrated over the domain: 21.119 at time: 0.220\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.220\n",
+ "d (def. map) integrated over the domain: 380.093 at time: 0.220\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.220\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.220\n",
+ "\n",
+ "J integrated over the domain: 17.203 at time: 0.230\n",
+ "J_n integrated over the domain: 19.393 at time: 0.230\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.230\n",
+ "d (def. map) integrated over the domain: 299.941 at time: 0.230\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.230\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.230\n",
+ "\n",
+ "J integrated over the domain: 14.686 at time: 0.240\n",
+ "J_n integrated over the domain: 17.203 at time: 0.240\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.240\n",
+ "d (def. map) integrated over the domain: 219.674 at time: 0.240\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.240\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.240\n",
+ "\n",
+ "J integrated over the domain: 12.000 at time: 0.250\n",
+ "J_n integrated over the domain: 14.686 at time: 0.250\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.250\n",
+ "d (def. map) integrated over the domain: 148.000 at time: 0.250\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.250\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.250\n",
+ "\n",
+ "J integrated over the domain: 9.314 at time: 0.260\n",
+ "J_n integrated over the domain: 12.000 at time: 0.260\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.260\n",
+ "d (def. map) integrated over the domain: 90.753 at time: 0.260\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.260\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.260\n",
+ "\n",
+ "J integrated over the domain: 6.797 at time: 0.270\n",
+ "J_n integrated over the domain: 9.314 at time: 0.270\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.270\n",
+ "d (def. map) integrated over the domain: 50.200 at time: 0.270\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.270\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.270\n",
+ "\n",
+ "J integrated over the domain: 4.607 at time: 0.280\n",
+ "J_n integrated over the domain: 6.797 at time: 0.280\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.280\n",
+ "d (def. map) integrated over the domain: 25.223 at time: 0.280\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.280\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.280\n",
+ "\n",
+ "J integrated over the domain: 2.881 at time: 0.290\n",
+ "J_n integrated over the domain: 4.607 at time: 0.290\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.290\n",
+ "d (def. map) integrated over the domain: 12.302 at time: 0.290\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.290\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.290\n",
+ "\n",
+ "J integrated over the domain: 1.729 at time: 0.300\n",
+ "J_n integrated over the domain: 2.881 at time: 0.300\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.300\n",
+ "d (def. map) integrated over the domain: 6.988 at time: 0.300\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.300\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.300\n",
+ "\n",
+ "J integrated over the domain: 1.221 at time: 0.310\n",
+ "J_n integrated over the domain: 1.729 at time: 0.310\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.310\n",
+ "d (def. map) integrated over the domain: 5.492 at time: 0.310\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.310\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.310\n",
+ "\n",
+ "J integrated over the domain: 1.391 at time: 0.320\n",
+ "J_n integrated over the domain: 1.221 at time: 0.320\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.320\n",
+ "d (def. map) integrated over the domain: 5.936 at time: 0.320\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.320\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.320\n",
+ "\n",
+ "J integrated over the domain: 2.228 at time: 0.330\n",
+ "J_n integrated over the domain: 1.391 at time: 0.330\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.330\n",
+ "d (def. map) integrated over the domain: 8.963 at time: 0.330\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.330\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.330\n",
+ "\n",
+ "J integrated over the domain: 3.678 at time: 0.340\n",
+ "J_n integrated over the domain: 2.228 at time: 0.340\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.340\n",
+ "d (def. map) integrated over the domain: 17.531 at time: 0.340\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.340\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.340\n",
+ "\n",
+ "J integrated over the domain: 5.652 at time: 0.350\n",
+ "J_n integrated over the domain: 3.678 at time: 0.350\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.350\n",
+ "d (def. map) integrated over the domain: 35.944 at time: 0.350\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.350\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.350\n",
+ "\n",
+ "J integrated over the domain: 8.024 at time: 0.360\n",
+ "J_n integrated over the domain: 5.652 at time: 0.360\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.360\n",
+ "d (def. map) integrated over the domain: 68.389 at time: 0.360\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.360\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.360\n",
+ "\n",
+ "J integrated over the domain: 10.646 at time: 0.370\n",
+ "J_n integrated over the domain: 8.024 at time: 0.370\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.370\n",
+ "d (def. map) integrated over the domain: 117.346 at time: 0.370\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.370\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.370\n",
+ "\n"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "J integrated over the domain: 13.354 at time: 0.380\n",
+ "J_n integrated over the domain: 10.646 at time: 0.380\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.380\n",
+ "d (def. map) integrated over the domain: 182.319 at time: 0.380\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.380\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.380\n",
+ "\n",
+ "J integrated over the domain: 15.976 at time: 0.390\n",
+ "J_n integrated over the domain: 13.354 at time: 0.390\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.390\n",
+ "d (def. map) integrated over the domain: 259.224 at time: 0.390\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.390\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.390\n",
+ "\n",
+ "J integrated over the domain: 18.348 at time: 0.400\n",
+ "J_n integrated over the domain: 15.976 at time: 0.400\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.400\n",
+ "d (def. map) integrated over the domain: 340.652 at time: 0.400\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.400\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.400\n",
+ "\n",
+ "J integrated over the domain: 20.322 at time: 0.410\n",
+ "J_n integrated over the domain: 18.348 at time: 0.410\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.410\n",
+ "d (def. map) integrated over the domain: 416.965 at time: 0.410\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.410\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.410\n",
+ "\n",
+ "J integrated over the domain: 21.772 at time: 0.420\n",
+ "J_n integrated over the domain: 20.322 at time: 0.420\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.420\n",
+ "d (def. map) integrated over the domain: 478.026 at time: 0.420\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.420\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.420\n",
+ "\n",
+ "J integrated over the domain: 22.609 at time: 0.430\n",
+ "J_n integrated over the domain: 21.772 at time: 0.430\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.430\n",
+ "d (def. map) integrated over the domain: 515.153 at time: 0.430\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.430\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.430\n",
+ "\n",
+ "J integrated over the domain: 22.779 at time: 0.440\n",
+ "J_n integrated over the domain: 22.609 at time: 0.440\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.440\n",
+ "d (def. map) integrated over the domain: 522.869 at time: 0.440\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.440\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.440\n",
+ "\n",
+ "J integrated over the domain: 22.271 at time: 0.450\n",
+ "J_n integrated over the domain: 22.779 at time: 0.450\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.450\n",
+ "d (def. map) integrated over the domain: 500.016 at time: 0.450\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.450\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.450\n",
+ "\n",
+ "J integrated over the domain: 21.119 at time: 0.460\n",
+ "J_n integrated over the domain: 22.271 at time: 0.460\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.460\n",
+ "d (def. map) integrated over the domain: 450.001 at time: 0.460\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.460\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.460\n",
+ "\n",
+ "J integrated over the domain: 19.393 at time: 0.470\n",
+ "J_n integrated over the domain: 21.119 at time: 0.470\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.470\n",
+ "d (def. map) integrated over the domain: 380.093 at time: 0.470\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.470\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.470\n",
+ "\n",
+ "J integrated over the domain: 17.203 at time: 0.480\n",
+ "J_n integrated over the domain: 19.393 at time: 0.480\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.480\n",
+ "d (def. map) integrated over the domain: 299.941 at time: 0.480\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.480\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.480\n",
+ "\n",
+ "J integrated over the domain: 14.686 at time: 0.490\n",
+ "J_n integrated over the domain: 17.203 at time: 0.490\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.490\n",
+ "d (def. map) integrated over the domain: 219.674 at time: 0.490\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.490\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.490\n",
+ "\n",
+ "J integrated over the domain: 12.000 at time: 0.500\n",
+ "J_n integrated over the domain: 14.686 at time: 0.500\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.500\n",
+ "d (def. map) integrated over the domain: 148.000 at time: 0.500\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.500\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.500\n",
+ "\n",
+ "J integrated over the domain: 9.314 at time: 0.510\n",
+ "J_n integrated over the domain: 12.000 at time: 0.510\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.510\n",
+ "d (def. map) integrated over the domain: 90.753 at time: 0.510\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.510\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.510\n",
+ "\n",
+ "J integrated over the domain: 6.797 at time: 0.520\n",
+ "J_n integrated over the domain: 9.314 at time: 0.520\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.520\n",
+ "d (def. map) integrated over the domain: 50.200 at time: 0.520\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.520\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.520\n",
+ "\n",
+ "J integrated over the domain: 4.607 at time: 0.530\n",
+ "J_n integrated over the domain: 6.797 at time: 0.530\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.530\n",
+ "d (def. map) integrated over the domain: 25.223 at time: 0.530\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.530\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.530\n",
+ "\n",
+ "J integrated over the domain: 2.881 at time: 0.540\n",
+ "J_n integrated over the domain: 4.607 at time: 0.540\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.540\n",
+ "d (def. map) integrated over the domain: 12.302 at time: 0.540\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.540\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.540\n",
+ "\n",
+ "J integrated over the domain: 1.729 at time: 0.550\n",
+ "J_n integrated over the domain: 2.881 at time: 0.550\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.550\n",
+ "d (def. map) integrated over the domain: 6.988 at time: 0.550\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.550\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.550\n",
+ "\n",
+ "J integrated over the domain: 1.221 at time: 0.560\n",
+ "J_n integrated over the domain: 1.729 at time: 0.560\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.560\n",
+ "d (def. map) integrated over the domain: 5.492 at time: 0.560\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.560\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.560\n",
+ "\n",
+ "J integrated over the domain: 1.391 at time: 0.570\n",
+ "J_n integrated over the domain: 1.221 at time: 0.570\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.570\n",
+ "d (def. map) integrated over the domain: 5.936 at time: 0.570\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.570\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.570\n",
+ "\n",
+ "J integrated over the domain: 2.228 at time: 0.580\n",
+ "J_n integrated over the domain: 1.391 at time: 0.580\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.580\n",
+ "d (def. map) integrated over the domain: 8.963 at time: 0.580\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.580\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.580\n",
+ "\n",
+ "J integrated over the domain: 3.678 at time: 0.590\n",
+ "J_n integrated over the domain: 2.228 at time: 0.590\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.590\n",
+ "d (def. map) integrated over the domain: 17.531 at time: 0.590\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.590\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.590\n",
+ "\n",
+ "J integrated over the domain: 5.652 at time: 0.600\n",
+ "J_n integrated over the domain: 3.678 at time: 0.600\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.600\n",
+ "d (def. map) integrated over the domain: 35.944 at time: 0.600\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.600\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.600\n",
+ "\n",
+ "J integrated over the domain: 8.024 at time: 0.610\n",
+ "J_n integrated over the domain: 5.652 at time: 0.610\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.610\n",
+ "d (def. map) integrated over the domain: 68.389 at time: 0.610\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.610\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.610\n",
+ "\n"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "J integrated over the domain: 10.646 at time: 0.620\n",
+ "J_n integrated over the domain: 8.024 at time: 0.620\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.620\n",
+ "d (def. map) integrated over the domain: 117.346 at time: 0.620\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.620\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.620\n",
+ "\n",
+ "J integrated over the domain: 13.354 at time: 0.630\n",
+ "J_n integrated over the domain: 10.646 at time: 0.630\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.630\n",
+ "d (def. map) integrated over the domain: 182.319 at time: 0.630\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.630\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.630\n",
+ "\n",
+ "J integrated over the domain: 15.976 at time: 0.640\n",
+ "J_n integrated over the domain: 13.354 at time: 0.640\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.640\n",
+ "d (def. map) integrated over the domain: 259.224 at time: 0.640\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.640\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.640\n",
+ "\n",
+ "J integrated over the domain: 18.348 at time: 0.650\n",
+ "J_n integrated over the domain: 15.976 at time: 0.650\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.650\n",
+ "d (def. map) integrated over the domain: 340.652 at time: 0.650\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.650\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.650\n",
+ "\n",
+ "J integrated over the domain: 20.322 at time: 0.660\n",
+ "J_n integrated over the domain: 18.348 at time: 0.660\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.660\n",
+ "d (def. map) integrated over the domain: 416.965 at time: 0.660\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.660\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.660\n",
+ "\n",
+ "J integrated over the domain: 21.772 at time: 0.670\n",
+ "J_n integrated over the domain: 20.322 at time: 0.670\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.670\n",
+ "d (def. map) integrated over the domain: 478.026 at time: 0.670\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.670\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.670\n",
+ "\n",
+ "J integrated over the domain: 22.609 at time: 0.680\n",
+ "J_n integrated over the domain: 21.772 at time: 0.680\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.680\n",
+ "d (def. map) integrated over the domain: 515.153 at time: 0.680\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.680\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.680\n",
+ "\n",
+ "J integrated over the domain: 22.779 at time: 0.690\n",
+ "J_n integrated over the domain: 22.609 at time: 0.690\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.690\n",
+ "d (def. map) integrated over the domain: 522.869 at time: 0.690\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.690\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.690\n",
+ "\n",
+ "J integrated over the domain: 22.271 at time: 0.700\n",
+ "J_n integrated over the domain: 22.779 at time: 0.700\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.700\n",
+ "d (def. map) integrated over the domain: 500.016 at time: 0.700\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.700\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.700\n",
+ "\n",
+ "J integrated over the domain: 21.119 at time: 0.710\n",
+ "J_n integrated over the domain: 22.271 at time: 0.710\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.710\n",
+ "d (def. map) integrated over the domain: 450.001 at time: 0.710\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.710\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.710\n",
+ "\n",
+ "J integrated over the domain: 19.393 at time: 0.720\n",
+ "J_n integrated over the domain: 21.119 at time: 0.720\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.720\n",
+ "d (def. map) integrated over the domain: 380.093 at time: 0.720\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.720\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.720\n",
+ "\n",
+ "J integrated over the domain: 17.203 at time: 0.730\n",
+ "J_n integrated over the domain: 19.393 at time: 0.730\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.730\n",
+ "d (def. map) integrated over the domain: 299.941 at time: 0.730\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.730\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.730\n",
+ "\n",
+ "J integrated over the domain: 14.686 at time: 0.740\n",
+ "J_n integrated over the domain: 17.203 at time: 0.740\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.740\n",
+ "d (def. map) integrated over the domain: 219.674 at time: 0.740\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.740\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.740\n",
+ "\n",
+ "J integrated over the domain: 12.000 at time: 0.750\n",
+ "J_n integrated over the domain: 14.686 at time: 0.750\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.750\n",
+ "d (def. map) integrated over the domain: 148.000 at time: 0.750\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.750\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.750\n",
+ "\n",
+ "J integrated over the domain: 9.314 at time: 0.760\n",
+ "J_n integrated over the domain: 12.000 at time: 0.760\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.760\n",
+ "d (def. map) integrated over the domain: 90.753 at time: 0.760\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.760\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.760\n",
+ "\n",
+ "J integrated over the domain: 6.797 at time: 0.770\n",
+ "J_n integrated over the domain: 9.314 at time: 0.770\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.770\n",
+ "d (def. map) integrated over the domain: 50.200 at time: 0.770\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.770\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.770\n",
+ "\n",
+ "J integrated over the domain: 4.607 at time: 0.780\n",
+ "J_n integrated over the domain: 6.797 at time: 0.780\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.780\n",
+ "d (def. map) integrated over the domain: 25.223 at time: 0.780\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.780\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.780\n",
+ "\n",
+ "J integrated over the domain: 2.881 at time: 0.790\n",
+ "J_n integrated over the domain: 4.607 at time: 0.790\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.790\n",
+ "d (def. map) integrated over the domain: 12.302 at time: 0.790\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.790\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.790\n",
+ "\n",
+ "J integrated over the domain: 1.729 at time: 0.800\n",
+ "J_n integrated over the domain: 2.881 at time: 0.800\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.800\n",
+ "d (def. map) integrated over the domain: 6.988 at time: 0.800\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.800\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.800\n",
+ "\n",
+ "J integrated over the domain: 1.221 at time: 0.810\n",
+ "J_n integrated over the domain: 1.729 at time: 0.810\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.810\n",
+ "d (def. map) integrated over the domain: 5.492 at time: 0.810\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.810\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.810\n",
+ "\n",
+ "J integrated over the domain: 1.391 at time: 0.820\n",
+ "J_n integrated over the domain: 1.221 at time: 0.820\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.820\n",
+ "d (def. map) integrated over the domain: 5.936 at time: 0.820\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.820\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.820\n",
+ "\n",
+ "J integrated over the domain: 2.228 at time: 0.830\n",
+ "J_n integrated over the domain: 1.391 at time: 0.830\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.830\n",
+ "d (def. map) integrated over the domain: 8.963 at time: 0.830\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.830\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.830\n",
+ "\n",
+ "J integrated over the domain: 3.678 at time: 0.840\n",
+ "J_n integrated over the domain: 2.228 at time: 0.840\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.840\n",
+ "d (def. map) integrated over the domain: 17.531 at time: 0.840\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.840\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.840\n",
+ "\n",
+ "J integrated over the domain: 5.652 at time: 0.850\n",
+ "J_n integrated over the domain: 3.678 at time: 0.850\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.850\n",
+ "d (def. map) integrated over the domain: 35.944 at time: 0.850\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.850\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.850\n",
+ "\n"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "J integrated over the domain: 8.024 at time: 0.860\n",
+ "J_n integrated over the domain: 5.652 at time: 0.860\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.860\n",
+ "d (def. map) integrated over the domain: 68.389 at time: 0.860\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.860\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.860\n",
+ "\n",
+ "J integrated over the domain: 10.646 at time: 0.870\n",
+ "J_n integrated over the domain: 8.024 at time: 0.870\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.870\n",
+ "d (def. map) integrated over the domain: 117.346 at time: 0.870\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.870\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.870\n",
+ "\n",
+ "J integrated over the domain: 13.354 at time: 0.880\n",
+ "J_n integrated over the domain: 10.646 at time: 0.880\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.880\n",
+ "d (def. map) integrated over the domain: 182.319 at time: 0.880\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.880\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.880\n",
+ "\n",
+ "J integrated over the domain: 15.976 at time: 0.890\n",
+ "J_n integrated over the domain: 13.354 at time: 0.890\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.890\n",
+ "d (def. map) integrated over the domain: 259.224 at time: 0.890\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.890\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.890\n",
+ "\n",
+ "J integrated over the domain: 18.348 at time: 0.900\n",
+ "J_n integrated over the domain: 15.976 at time: 0.900\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.900\n",
+ "d (def. map) integrated over the domain: 340.652 at time: 0.900\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.900\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.900\n",
+ "\n",
+ "J integrated over the domain: 20.322 at time: 0.910\n",
+ "J_n integrated over the domain: 18.348 at time: 0.910\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.910\n",
+ "d (def. map) integrated over the domain: 416.965 at time: 0.910\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.910\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.910\n",
+ "\n",
+ "J integrated over the domain: 21.772 at time: 0.920\n",
+ "J_n integrated over the domain: 20.322 at time: 0.920\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.920\n",
+ "d (def. map) integrated over the domain: 478.026 at time: 0.920\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.920\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.920\n",
+ "\n",
+ "J integrated over the domain: 22.609 at time: 0.930\n",
+ "J_n integrated over the domain: 21.772 at time: 0.930\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.930\n",
+ "d (def. map) integrated over the domain: 515.153 at time: 0.930\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.930\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.930\n",
+ "\n",
+ "J integrated over the domain: 22.779 at time: 0.940\n",
+ "J_n integrated over the domain: 22.609 at time: 0.940\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.940\n",
+ "d (def. map) integrated over the domain: 522.869 at time: 0.940\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.940\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.940\n",
+ "\n",
+ "J integrated over the domain: 22.271 at time: 0.950\n",
+ "J_n integrated over the domain: 22.779 at time: 0.950\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.950\n",
+ "d (def. map) integrated over the domain: 500.016 at time: 0.950\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.950\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.950\n",
+ "\n",
+ "J integrated over the domain: 21.119 at time: 0.960\n",
+ "J_n integrated over the domain: 22.271 at time: 0.960\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.960\n",
+ "d (def. map) integrated over the domain: 450.001 at time: 0.960\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.960\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.960\n",
+ "\n",
+ "J integrated over the domain: 19.393 at time: 0.970\n",
+ "J_n integrated over the domain: 21.119 at time: 0.970\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.970\n",
+ "d (def. map) integrated over the domain: 380.093 at time: 0.970\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.970\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.970\n",
+ "\n",
+ "J integrated over the domain: 17.203 at time: 0.980\n",
+ "J_n integrated over the domain: 19.393 at time: 0.980\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.980\n",
+ "d (def. map) integrated over the domain: 299.941 at time: 0.980\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.980\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.980\n",
+ "\n",
+ "J integrated over the domain: 14.686 at time: 0.990\n",
+ "J_n integrated over the domain: 17.203 at time: 0.990\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.990\n",
+ "d (def. map) integrated over the domain: 219.674 at time: 0.990\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.990\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.990\n",
+ "\n",
+ "J integrated over the domain: 12.000 at time: 1.000\n",
+ "J_n integrated over the domain: 14.686 at time: 1.000\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.000\n",
+ "d (def. map) integrated over the domain: 148.000 at time: 1.000\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.000\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.000\n",
+ "\n",
+ "J integrated over the domain: 9.314 at time: 1.010\n",
+ "J_n integrated over the domain: 12.000 at time: 1.010\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.010\n",
+ "d (def. map) integrated over the domain: 90.753 at time: 1.010\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.010\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.010\n",
+ "\n",
+ "J integrated over the domain: 6.797 at time: 1.020\n",
+ "J_n integrated over the domain: 9.314 at time: 1.020\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.020\n",
+ "d (def. map) integrated over the domain: 50.200 at time: 1.020\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.020\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.020\n",
+ "\n",
+ "J integrated over the domain: 4.607 at time: 1.030\n",
+ "J_n integrated over the domain: 6.797 at time: 1.030\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.030\n",
+ "d (def. map) integrated over the domain: 25.223 at time: 1.030\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.030\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.030\n",
+ "\n",
+ "J integrated over the domain: 2.881 at time: 1.040\n",
+ "J_n integrated over the domain: 4.607 at time: 1.040\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.040\n",
+ "d (def. map) integrated over the domain: 12.302 at time: 1.040\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.040\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.040\n",
+ "\n",
+ "J integrated over the domain: 1.729 at time: 1.050\n",
+ "J_n integrated over the domain: 2.881 at time: 1.050\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.050\n",
+ "d (def. map) integrated over the domain: 6.988 at time: 1.050\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.050\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.050\n",
+ "\n",
+ "J integrated over the domain: 1.221 at time: 1.060\n",
+ "J_n integrated over the domain: 1.729 at time: 1.060\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.060\n",
+ "d (def. map) integrated over the domain: 5.492 at time: 1.060\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.060\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.060\n",
+ "\n",
+ "J integrated over the domain: 1.391 at time: 1.070\n",
+ "J_n integrated over the domain: 1.221 at time: 1.070\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.070\n",
+ "d (def. map) integrated over the domain: 5.936 at time: 1.070\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.070\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.070\n",
+ "\n",
+ "J integrated over the domain: 2.228 at time: 1.080\n",
+ "J_n integrated over the domain: 1.391 at time: 1.080\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.080\n",
+ "d (def. map) integrated over the domain: 8.963 at time: 1.080\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.080\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.080\n",
+ "\n",
+ "J integrated over the domain: 3.678 at time: 1.090\n",
+ "J_n integrated over the domain: 2.228 at time: 1.090\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.090\n",
+ "d (def. map) integrated over the domain: 17.531 at time: 1.090\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.090\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.090\n",
+ "\n"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "J integrated over the domain: 5.652 at time: 1.100\n",
+ "J_n integrated over the domain: 3.678 at time: 1.100\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.100\n",
+ "d (def. map) integrated over the domain: 35.944 at time: 1.100\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.100\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.100\n",
+ "\n",
+ "J integrated over the domain: 8.024 at time: 1.110\n",
+ "J_n integrated over the domain: 5.652 at time: 1.110\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.110\n",
+ "d (def. map) integrated over the domain: 68.389 at time: 1.110\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.110\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.110\n",
+ "\n",
+ "J integrated over the domain: 10.646 at time: 1.120\n",
+ "J_n integrated over the domain: 8.024 at time: 1.120\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.120\n",
+ "d (def. map) integrated over the domain: 117.346 at time: 1.120\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.120\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.120\n",
+ "\n",
+ "J integrated over the domain: 13.354 at time: 1.130\n",
+ "J_n integrated over the domain: 10.646 at time: 1.130\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.130\n",
+ "d (def. map) integrated over the domain: 182.319 at time: 1.130\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.130\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.130\n",
+ "\n",
+ "J integrated over the domain: 15.976 at time: 1.140\n",
+ "J_n integrated over the domain: 13.354 at time: 1.140\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.140\n",
+ "d (def. map) integrated over the domain: 259.224 at time: 1.140\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.140\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.140\n",
+ "\n",
+ "J integrated over the domain: 18.348 at time: 1.150\n",
+ "J_n integrated over the domain: 15.976 at time: 1.150\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.150\n",
+ "d (def. map) integrated over the domain: 340.652 at time: 1.150\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.150\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.150\n",
+ "\n",
+ "J integrated over the domain: 20.322 at time: 1.160\n",
+ "J_n integrated over the domain: 18.348 at time: 1.160\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.160\n",
+ "d (def. map) integrated over the domain: 416.965 at time: 1.160\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.160\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.160\n",
+ "\n",
+ "J integrated over the domain: 21.772 at time: 1.170\n",
+ "J_n integrated over the domain: 20.322 at time: 1.170\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.170\n",
+ "d (def. map) integrated over the domain: 478.026 at time: 1.170\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.170\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.170\n",
+ "\n",
+ "J integrated over the domain: 22.609 at time: 1.180\n",
+ "J_n integrated over the domain: 21.772 at time: 1.180\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.180\n",
+ "d (def. map) integrated over the domain: 515.153 at time: 1.180\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.180\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.180\n",
+ "\n",
+ "J integrated over the domain: 22.779 at time: 1.190\n",
+ "J_n integrated over the domain: 22.609 at time: 1.190\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.190\n",
+ "d (def. map) integrated over the domain: 522.869 at time: 1.190\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.190\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.190\n",
+ "\n",
+ "J integrated over the domain: 22.271 at time: 1.200\n",
+ "J_n integrated over the domain: 22.779 at time: 1.200\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.200\n",
+ "d (def. map) integrated over the domain: 500.016 at time: 1.200\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.200\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.200\n",
+ "\n",
+ "J integrated over the domain: 21.119 at time: 1.210\n",
+ "J_n integrated over the domain: 22.271 at time: 1.210\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.210\n",
+ "d (def. map) integrated over the domain: 450.001 at time: 1.210\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.210\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.210\n",
+ "\n",
+ "J integrated over the domain: 19.393 at time: 1.220\n",
+ "J_n integrated over the domain: 21.119 at time: 1.220\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.220\n",
+ "d (def. map) integrated over the domain: 380.093 at time: 1.220\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.220\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.220\n",
+ "\n",
+ "J integrated over the domain: 17.203 at time: 1.230\n",
+ "J_n integrated over the domain: 19.393 at time: 1.230\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.230\n",
+ "d (def. map) integrated over the domain: 299.941 at time: 1.230\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.230\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.230\n",
+ "\n",
+ "J integrated over the domain: 14.686 at time: 1.240\n",
+ "J_n integrated over the domain: 17.203 at time: 1.240\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.240\n",
+ "d (def. map) integrated over the domain: 219.674 at time: 1.240\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.240\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.240\n",
+ "\n",
+ "J integrated over the domain: 12.000 at time: 1.250\n",
+ "J_n integrated over the domain: 14.686 at time: 1.250\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.250\n",
+ "d (def. map) integrated over the domain: 148.000 at time: 1.250\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.250\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.250\n",
+ "\n",
+ "J integrated over the domain: 9.314 at time: 1.260\n",
+ "J_n integrated over the domain: 12.000 at time: 1.260\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.260\n",
+ "d (def. map) integrated over the domain: 90.753 at time: 1.260\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.260\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.260\n",
+ "\n",
+ "J integrated over the domain: 6.797 at time: 1.270\n",
+ "J_n integrated over the domain: 9.314 at time: 1.270\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.270\n",
+ "d (def. map) integrated over the domain: 50.200 at time: 1.270\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.270\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.270\n",
+ "\n",
+ "J integrated over the domain: 4.607 at time: 1.280\n",
+ "J_n integrated over the domain: 6.797 at time: 1.280\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.280\n",
+ "d (def. map) integrated over the domain: 25.223 at time: 1.280\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.280\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.280\n",
+ "\n",
+ "J integrated over the domain: 2.881 at time: 1.290\n",
+ "J_n integrated over the domain: 4.607 at time: 1.290\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.290\n",
+ "d (def. map) integrated over the domain: 12.302 at time: 1.290\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.290\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.290\n",
+ "\n",
+ "J integrated over the domain: 1.729 at time: 1.300\n",
+ "J_n integrated over the domain: 2.881 at time: 1.300\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.300\n",
+ "d (def. map) integrated over the domain: 6.988 at time: 1.300\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.300\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.300\n",
+ "\n",
+ "J integrated over the domain: 1.221 at time: 1.310\n",
+ "J_n integrated over the domain: 1.729 at time: 1.310\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.310\n",
+ "d (def. map) integrated over the domain: 5.492 at time: 1.310\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.310\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.310\n",
+ "\n",
+ "J integrated over the domain: 1.391 at time: 1.320\n",
+ "J_n integrated over the domain: 1.221 at time: 1.320\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.320\n",
+ "d (def. map) integrated over the domain: 5.936 at time: 1.320\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.320\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.320\n",
+ "\n",
+ "J integrated over the domain: 2.228 at time: 1.330\n",
+ "J_n integrated over the domain: 1.391 at time: 1.330\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.330\n",
+ "d (def. map) integrated over the domain: 8.963 at time: 1.330\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.330\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.330\n",
+ "\n"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "J integrated over the domain: 3.678 at time: 1.340\n",
+ "J_n integrated over the domain: 2.228 at time: 1.340\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.340\n",
+ "d (def. map) integrated over the domain: 17.531 at time: 1.340\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.340\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.340\n",
+ "\n",
+ "J integrated over the domain: 5.652 at time: 1.350\n",
+ "J_n integrated over the domain: 3.678 at time: 1.350\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.350\n",
+ "d (def. map) integrated over the domain: 35.944 at time: 1.350\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.350\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.350\n",
+ "\n",
+ "J integrated over the domain: 8.024 at time: 1.360\n",
+ "J_n integrated over the domain: 5.652 at time: 1.360\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.360\n",
+ "d (def. map) integrated over the domain: 68.389 at time: 1.360\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.360\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.360\n",
+ "\n",
+ "J integrated over the domain: 10.646 at time: 1.370\n",
+ "J_n integrated over the domain: 8.024 at time: 1.370\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.370\n",
+ "d (def. map) integrated over the domain: 117.346 at time: 1.370\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.370\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.370\n",
+ "\n",
+ "J integrated over the domain: 13.354 at time: 1.380\n",
+ "J_n integrated over the domain: 10.646 at time: 1.380\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.380\n",
+ "d (def. map) integrated over the domain: 182.319 at time: 1.380\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.380\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.380\n",
+ "\n",
+ "J integrated over the domain: 15.976 at time: 1.390\n",
+ "J_n integrated over the domain: 13.354 at time: 1.390\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.390\n",
+ "d (def. map) integrated over the domain: 259.224 at time: 1.390\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.390\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.390\n",
+ "\n",
+ "J integrated over the domain: 18.348 at time: 1.400\n",
+ "J_n integrated over the domain: 15.976 at time: 1.400\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.400\n",
+ "d (def. map) integrated over the domain: 340.652 at time: 1.400\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.400\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.400\n",
+ "\n",
+ "J integrated over the domain: 20.322 at time: 1.410\n",
+ "J_n integrated over the domain: 18.348 at time: 1.410\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.410\n",
+ "d (def. map) integrated over the domain: 416.965 at time: 1.410\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.410\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.410\n",
+ "\n",
+ "J integrated over the domain: 21.772 at time: 1.420\n",
+ "J_n integrated over the domain: 20.322 at time: 1.420\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.420\n",
+ "d (def. map) integrated over the domain: 478.026 at time: 1.420\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.420\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.420\n",
+ "\n",
+ "J integrated over the domain: 22.609 at time: 1.430\n",
+ "J_n integrated over the domain: 21.772 at time: 1.430\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.430\n",
+ "d (def. map) integrated over the domain: 515.153 at time: 1.430\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.430\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.430\n",
+ "\n",
+ "J integrated over the domain: 22.779 at time: 1.440\n",
+ "J_n integrated over the domain: 22.609 at time: 1.440\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.440\n",
+ "d (def. map) integrated over the domain: 522.869 at time: 1.440\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.440\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.440\n",
+ "\n",
+ "J integrated over the domain: 22.271 at time: 1.450\n",
+ "J_n integrated over the domain: 22.779 at time: 1.450\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.450\n",
+ "d (def. map) integrated over the domain: 500.016 at time: 1.450\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.450\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.450\n",
+ "\n",
+ "J integrated over the domain: 21.119 at time: 1.460\n",
+ "J_n integrated over the domain: 22.271 at time: 1.460\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.460\n",
+ "d (def. map) integrated over the domain: 450.001 at time: 1.460\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.460\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.460\n",
+ "\n",
+ "J integrated over the domain: 19.393 at time: 1.470\n",
+ "J_n integrated over the domain: 21.119 at time: 1.470\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.470\n",
+ "d (def. map) integrated over the domain: 380.093 at time: 1.470\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.470\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.470\n",
+ "\n",
+ "J integrated over the domain: 17.203 at time: 1.480\n",
+ "J_n integrated over the domain: 19.393 at time: 1.480\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.480\n",
+ "d (def. map) integrated over the domain: 299.941 at time: 1.480\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.480\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.480\n",
+ "\n",
+ "J integrated over the domain: 14.686 at time: 1.490\n",
+ "J_n integrated over the domain: 17.203 at time: 1.490\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.490\n",
+ "d (def. map) integrated over the domain: 219.674 at time: 1.490\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.490\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.490\n",
+ "\n",
+ "J integrated over the domain: 12.000 at time: 1.500\n",
+ "J_n integrated over the domain: 14.686 at time: 1.500\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.500\n",
+ "d (def. map) integrated over the domain: 148.000 at time: 1.500\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.500\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.500\n",
+ "\n",
+ "J integrated over the domain: 9.314 at time: 1.510\n",
+ "J_n integrated over the domain: 12.000 at time: 1.510\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.510\n",
+ "d (def. map) integrated over the domain: 90.753 at time: 1.510\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.510\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.510\n",
+ "\n",
+ "J integrated over the domain: 6.797 at time: 1.520\n",
+ "J_n integrated over the domain: 9.314 at time: 1.520\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.520\n",
+ "d (def. map) integrated over the domain: 50.200 at time: 1.520\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.520\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.520\n",
+ "\n",
+ "J integrated over the domain: 4.607 at time: 1.530\n",
+ "J_n integrated over the domain: 6.797 at time: 1.530\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.530\n",
+ "d (def. map) integrated over the domain: 25.223 at time: 1.530\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.530\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.530\n",
+ "\n",
+ "J integrated over the domain: 2.881 at time: 1.540\n",
+ "J_n integrated over the domain: 4.607 at time: 1.540\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.540\n",
+ "d (def. map) integrated over the domain: 12.302 at time: 1.540\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.540\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.540\n",
+ "\n",
+ "J integrated over the domain: 1.729 at time: 1.550\n",
+ "J_n integrated over the domain: 2.881 at time: 1.550\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.550\n",
+ "d (def. map) integrated over the domain: 6.988 at time: 1.550\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.550\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.550\n",
+ "\n",
+ "J integrated over the domain: 1.221 at time: 1.560\n",
+ "J_n integrated over the domain: 1.729 at time: 1.560\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.560\n",
+ "d (def. map) integrated over the domain: 5.492 at time: 1.560\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.560\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.560\n",
+ "\n",
+ "J integrated over the domain: 1.391 at time: 1.570\n",
+ "J_n integrated over the domain: 1.221 at time: 1.570\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.570\n",
+ "d (def. map) integrated over the domain: 5.936 at time: 1.570\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.570\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.570\n",
+ "\n"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "J integrated over the domain: 2.228 at time: 1.580\n",
+ "J_n integrated over the domain: 1.391 at time: 1.580\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.580\n",
+ "d (def. map) integrated over the domain: 8.963 at time: 1.580\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.580\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.580\n",
+ "\n",
+ "J integrated over the domain: 3.678 at time: 1.590\n",
+ "J_n integrated over the domain: 2.228 at time: 1.590\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.590\n",
+ "d (def. map) integrated over the domain: 17.531 at time: 1.590\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.590\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.590\n",
+ "\n",
+ "J integrated over the domain: 5.652 at time: 1.600\n",
+ "J_n integrated over the domain: 3.678 at time: 1.600\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.600\n",
+ "d (def. map) integrated over the domain: 35.944 at time: 1.600\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.600\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.600\n",
+ "\n",
+ "J integrated over the domain: 8.024 at time: 1.610\n",
+ "J_n integrated over the domain: 5.652 at time: 1.610\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.610\n",
+ "d (def. map) integrated over the domain: 68.389 at time: 1.610\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.610\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.610\n",
+ "\n",
+ "J integrated over the domain: 10.646 at time: 1.620\n",
+ "J_n integrated over the domain: 8.024 at time: 1.620\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.620\n",
+ "d (def. map) integrated over the domain: 117.346 at time: 1.620\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.620\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.620\n",
+ "\n",
+ "J integrated over the domain: 13.354 at time: 1.630\n",
+ "J_n integrated over the domain: 10.646 at time: 1.630\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.630\n",
+ "d (def. map) integrated over the domain: 182.319 at time: 1.630\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.630\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.630\n",
+ "\n",
+ "J integrated over the domain: 15.976 at time: 1.640\n",
+ "J_n integrated over the domain: 13.354 at time: 1.640\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.640\n",
+ "d (def. map) integrated over the domain: 259.224 at time: 1.640\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.640\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.640\n",
+ "\n",
+ "J integrated over the domain: 18.348 at time: 1.650\n",
+ "J_n integrated over the domain: 15.976 at time: 1.650\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.650\n",
+ "d (def. map) integrated over the domain: 340.652 at time: 1.650\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.650\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.650\n",
+ "\n",
+ "J integrated over the domain: 20.322 at time: 1.660\n",
+ "J_n integrated over the domain: 18.348 at time: 1.660\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.660\n",
+ "d (def. map) integrated over the domain: 416.965 at time: 1.660\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.660\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.660\n",
+ "\n",
+ "J integrated over the domain: 21.772 at time: 1.670\n",
+ "J_n integrated over the domain: 20.322 at time: 1.670\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.670\n",
+ "d (def. map) integrated over the domain: 478.026 at time: 1.670\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.670\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.670\n",
+ "\n",
+ "J integrated over the domain: 22.609 at time: 1.680\n",
+ "J_n integrated over the domain: 21.772 at time: 1.680\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.680\n",
+ "d (def. map) integrated over the domain: 515.153 at time: 1.680\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.680\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.680\n",
+ "\n",
+ "J integrated over the domain: 22.779 at time: 1.690\n",
+ "J_n integrated over the domain: 22.609 at time: 1.690\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.690\n",
+ "d (def. map) integrated over the domain: 522.869 at time: 1.690\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.690\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.690\n",
+ "\n",
+ "J integrated over the domain: 22.271 at time: 1.700\n",
+ "J_n integrated over the domain: 22.779 at time: 1.700\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.700\n",
+ "d (def. map) integrated over the domain: 500.016 at time: 1.700\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.700\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.700\n",
+ "\n",
+ "J integrated over the domain: 21.119 at time: 1.710\n",
+ "J_n integrated over the domain: 22.271 at time: 1.710\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.710\n",
+ "d (def. map) integrated over the domain: 450.001 at time: 1.710\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.710\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.710\n",
+ "\n",
+ "J integrated over the domain: 19.393 at time: 1.720\n",
+ "J_n integrated over the domain: 21.119 at time: 1.720\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.720\n",
+ "d (def. map) integrated over the domain: 380.093 at time: 1.720\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.720\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.720\n",
+ "\n",
+ "J integrated over the domain: 17.203 at time: 1.730\n",
+ "J_n integrated over the domain: 19.393 at time: 1.730\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.730\n",
+ "d (def. map) integrated over the domain: 299.941 at time: 1.730\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.730\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.730\n",
+ "\n",
+ "J integrated over the domain: 14.686 at time: 1.740\n",
+ "J_n integrated over the domain: 17.203 at time: 1.740\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.740\n",
+ "d (def. map) integrated over the domain: 219.674 at time: 1.740\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.740\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.740\n",
+ "\n",
+ "J integrated over the domain: 12.000 at time: 1.750\n",
+ "J_n integrated over the domain: 14.686 at time: 1.750\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.750\n",
+ "d (def. map) integrated over the domain: 148.000 at time: 1.750\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.750\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.750\n",
+ "\n",
+ "J integrated over the domain: 9.314 at time: 1.760\n",
+ "J_n integrated over the domain: 12.000 at time: 1.760\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.760\n",
+ "d (def. map) integrated over the domain: 90.753 at time: 1.760\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.760\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.760\n",
+ "\n",
+ "J integrated over the domain: 6.797 at time: 1.770\n",
+ "J_n integrated over the domain: 9.314 at time: 1.770\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.770\n",
+ "d (def. map) integrated over the domain: 50.200 at time: 1.770\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.770\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.770\n",
+ "\n",
+ "J integrated over the domain: 4.607 at time: 1.780\n",
+ "J_n integrated over the domain: 6.797 at time: 1.780\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.780\n",
+ "d (def. map) integrated over the domain: 25.223 at time: 1.780\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.780\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.780\n",
+ "\n",
+ "J integrated over the domain: 2.881 at time: 1.790\n",
+ "J_n integrated over the domain: 4.607 at time: 1.790\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.790\n",
+ "d (def. map) integrated over the domain: 12.302 at time: 1.790\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.790\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.790\n",
+ "\n",
+ "J integrated over the domain: 1.729 at time: 1.800\n",
+ "J_n integrated over the domain: 2.881 at time: 1.800\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.800\n",
+ "d (def. map) integrated over the domain: 6.988 at time: 1.800\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.800\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.800\n",
+ "\n",
+ "J integrated over the domain: 1.221 at time: 1.810\n",
+ "J_n integrated over the domain: 1.729 at time: 1.810\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.810\n",
+ "d (def. map) integrated over the domain: 5.492 at time: 1.810\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.810\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.810\n",
+ "\n"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "J integrated over the domain: 1.391 at time: 1.820\n",
+ "J_n integrated over the domain: 1.221 at time: 1.820\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.820\n",
+ "d (def. map) integrated over the domain: 5.936 at time: 1.820\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.820\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.820\n",
+ "\n",
+ "J integrated over the domain: 2.228 at time: 1.830\n",
+ "J_n integrated over the domain: 1.391 at time: 1.830\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.830\n",
+ "d (def. map) integrated over the domain: 8.963 at time: 1.830\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.830\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.830\n",
+ "\n",
+ "J integrated over the domain: 3.678 at time: 1.840\n",
+ "J_n integrated over the domain: 2.228 at time: 1.840\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.840\n",
+ "d (def. map) integrated over the domain: 17.531 at time: 1.840\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.840\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.840\n",
+ "\n",
+ "J integrated over the domain: 5.652 at time: 1.850\n",
+ "J_n integrated over the domain: 3.678 at time: 1.850\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.850\n",
+ "d (def. map) integrated over the domain: 35.944 at time: 1.850\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.850\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.850\n",
+ "\n",
+ "J integrated over the domain: 8.024 at time: 1.860\n",
+ "J_n integrated over the domain: 5.652 at time: 1.860\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.860\n",
+ "d (def. map) integrated over the domain: 68.389 at time: 1.860\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.860\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.860\n",
+ "\n",
+ "J integrated over the domain: 10.646 at time: 1.870\n",
+ "J_n integrated over the domain: 8.024 at time: 1.870\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.870\n",
+ "d (def. map) integrated over the domain: 117.346 at time: 1.870\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.870\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.870\n",
+ "\n",
+ "J integrated over the domain: 13.354 at time: 1.880\n",
+ "J_n integrated over the domain: 10.646 at time: 1.880\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.880\n",
+ "d (def. map) integrated over the domain: 182.319 at time: 1.880\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.880\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.880\n",
+ "\n",
+ "J integrated over the domain: 15.976 at time: 1.890\n",
+ "J_n integrated over the domain: 13.354 at time: 1.890\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.890\n",
+ "d (def. map) integrated over the domain: 259.224 at time: 1.890\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.890\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.890\n",
+ "\n",
+ "J integrated over the domain: 18.348 at time: 1.900\n",
+ "J_n integrated over the domain: 15.976 at time: 1.900\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.900\n",
+ "d (def. map) integrated over the domain: 340.652 at time: 1.900\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.900\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.900\n",
+ "\n",
+ "J integrated over the domain: 20.322 at time: 1.910\n",
+ "J_n integrated over the domain: 18.348 at time: 1.910\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.910\n",
+ "d (def. map) integrated over the domain: 416.965 at time: 1.910\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.910\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.910\n",
+ "\n",
+ "J integrated over the domain: 21.772 at time: 1.920\n",
+ "J_n integrated over the domain: 20.322 at time: 1.920\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.920\n",
+ "d (def. map) integrated over the domain: 478.026 at time: 1.920\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.920\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.920\n",
+ "\n",
+ "J integrated over the domain: 22.609 at time: 1.930\n",
+ "J_n integrated over the domain: 21.772 at time: 1.930\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.930\n",
+ "d (def. map) integrated over the domain: 515.153 at time: 1.930\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.930\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.930\n",
+ "\n",
+ "J integrated over the domain: 22.779 at time: 1.940\n",
+ "J_n integrated over the domain: 22.609 at time: 1.940\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.940\n",
+ "d (def. map) integrated over the domain: 522.869 at time: 1.940\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.940\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.940\n",
+ "\n",
+ "J integrated over the domain: 22.271 at time: 1.950\n",
+ "J_n integrated over the domain: 22.779 at time: 1.950\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.950\n",
+ "d (def. map) integrated over the domain: 500.016 at time: 1.950\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.950\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.950\n",
+ "\n",
+ "J integrated over the domain: 21.119 at time: 1.960\n",
+ "J_n integrated over the domain: 22.271 at time: 1.960\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.960\n",
+ "d (def. map) integrated over the domain: 450.001 at time: 1.960\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.960\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.960\n",
+ "\n",
+ "J integrated over the domain: 19.393 at time: 1.970\n",
+ "J_n integrated over the domain: 21.119 at time: 1.970\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.970\n",
+ "d (def. map) integrated over the domain: 380.093 at time: 1.970\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.970\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.970\n",
+ "\n",
+ "J integrated over the domain: 17.203 at time: 1.980\n",
+ "J_n integrated over the domain: 19.393 at time: 1.980\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.980\n",
+ "d (def. map) integrated over the domain: 299.941 at time: 1.980\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.980\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.980\n",
+ "\n",
+ "J integrated over the domain: 14.686 at time: 1.990\n",
+ "J_n integrated over the domain: 17.203 at time: 1.990\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.990\n",
+ "d (def. map) integrated over the domain: 219.674 at time: 1.990\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.990\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.990\n",
+ "\n",
+ "J integrated over the domain: 12.000 at time: 2.000\n",
+ "J_n integrated over the domain: 14.686 at time: 2.000\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 2.000\n",
+ "d (def. map) integrated over the domain: 148.000 at time: 2.000\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 2.000\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 2.000\n",
+ "\n",
+ "Number of degrees of freedom: 14387\n",
+ "Solution Computed in 106.06 seconds\n",
+ "\n",
+ "----------------Computation Completed!----------------\n",
+ "\n",
+ "\n",
+ "----------------Simulations Done!----------------.\n",
+ "\n",
+ "Initializing testing of two deformation cases with input parameters:\n",
+ " Solver to use -solver_to_use- : LU\n",
+ " \n",
+ "\n",
+ "Initializing iNSE problem with Deformation type: High_Osc_exp\n",
+ "\n",
+ "\n",
+ "Setup with initial condition: True\n",
+ "Using a non-zero initial condition (2D-Gaussian) for the velocity field!\n",
+ "Defining forms associated to Chorin-Temam scheme...\n",
+ "Using LU Solver...\n",
+ "Starting iteration over time...\n",
+ "E (Energy) of initial t. velocity: 0.01648 at time 0.000\n",
+ "\n",
+ "J integrated over the domain: 14.686 at time: 0.010\n",
+ "J_n integrated over the domain: 12.000 at time: 0.010\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.010\n",
+ "d (def. map) integrated over the domain: 219.674 at time: 0.010\n",
+ "Strain energy E( eps(|u|^2) ): 0.00005 at time 0.010\n",
+ "Residual of scheme -> 'delta' value: 0.00004 at time 0.010\n",
+ "\n",
+ "J integrated over the domain: 17.203 at time: 0.020\n",
+ "J_n integrated over the domain: 14.686 at time: 0.020\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.020\n",
+ "d (def. map) integrated over the domain: 299.941 at time: 0.020\n",
+ "Strain energy E( eps(|u|^2) ): 0.00007 at time 0.020\n",
+ "Residual of scheme -> 'delta' value: -0.00004 at time 0.020\n",
+ "\n",
+ "J integrated over the domain: 19.393 at time: 0.030\n",
+ "J_n integrated over the domain: 17.203 at time: 0.030\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.030\n",
+ "d (def. map) integrated over the domain: 380.093 at time: 0.030\n",
+ "Strain energy E( eps(|u|^2) ): 0.00006 at time 0.030\n",
+ "Residual of scheme -> 'delta' value: -0.00002 at time 0.030\n",
+ "\n",
+ "J integrated over the domain: 21.119 at time: 0.040\n",
+ "J_n integrated over the domain: 19.393 at time: 0.040\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.040\n",
+ "d (def. map) integrated over the domain: 450.001 at time: 0.040\n",
+ "Strain energy E( eps(|u|^2) ): 0.00006 at time 0.040\n",
+ "Residual of scheme -> 'delta' value: -0.00001 at time 0.040\n",
+ "\n"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "J integrated over the domain: 22.271 at time: 0.050\n",
+ "J_n integrated over the domain: 21.119 at time: 0.050\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.050\n",
+ "d (def. map) integrated over the domain: 500.016 at time: 0.050\n",
+ "Strain energy E( eps(|u|^2) ): 0.00005 at time 0.050\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.050\n",
+ "\n",
+ "J integrated over the domain: 22.779 at time: 0.060\n",
+ "J_n integrated over the domain: 22.271 at time: 0.060\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.060\n",
+ "d (def. map) integrated over the domain: 522.869 at time: 0.060\n",
+ "Strain energy E( eps(|u|^2) ): 0.00005 at time 0.060\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.060\n",
+ "\n",
+ "J integrated over the domain: 22.609 at time: 0.070\n",
+ "J_n integrated over the domain: 22.779 at time: 0.070\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.070\n",
+ "d (def. map) integrated over the domain: 515.153 at time: 0.070\n",
+ "Strain energy E( eps(|u|^2) ): 0.00005 at time 0.070\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.070\n",
+ "\n",
+ "J integrated over the domain: 21.772 at time: 0.080\n",
+ "J_n integrated over the domain: 22.609 at time: 0.080\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.080\n",
+ "d (def. map) integrated over the domain: 478.026 at time: 0.080\n",
+ "Strain energy E( eps(|u|^2) ): 0.00004 at time 0.080\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.080\n",
+ "\n",
+ "J integrated over the domain: 20.322 at time: 0.090\n",
+ "J_n integrated over the domain: 21.772 at time: 0.090\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.090\n",
+ "d (def. map) integrated over the domain: 416.965 at time: 0.090\n",
+ "Strain energy E( eps(|u|^2) ): 0.00004 at time 0.090\n",
+ "Residual of scheme -> 'delta' value: -0.00001 at time 0.090\n",
+ "\n",
+ "J integrated over the domain: 18.348 at time: 0.100\n",
+ "J_n integrated over the domain: 20.322 at time: 0.100\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.100\n",
+ "d (def. map) integrated over the domain: 340.652 at time: 0.100\n",
+ "Strain energy E( eps(|u|^2) ): 0.00004 at time 0.100\n",
+ "Residual of scheme -> 'delta' value: -0.00002 at time 0.100\n",
+ "\n",
+ "J integrated over the domain: 15.976 at time: 0.110\n",
+ "J_n integrated over the domain: 18.348 at time: 0.110\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.110\n",
+ "d (def. map) integrated over the domain: 259.224 at time: 0.110\n",
+ "Strain energy E( eps(|u|^2) ): 0.00004 at time 0.110\n",
+ "Residual of scheme -> 'delta' value: -0.00003 at time 0.110\n",
+ "\n",
+ "J integrated over the domain: 13.354 at time: 0.120\n",
+ "J_n integrated over the domain: 15.976 at time: 0.120\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.120\n",
+ "d (def. map) integrated over the domain: 182.319 at time: 0.120\n",
+ "Strain energy E( eps(|u|^2) ): 0.00006 at time 0.120\n",
+ "Residual of scheme -> 'delta' value: -0.00003 at time 0.120\n",
+ "\n",
+ "J integrated over the domain: 10.646 at time: 0.130\n",
+ "J_n integrated over the domain: 13.354 at time: 0.130\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.130\n",
+ "d (def. map) integrated over the domain: 117.346 at time: 0.130\n",
+ "Strain energy E( eps(|u|^2) ): 0.00014 at time 0.130\n",
+ "Residual of scheme -> 'delta' value: -0.00004 at time 0.130\n",
+ "\n",
+ "J integrated over the domain: 8.024 at time: 0.140\n",
+ "J_n integrated over the domain: 10.646 at time: 0.140\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.140\n",
+ "d (def. map) integrated over the domain: 68.389 at time: 0.140\n",
+ "Strain energy E( eps(|u|^2) ): 0.00023 at time 0.140\n",
+ "Residual of scheme -> 'delta' value: -0.00008 at time 0.140\n",
+ "\n",
+ "J integrated over the domain: 5.652 at time: 0.150\n",
+ "J_n integrated over the domain: 8.024 at time: 0.150\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.150\n",
+ "d (def. map) integrated over the domain: 35.944 at time: 0.150\n",
+ "Strain energy E( eps(|u|^2) ): 0.00021 at time 0.150\n",
+ "Residual of scheme -> 'delta' value: -0.00012 at time 0.150\n",
+ "\n",
+ "J integrated over the domain: 3.678 at time: 0.160\n",
+ "J_n integrated over the domain: 5.652 at time: 0.160\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.160\n",
+ "d (def. map) integrated over the domain: 17.531 at time: 0.160\n",
+ "Strain energy E( eps(|u|^2) ): 0.00011 at time 0.160\n",
+ "Residual of scheme -> 'delta' value: -0.00011 at time 0.160\n",
+ "\n",
+ "J integrated over the domain: 2.228 at time: 0.170\n",
+ "J_n integrated over the domain: 3.678 at time: 0.170\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.170\n",
+ "d (def. map) integrated over the domain: 8.963 at time: 0.170\n",
+ "Strain energy E( eps(|u|^2) ): 0.00003 at time 0.170\n",
+ "Residual of scheme -> 'delta' value: -0.00006 at time 0.170\n",
+ "\n",
+ "J integrated over the domain: 1.391 at time: 0.180\n",
+ "J_n integrated over the domain: 2.228 at time: 0.180\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.180\n",
+ "d (def. map) integrated over the domain: 5.936 at time: 0.180\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.180\n",
+ "Residual of scheme -> 'delta' value: -0.00001 at time 0.180\n",
+ "\n",
+ "J integrated over the domain: 1.221 at time: 0.190\n",
+ "J_n integrated over the domain: 1.391 at time: 0.190\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.190\n",
+ "d (def. map) integrated over the domain: 5.492 at time: 0.190\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.190\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.190\n",
+ "\n",
+ "J integrated over the domain: 1.729 at time: 0.200\n",
+ "J_n integrated over the domain: 1.221 at time: 0.200\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.200\n",
+ "d (def. map) integrated over the domain: 6.988 at time: 0.200\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.200\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.200\n",
+ "\n",
+ "J integrated over the domain: 2.881 at time: 0.210\n",
+ "J_n integrated over the domain: 1.729 at time: 0.210\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.210\n",
+ "d (def. map) integrated over the domain: 12.302 at time: 0.210\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.210\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.210\n",
+ "\n",
+ "J integrated over the domain: 4.607 at time: 0.220\n",
+ "J_n integrated over the domain: 2.881 at time: 0.220\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.220\n",
+ "d (def. map) integrated over the domain: 25.223 at time: 0.220\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.220\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.220\n",
+ "\n",
+ "J integrated over the domain: 6.797 at time: 0.230\n",
+ "J_n integrated over the domain: 4.607 at time: 0.230\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.230\n",
+ "d (def. map) integrated over the domain: 50.200 at time: 0.230\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.230\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.230\n",
+ "\n",
+ "J integrated over the domain: 9.314 at time: 0.240\n",
+ "J_n integrated over the domain: 6.797 at time: 0.240\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.240\n",
+ "d (def. map) integrated over the domain: 90.753 at time: 0.240\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.240\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.240\n",
+ "\n",
+ "J integrated over the domain: 12.000 at time: 0.250\n",
+ "J_n integrated over the domain: 9.314 at time: 0.250\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.250\n",
+ "d (def. map) integrated over the domain: 148.000 at time: 0.250\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.250\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.250\n",
+ "\n",
+ "J integrated over the domain: 14.686 at time: 0.260\n",
+ "J_n integrated over the domain: 12.000 at time: 0.260\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.260\n",
+ "d (def. map) integrated over the domain: 219.674 at time: 0.260\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.260\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.260\n",
+ "\n",
+ "J integrated over the domain: 17.203 at time: 0.270\n",
+ "J_n integrated over the domain: 14.686 at time: 0.270\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.270\n",
+ "d (def. map) integrated over the domain: 299.941 at time: 0.270\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.270\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.270\n",
+ "\n",
+ "J integrated over the domain: 19.393 at time: 0.280\n",
+ "J_n integrated over the domain: 17.203 at time: 0.280\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.280\n",
+ "d (def. map) integrated over the domain: 380.093 at time: 0.280\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.280\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.280\n",
+ "\n"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "J integrated over the domain: 21.119 at time: 0.290\n",
+ "J_n integrated over the domain: 19.393 at time: 0.290\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.290\n",
+ "d (def. map) integrated over the domain: 450.001 at time: 0.290\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.290\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.290\n",
+ "\n",
+ "J integrated over the domain: 22.271 at time: 0.300\n",
+ "J_n integrated over the domain: 21.119 at time: 0.300\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.300\n",
+ "d (def. map) integrated over the domain: 500.016 at time: 0.300\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.300\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.300\n",
+ "\n",
+ "J integrated over the domain: 22.779 at time: 0.310\n",
+ "J_n integrated over the domain: 22.271 at time: 0.310\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.310\n",
+ "d (def. map) integrated over the domain: 522.869 at time: 0.310\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.310\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.310\n",
+ "\n",
+ "J integrated over the domain: 22.609 at time: 0.320\n",
+ "J_n integrated over the domain: 22.779 at time: 0.320\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.320\n",
+ "d (def. map) integrated over the domain: 515.153 at time: 0.320\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.320\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.320\n",
+ "\n",
+ "J integrated over the domain: 21.772 at time: 0.330\n",
+ "J_n integrated over the domain: 22.609 at time: 0.330\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.330\n",
+ "d (def. map) integrated over the domain: 478.026 at time: 0.330\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.330\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.330\n",
+ "\n",
+ "J integrated over the domain: 20.322 at time: 0.340\n",
+ "J_n integrated over the domain: 21.772 at time: 0.340\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.340\n",
+ "d (def. map) integrated over the domain: 416.965 at time: 0.340\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.340\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.340\n",
+ "\n",
+ "J integrated over the domain: 18.348 at time: 0.350\n",
+ "J_n integrated over the domain: 20.322 at time: 0.350\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.350\n",
+ "d (def. map) integrated over the domain: 340.652 at time: 0.350\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.350\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.350\n",
+ "\n",
+ "J integrated over the domain: 15.976 at time: 0.360\n",
+ "J_n integrated over the domain: 18.348 at time: 0.360\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.360\n",
+ "d (def. map) integrated over the domain: 259.224 at time: 0.360\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.360\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.360\n",
+ "\n",
+ "J integrated over the domain: 13.354 at time: 0.370\n",
+ "J_n integrated over the domain: 15.976 at time: 0.370\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.370\n",
+ "d (def. map) integrated over the domain: 182.319 at time: 0.370\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.370\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.370\n",
+ "\n",
+ "J integrated over the domain: 10.646 at time: 0.380\n",
+ "J_n integrated over the domain: 13.354 at time: 0.380\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.380\n",
+ "d (def. map) integrated over the domain: 117.346 at time: 0.380\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.380\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.380\n",
+ "\n",
+ "J integrated over the domain: 8.024 at time: 0.390\n",
+ "J_n integrated over the domain: 10.646 at time: 0.390\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.390\n",
+ "d (def. map) integrated over the domain: 68.389 at time: 0.390\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.390\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.390\n",
+ "\n",
+ "J integrated over the domain: 5.652 at time: 0.400\n",
+ "J_n integrated over the domain: 8.024 at time: 0.400\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.400\n",
+ "d (def. map) integrated over the domain: 35.944 at time: 0.400\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.400\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.400\n",
+ "\n",
+ "J integrated over the domain: 3.678 at time: 0.410\n",
+ "J_n integrated over the domain: 5.652 at time: 0.410\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.410\n",
+ "d (def. map) integrated over the domain: 17.531 at time: 0.410\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.410\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.410\n",
+ "\n",
+ "J integrated over the domain: 2.228 at time: 0.420\n",
+ "J_n integrated over the domain: 3.678 at time: 0.420\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.420\n",
+ "d (def. map) integrated over the domain: 8.963 at time: 0.420\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.420\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.420\n",
+ "\n",
+ "J integrated over the domain: 1.391 at time: 0.430\n",
+ "J_n integrated over the domain: 2.228 at time: 0.430\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.430\n",
+ "d (def. map) integrated over the domain: 5.936 at time: 0.430\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.430\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.430\n",
+ "\n",
+ "J integrated over the domain: 1.221 at time: 0.440\n",
+ "J_n integrated over the domain: 1.391 at time: 0.440\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.440\n",
+ "d (def. map) integrated over the domain: 5.492 at time: 0.440\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.440\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.440\n",
+ "\n",
+ "J integrated over the domain: 1.729 at time: 0.450\n",
+ "J_n integrated over the domain: 1.221 at time: 0.450\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.450\n",
+ "d (def. map) integrated over the domain: 6.988 at time: 0.450\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.450\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.450\n",
+ "\n",
+ "J integrated over the domain: 2.881 at time: 0.460\n",
+ "J_n integrated over the domain: 1.729 at time: 0.460\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.460\n",
+ "d (def. map) integrated over the domain: 12.302 at time: 0.460\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.460\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.460\n",
+ "\n",
+ "J integrated over the domain: 4.607 at time: 0.470\n",
+ "J_n integrated over the domain: 2.881 at time: 0.470\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.470\n",
+ "d (def. map) integrated over the domain: 25.223 at time: 0.470\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.470\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.470\n",
+ "\n",
+ "J integrated over the domain: 6.797 at time: 0.480\n",
+ "J_n integrated over the domain: 4.607 at time: 0.480\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.480\n",
+ "d (def. map) integrated over the domain: 50.200 at time: 0.480\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.480\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.480\n",
+ "\n",
+ "J integrated over the domain: 9.314 at time: 0.490\n",
+ "J_n integrated over the domain: 6.797 at time: 0.490\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.490\n",
+ "d (def. map) integrated over the domain: 90.753 at time: 0.490\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.490\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.490\n",
+ "\n",
+ "J integrated over the domain: 12.000 at time: 0.500\n",
+ "J_n integrated over the domain: 9.314 at time: 0.500\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.500\n",
+ "d (def. map) integrated over the domain: 148.000 at time: 0.500\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.500\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.500\n",
+ "\n",
+ "J integrated over the domain: 14.686 at time: 0.510\n",
+ "J_n integrated over the domain: 12.000 at time: 0.510\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.510\n",
+ "d (def. map) integrated over the domain: 219.674 at time: 0.510\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.510\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.510\n",
+ "\n",
+ "J integrated over the domain: 17.203 at time: 0.520\n",
+ "J_n integrated over the domain: 14.686 at time: 0.520\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.520\n",
+ "d (def. map) integrated over the domain: 299.941 at time: 0.520\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.520\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.520\n",
+ "\n"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "J integrated over the domain: 19.393 at time: 0.530\n",
+ "J_n integrated over the domain: 17.203 at time: 0.530\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.530\n",
+ "d (def. map) integrated over the domain: 380.093 at time: 0.530\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.530\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.530\n",
+ "\n",
+ "J integrated over the domain: 21.119 at time: 0.540\n",
+ "J_n integrated over the domain: 19.393 at time: 0.540\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.540\n",
+ "d (def. map) integrated over the domain: 450.001 at time: 0.540\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.540\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.540\n",
+ "\n",
+ "J integrated over the domain: 22.271 at time: 0.550\n",
+ "J_n integrated over the domain: 21.119 at time: 0.550\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.550\n",
+ "d (def. map) integrated over the domain: 500.016 at time: 0.550\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.550\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.550\n",
+ "\n",
+ "J integrated over the domain: 22.779 at time: 0.560\n",
+ "J_n integrated over the domain: 22.271 at time: 0.560\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.560\n",
+ "d (def. map) integrated over the domain: 522.869 at time: 0.560\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.560\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.560\n",
+ "\n",
+ "J integrated over the domain: 22.609 at time: 0.570\n",
+ "J_n integrated over the domain: 22.779 at time: 0.570\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.570\n",
+ "d (def. map) integrated over the domain: 515.153 at time: 0.570\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.570\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.570\n",
+ "\n",
+ "J integrated over the domain: 21.772 at time: 0.580\n",
+ "J_n integrated over the domain: 22.609 at time: 0.580\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.580\n",
+ "d (def. map) integrated over the domain: 478.026 at time: 0.580\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.580\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.580\n",
+ "\n",
+ "J integrated over the domain: 20.322 at time: 0.590\n",
+ "J_n integrated over the domain: 21.772 at time: 0.590\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.590\n",
+ "d (def. map) integrated over the domain: 416.965 at time: 0.590\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.590\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.590\n",
+ "\n",
+ "J integrated over the domain: 18.348 at time: 0.600\n",
+ "J_n integrated over the domain: 20.322 at time: 0.600\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.600\n",
+ "d (def. map) integrated over the domain: 340.652 at time: 0.600\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.600\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.600\n",
+ "\n",
+ "J integrated over the domain: 15.976 at time: 0.610\n",
+ "J_n integrated over the domain: 18.348 at time: 0.610\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.610\n",
+ "d (def. map) integrated over the domain: 259.224 at time: 0.610\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.610\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.610\n",
+ "\n",
+ "J integrated over the domain: 13.354 at time: 0.620\n",
+ "J_n integrated over the domain: 15.976 at time: 0.620\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.620\n",
+ "d (def. map) integrated over the domain: 182.319 at time: 0.620\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.620\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.620\n",
+ "\n",
+ "J integrated over the domain: 10.646 at time: 0.630\n",
+ "J_n integrated over the domain: 13.354 at time: 0.630\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.630\n",
+ "d (def. map) integrated over the domain: 117.346 at time: 0.630\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.630\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.630\n",
+ "\n",
+ "J integrated over the domain: 8.024 at time: 0.640\n",
+ "J_n integrated over the domain: 10.646 at time: 0.640\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.640\n",
+ "d (def. map) integrated over the domain: 68.389 at time: 0.640\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.640\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.640\n",
+ "\n",
+ "J integrated over the domain: 5.652 at time: 0.650\n",
+ "J_n integrated over the domain: 8.024 at time: 0.650\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.650\n",
+ "d (def. map) integrated over the domain: 35.944 at time: 0.650\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.650\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.650\n",
+ "\n",
+ "J integrated over the domain: 3.678 at time: 0.660\n",
+ "J_n integrated over the domain: 5.652 at time: 0.660\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.660\n",
+ "d (def. map) integrated over the domain: 17.531 at time: 0.660\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.660\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.660\n",
+ "\n",
+ "J integrated over the domain: 2.228 at time: 0.670\n",
+ "J_n integrated over the domain: 3.678 at time: 0.670\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.670\n",
+ "d (def. map) integrated over the domain: 8.963 at time: 0.670\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.670\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.670\n",
+ "\n",
+ "J integrated over the domain: 1.391 at time: 0.680\n",
+ "J_n integrated over the domain: 2.228 at time: 0.680\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.680\n",
+ "d (def. map) integrated over the domain: 5.936 at time: 0.680\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.680\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.680\n",
+ "\n",
+ "J integrated over the domain: 1.221 at time: 0.690\n",
+ "J_n integrated over the domain: 1.391 at time: 0.690\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.690\n",
+ "d (def. map) integrated over the domain: 5.492 at time: 0.690\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.690\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.690\n",
+ "\n",
+ "J integrated over the domain: 1.729 at time: 0.700\n",
+ "J_n integrated over the domain: 1.221 at time: 0.700\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.700\n",
+ "d (def. map) integrated over the domain: 6.988 at time: 0.700\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.700\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.700\n",
+ "\n",
+ "J integrated over the domain: 2.881 at time: 0.710\n",
+ "J_n integrated over the domain: 1.729 at time: 0.710\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.710\n",
+ "d (def. map) integrated over the domain: 12.302 at time: 0.710\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.710\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.710\n",
+ "\n",
+ "J integrated over the domain: 4.607 at time: 0.720\n",
+ "J_n integrated over the domain: 2.881 at time: 0.720\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.720\n",
+ "d (def. map) integrated over the domain: 25.223 at time: 0.720\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.720\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.720\n",
+ "\n",
+ "J integrated over the domain: 6.797 at time: 0.730\n",
+ "J_n integrated over the domain: 4.607 at time: 0.730\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.730\n",
+ "d (def. map) integrated over the domain: 50.200 at time: 0.730\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.730\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.730\n",
+ "\n",
+ "J integrated over the domain: 9.314 at time: 0.740\n",
+ "J_n integrated over the domain: 6.797 at time: 0.740\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.740\n",
+ "d (def. map) integrated over the domain: 90.753 at time: 0.740\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.740\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.740\n",
+ "\n",
+ "J integrated over the domain: 12.000 at time: 0.750\n",
+ "J_n integrated over the domain: 9.314 at time: 0.750\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.750\n",
+ "d (def. map) integrated over the domain: 148.000 at time: 0.750\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.750\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.750\n",
+ "\n",
+ "J integrated over the domain: 14.686 at time: 0.760\n",
+ "J_n integrated over the domain: 12.000 at time: 0.760\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.760\n",
+ "d (def. map) integrated over the domain: 219.674 at time: 0.760\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.760\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.760\n",
+ "\n",
+ "J integrated over the domain: 17.203 at time: 0.770\n",
+ "J_n integrated over the domain: 14.686 at time: 0.770\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.770\n",
+ "d (def. map) integrated over the domain: 299.941 at time: 0.770\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.770\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.770\n",
+ "\n"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "J integrated over the domain: 19.393 at time: 0.780\n",
+ "J_n integrated over the domain: 17.203 at time: 0.780\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.780\n",
+ "d (def. map) integrated over the domain: 380.093 at time: 0.780\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.780\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.780\n",
+ "\n",
+ "J integrated over the domain: 21.119 at time: 0.790\n",
+ "J_n integrated over the domain: 19.393 at time: 0.790\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.790\n",
+ "d (def. map) integrated over the domain: 450.001 at time: 0.790\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.790\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.790\n",
+ "\n",
+ "J integrated over the domain: 22.271 at time: 0.800\n",
+ "J_n integrated over the domain: 21.119 at time: 0.800\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.800\n",
+ "d (def. map) integrated over the domain: 500.016 at time: 0.800\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.800\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.800\n",
+ "\n",
+ "J integrated over the domain: 22.779 at time: 0.810\n",
+ "J_n integrated over the domain: 22.271 at time: 0.810\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.810\n",
+ "d (def. map) integrated over the domain: 522.869 at time: 0.810\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.810\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.810\n",
+ "\n",
+ "J integrated over the domain: 22.609 at time: 0.820\n",
+ "J_n integrated over the domain: 22.779 at time: 0.820\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.820\n",
+ "d (def. map) integrated over the domain: 515.153 at time: 0.820\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.820\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.820\n",
+ "\n",
+ "J integrated over the domain: 21.772 at time: 0.830\n",
+ "J_n integrated over the domain: 22.609 at time: 0.830\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.830\n",
+ "d (def. map) integrated over the domain: 478.026 at time: 0.830\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.830\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.830\n",
+ "\n",
+ "J integrated over the domain: 20.322 at time: 0.840\n",
+ "J_n integrated over the domain: 21.772 at time: 0.840\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.840\n",
+ "d (def. map) integrated over the domain: 416.965 at time: 0.840\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.840\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.840\n",
+ "\n",
+ "J integrated over the domain: 18.348 at time: 0.850\n",
+ "J_n integrated over the domain: 20.322 at time: 0.850\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.850\n",
+ "d (def. map) integrated over the domain: 340.652 at time: 0.850\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.850\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.850\n",
+ "\n",
+ "J integrated over the domain: 15.976 at time: 0.860\n",
+ "J_n integrated over the domain: 18.348 at time: 0.860\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.860\n",
+ "d (def. map) integrated over the domain: 259.224 at time: 0.860\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.860\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.860\n",
+ "\n",
+ "J integrated over the domain: 13.354 at time: 0.870\n",
+ "J_n integrated over the domain: 15.976 at time: 0.870\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.870\n",
+ "d (def. map) integrated over the domain: 182.319 at time: 0.870\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.870\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.870\n",
+ "\n",
+ "J integrated over the domain: 10.646 at time: 0.880\n",
+ "J_n integrated over the domain: 13.354 at time: 0.880\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.880\n",
+ "d (def. map) integrated over the domain: 117.346 at time: 0.880\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.880\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.880\n",
+ "\n",
+ "J integrated over the domain: 8.024 at time: 0.890\n",
+ "J_n integrated over the domain: 10.646 at time: 0.890\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.890\n",
+ "d (def. map) integrated over the domain: 68.389 at time: 0.890\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.890\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.890\n",
+ "\n",
+ "J integrated over the domain: 5.652 at time: 0.900\n",
+ "J_n integrated over the domain: 8.024 at time: 0.900\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.900\n",
+ "d (def. map) integrated over the domain: 35.944 at time: 0.900\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.900\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.900\n",
+ "\n",
+ "J integrated over the domain: 3.678 at time: 0.910\n",
+ "J_n integrated over the domain: 5.652 at time: 0.910\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.910\n",
+ "d (def. map) integrated over the domain: 17.531 at time: 0.910\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.910\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.910\n",
+ "\n",
+ "J integrated over the domain: 2.228 at time: 0.920\n",
+ "J_n integrated over the domain: 3.678 at time: 0.920\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.920\n",
+ "d (def. map) integrated over the domain: 8.963 at time: 0.920\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.920\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.920\n",
+ "\n",
+ "J integrated over the domain: 1.391 at time: 0.930\n",
+ "J_n integrated over the domain: 2.228 at time: 0.930\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.930\n",
+ "d (def. map) integrated over the domain: 5.936 at time: 0.930\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.930\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.930\n",
+ "\n",
+ "J integrated over the domain: 1.221 at time: 0.940\n",
+ "J_n integrated over the domain: 1.391 at time: 0.940\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.940\n",
+ "d (def. map) integrated over the domain: 5.492 at time: 0.940\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.940\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.940\n",
+ "\n",
+ "J integrated over the domain: 1.729 at time: 0.950\n",
+ "J_n integrated over the domain: 1.221 at time: 0.950\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.950\n",
+ "d (def. map) integrated over the domain: 6.988 at time: 0.950\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.950\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.950\n",
+ "\n",
+ "J integrated over the domain: 2.881 at time: 0.960\n",
+ "J_n integrated over the domain: 1.729 at time: 0.960\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.960\n",
+ "d (def. map) integrated over the domain: 12.302 at time: 0.960\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.960\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.960\n",
+ "\n",
+ "J integrated over the domain: 4.607 at time: 0.970\n",
+ "J_n integrated over the domain: 2.881 at time: 0.970\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.970\n",
+ "d (def. map) integrated over the domain: 25.223 at time: 0.970\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.970\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.970\n",
+ "\n",
+ "J integrated over the domain: 6.797 at time: 0.980\n",
+ "J_n integrated over the domain: 4.607 at time: 0.980\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.980\n",
+ "d (def. map) integrated over the domain: 50.200 at time: 0.980\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.980\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.980\n",
+ "\n",
+ "J integrated over the domain: 9.314 at time: 0.990\n",
+ "J_n integrated over the domain: 6.797 at time: 0.990\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.990\n",
+ "d (def. map) integrated over the domain: 90.753 at time: 0.990\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.990\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.990\n",
+ "\n",
+ "J integrated over the domain: 12.000 at time: 1.000\n",
+ "J_n integrated over the domain: 9.314 at time: 1.000\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.000\n",
+ "d (def. map) integrated over the domain: 148.000 at time: 1.000\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.000\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.000\n",
+ "\n",
+ "J integrated over the domain: 14.686 at time: 1.010\n",
+ "J_n integrated over the domain: 12.000 at time: 1.010\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.010\n",
+ "d (def. map) integrated over the domain: 219.674 at time: 1.010\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.010\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.010\n",
+ "\n",
+ "J integrated over the domain: 17.203 at time: 1.020\n",
+ "J_n integrated over the domain: 14.686 at time: 1.020\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.020\n",
+ "d (def. map) integrated over the domain: 299.941 at time: 1.020\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.020\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.020\n",
+ "\n",
+ "J integrated over the domain: 19.393 at time: 1.030\n",
+ "J_n integrated over the domain: 17.203 at time: 1.030\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.030\n",
+ "d (def. map) integrated over the domain: 380.093 at time: 1.030\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.030\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.030\n",
+ "\n"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "J integrated over the domain: 21.119 at time: 1.040\n",
+ "J_n integrated over the domain: 19.393 at time: 1.040\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.040\n",
+ "d (def. map) integrated over the domain: 450.001 at time: 1.040\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.040\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.040\n",
+ "\n",
+ "J integrated over the domain: 22.271 at time: 1.050\n",
+ "J_n integrated over the domain: 21.119 at time: 1.050\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.050\n",
+ "d (def. map) integrated over the domain: 500.016 at time: 1.050\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.050\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.050\n",
+ "\n",
+ "J integrated over the domain: 22.779 at time: 1.060\n",
+ "J_n integrated over the domain: 22.271 at time: 1.060\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.060\n",
+ "d (def. map) integrated over the domain: 522.869 at time: 1.060\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.060\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.060\n",
+ "\n",
+ "J integrated over the domain: 22.609 at time: 1.070\n",
+ "J_n integrated over the domain: 22.779 at time: 1.070\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.070\n",
+ "d (def. map) integrated over the domain: 515.153 at time: 1.070\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.070\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.070\n",
+ "\n",
+ "J integrated over the domain: 21.772 at time: 1.080\n",
+ "J_n integrated over the domain: 22.609 at time: 1.080\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.080\n",
+ "d (def. map) integrated over the domain: 478.026 at time: 1.080\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.080\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.080\n",
+ "\n",
+ "J integrated over the domain: 20.322 at time: 1.090\n",
+ "J_n integrated over the domain: 21.772 at time: 1.090\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.090\n",
+ "d (def. map) integrated over the domain: 416.965 at time: 1.090\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.090\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.090\n",
+ "\n",
+ "J integrated over the domain: 18.348 at time: 1.100\n",
+ "J_n integrated over the domain: 20.322 at time: 1.100\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.100\n",
+ "d (def. map) integrated over the domain: 340.652 at time: 1.100\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.100\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.100\n",
+ "\n",
+ "J integrated over the domain: 15.976 at time: 1.110\n",
+ "J_n integrated over the domain: 18.348 at time: 1.110\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.110\n",
+ "d (def. map) integrated over the domain: 259.224 at time: 1.110\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.110\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.110\n",
+ "\n",
+ "J integrated over the domain: 13.354 at time: 1.120\n",
+ "J_n integrated over the domain: 15.976 at time: 1.120\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.120\n",
+ "d (def. map) integrated over the domain: 182.319 at time: 1.120\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.120\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.120\n",
+ "\n",
+ "J integrated over the domain: 10.646 at time: 1.130\n",
+ "J_n integrated over the domain: 13.354 at time: 1.130\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.130\n",
+ "d (def. map) integrated over the domain: 117.346 at time: 1.130\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.130\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.130\n",
+ "\n",
+ "J integrated over the domain: 8.024 at time: 1.140\n",
+ "J_n integrated over the domain: 10.646 at time: 1.140\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.140\n",
+ "d (def. map) integrated over the domain: 68.389 at time: 1.140\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.140\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.140\n",
+ "\n",
+ "J integrated over the domain: 5.652 at time: 1.150\n",
+ "J_n integrated over the domain: 8.024 at time: 1.150\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.150\n",
+ "d (def. map) integrated over the domain: 35.944 at time: 1.150\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.150\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.150\n",
+ "\n",
+ "J integrated over the domain: 3.678 at time: 1.160\n",
+ "J_n integrated over the domain: 5.652 at time: 1.160\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.160\n",
+ "d (def. map) integrated over the domain: 17.531 at time: 1.160\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.160\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.160\n",
+ "\n",
+ "J integrated over the domain: 2.228 at time: 1.170\n",
+ "J_n integrated over the domain: 3.678 at time: 1.170\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.170\n",
+ "d (def. map) integrated over the domain: 8.963 at time: 1.170\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.170\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.170\n",
+ "\n",
+ "J integrated over the domain: 1.391 at time: 1.180\n",
+ "J_n integrated over the domain: 2.228 at time: 1.180\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.180\n",
+ "d (def. map) integrated over the domain: 5.936 at time: 1.180\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.180\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.180\n",
+ "\n",
+ "J integrated over the domain: 1.221 at time: 1.190\n",
+ "J_n integrated over the domain: 1.391 at time: 1.190\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.190\n",
+ "d (def. map) integrated over the domain: 5.492 at time: 1.190\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.190\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.190\n",
+ "\n",
+ "J integrated over the domain: 1.729 at time: 1.200\n",
+ "J_n integrated over the domain: 1.221 at time: 1.200\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.200\n",
+ "d (def. map) integrated over the domain: 6.988 at time: 1.200\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.200\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.200\n",
+ "\n",
+ "J integrated over the domain: 2.881 at time: 1.210\n",
+ "J_n integrated over the domain: 1.729 at time: 1.210\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.210\n",
+ "d (def. map) integrated over the domain: 12.302 at time: 1.210\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.210\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.210\n",
+ "\n",
+ "J integrated over the domain: 4.607 at time: 1.220\n",
+ "J_n integrated over the domain: 2.881 at time: 1.220\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.220\n",
+ "d (def. map) integrated over the domain: 25.223 at time: 1.220\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.220\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.220\n",
+ "\n",
+ "J integrated over the domain: 6.797 at time: 1.230\n",
+ "J_n integrated over the domain: 4.607 at time: 1.230\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.230\n",
+ "d (def. map) integrated over the domain: 50.200 at time: 1.230\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.230\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.230\n",
+ "\n",
+ "J integrated over the domain: 9.314 at time: 1.240\n",
+ "J_n integrated over the domain: 6.797 at time: 1.240\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.240\n",
+ "d (def. map) integrated over the domain: 90.753 at time: 1.240\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.240\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.240\n",
+ "\n",
+ "J integrated over the domain: 12.000 at time: 1.250\n",
+ "J_n integrated over the domain: 9.314 at time: 1.250\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.250\n",
+ "d (def. map) integrated over the domain: 148.000 at time: 1.250\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.250\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.250\n",
+ "\n",
+ "J integrated over the domain: 14.686 at time: 1.260\n",
+ "J_n integrated over the domain: 12.000 at time: 1.260\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.260\n",
+ "d (def. map) integrated over the domain: 219.674 at time: 1.260\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.260\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.260\n",
+ "\n",
+ "J integrated over the domain: 17.203 at time: 1.270\n",
+ "J_n integrated over the domain: 14.686 at time: 1.270\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.270\n",
+ "d (def. map) integrated over the domain: 299.941 at time: 1.270\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.270\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.270\n",
+ "\n"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "J integrated over the domain: 19.393 at time: 1.280\n",
+ "J_n integrated over the domain: 17.203 at time: 1.280\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.280\n",
+ "d (def. map) integrated over the domain: 380.093 at time: 1.280\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.280\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.280\n",
+ "\n",
+ "J integrated over the domain: 21.119 at time: 1.290\n",
+ "J_n integrated over the domain: 19.393 at time: 1.290\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.290\n",
+ "d (def. map) integrated over the domain: 450.001 at time: 1.290\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.290\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.290\n",
+ "\n",
+ "J integrated over the domain: 22.271 at time: 1.300\n",
+ "J_n integrated over the domain: 21.119 at time: 1.300\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.300\n",
+ "d (def. map) integrated over the domain: 500.016 at time: 1.300\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.300\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.300\n",
+ "\n",
+ "J integrated over the domain: 22.779 at time: 1.310\n",
+ "J_n integrated over the domain: 22.271 at time: 1.310\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.310\n",
+ "d (def. map) integrated over the domain: 522.869 at time: 1.310\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.310\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.310\n",
+ "\n",
+ "J integrated over the domain: 22.609 at time: 1.320\n",
+ "J_n integrated over the domain: 22.779 at time: 1.320\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.320\n",
+ "d (def. map) integrated over the domain: 515.153 at time: 1.320\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.320\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.320\n",
+ "\n",
+ "J integrated over the domain: 21.772 at time: 1.330\n",
+ "J_n integrated over the domain: 22.609 at time: 1.330\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.330\n",
+ "d (def. map) integrated over the domain: 478.026 at time: 1.330\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.330\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.330\n",
+ "\n",
+ "J integrated over the domain: 20.322 at time: 1.340\n",
+ "J_n integrated over the domain: 21.772 at time: 1.340\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.340\n",
+ "d (def. map) integrated over the domain: 416.965 at time: 1.340\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.340\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.340\n",
+ "\n",
+ "J integrated over the domain: 18.348 at time: 1.350\n",
+ "J_n integrated over the domain: 20.322 at time: 1.350\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.350\n",
+ "d (def. map) integrated over the domain: 340.652 at time: 1.350\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.350\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.350\n",
+ "\n",
+ "J integrated over the domain: 15.976 at time: 1.360\n",
+ "J_n integrated over the domain: 18.348 at time: 1.360\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.360\n",
+ "d (def. map) integrated over the domain: 259.224 at time: 1.360\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.360\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.360\n",
+ "\n",
+ "J integrated over the domain: 13.354 at time: 1.370\n",
+ "J_n integrated over the domain: 15.976 at time: 1.370\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.370\n",
+ "d (def. map) integrated over the domain: 182.319 at time: 1.370\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.370\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.370\n",
+ "\n",
+ "J integrated over the domain: 10.646 at time: 1.380\n",
+ "J_n integrated over the domain: 13.354 at time: 1.380\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.380\n",
+ "d (def. map) integrated over the domain: 117.346 at time: 1.380\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.380\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.380\n",
+ "\n",
+ "J integrated over the domain: 8.024 at time: 1.390\n",
+ "J_n integrated over the domain: 10.646 at time: 1.390\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.390\n",
+ "d (def. map) integrated over the domain: 68.389 at time: 1.390\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.390\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.390\n",
+ "\n",
+ "J integrated over the domain: 5.652 at time: 1.400\n",
+ "J_n integrated over the domain: 8.024 at time: 1.400\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.400\n",
+ "d (def. map) integrated over the domain: 35.944 at time: 1.400\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.400\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.400\n",
+ "\n",
+ "J integrated over the domain: 3.678 at time: 1.410\n",
+ "J_n integrated over the domain: 5.652 at time: 1.410\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.410\n",
+ "d (def. map) integrated over the domain: 17.531 at time: 1.410\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.410\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.410\n",
+ "\n",
+ "J integrated over the domain: 2.228 at time: 1.420\n",
+ "J_n integrated over the domain: 3.678 at time: 1.420\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.420\n",
+ "d (def. map) integrated over the domain: 8.963 at time: 1.420\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.420\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.420\n",
+ "\n",
+ "J integrated over the domain: 1.391 at time: 1.430\n",
+ "J_n integrated over the domain: 2.228 at time: 1.430\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.430\n",
+ "d (def. map) integrated over the domain: 5.936 at time: 1.430\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.430\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.430\n",
+ "\n",
+ "J integrated over the domain: 1.221 at time: 1.440\n",
+ "J_n integrated over the domain: 1.391 at time: 1.440\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.440\n",
+ "d (def. map) integrated over the domain: 5.492 at time: 1.440\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.440\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.440\n",
+ "\n",
+ "J integrated over the domain: 1.729 at time: 1.450\n",
+ "J_n integrated over the domain: 1.221 at time: 1.450\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.450\n",
+ "d (def. map) integrated over the domain: 6.988 at time: 1.450\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.450\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.450\n",
+ "\n",
+ "J integrated over the domain: 2.881 at time: 1.460\n",
+ "J_n integrated over the domain: 1.729 at time: 1.460\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.460\n",
+ "d (def. map) integrated over the domain: 12.302 at time: 1.460\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.460\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.460\n",
+ "\n",
+ "J integrated over the domain: 4.607 at time: 1.470\n",
+ "J_n integrated over the domain: 2.881 at time: 1.470\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.470\n",
+ "d (def. map) integrated over the domain: 25.223 at time: 1.470\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.470\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.470\n",
+ "\n",
+ "J integrated over the domain: 6.797 at time: 1.480\n",
+ "J_n integrated over the domain: 4.607 at time: 1.480\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.480\n",
+ "d (def. map) integrated over the domain: 50.200 at time: 1.480\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.480\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.480\n",
+ "\n",
+ "J integrated over the domain: 9.314 at time: 1.490\n",
+ "J_n integrated over the domain: 6.797 at time: 1.490\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.490\n",
+ "d (def. map) integrated over the domain: 90.753 at time: 1.490\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.490\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.490\n",
+ "\n",
+ "J integrated over the domain: 12.000 at time: 1.500\n",
+ "J_n integrated over the domain: 9.314 at time: 1.500\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.500\n",
+ "d (def. map) integrated over the domain: 148.000 at time: 1.500\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.500\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.500\n",
+ "\n",
+ "J integrated over the domain: 14.686 at time: 1.510\n",
+ "J_n integrated over the domain: 12.000 at time: 1.510\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.510\n",
+ "d (def. map) integrated over the domain: 219.674 at time: 1.510\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.510\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.510\n",
+ "\n",
+ "J integrated over the domain: 17.203 at time: 1.520\n",
+ "J_n integrated over the domain: 14.686 at time: 1.520\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.520\n",
+ "d (def. map) integrated over the domain: 299.941 at time: 1.520\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.520\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.520\n",
+ "\n"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "J integrated over the domain: 19.393 at time: 1.530\n",
+ "J_n integrated over the domain: 17.203 at time: 1.530\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.530\n",
+ "d (def. map) integrated over the domain: 380.093 at time: 1.530\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.530\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.530\n",
+ "\n",
+ "J integrated over the domain: 21.119 at time: 1.540\n",
+ "J_n integrated over the domain: 19.393 at time: 1.540\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.540\n",
+ "d (def. map) integrated over the domain: 450.001 at time: 1.540\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.540\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.540\n",
+ "\n",
+ "J integrated over the domain: 22.271 at time: 1.550\n",
+ "J_n integrated over the domain: 21.119 at time: 1.550\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.550\n",
+ "d (def. map) integrated over the domain: 500.016 at time: 1.550\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.550\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.550\n",
+ "\n",
+ "J integrated over the domain: 22.779 at time: 1.560\n",
+ "J_n integrated over the domain: 22.271 at time: 1.560\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.560\n",
+ "d (def. map) integrated over the domain: 522.869 at time: 1.560\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.560\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.560\n",
+ "\n",
+ "J integrated over the domain: 22.609 at time: 1.570\n",
+ "J_n integrated over the domain: 22.779 at time: 1.570\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.570\n",
+ "d (def. map) integrated over the domain: 515.153 at time: 1.570\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.570\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.570\n",
+ "\n",
+ "J integrated over the domain: 21.772 at time: 1.580\n",
+ "J_n integrated over the domain: 22.609 at time: 1.580\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.580\n",
+ "d (def. map) integrated over the domain: 478.026 at time: 1.580\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.580\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.580\n",
+ "\n",
+ "J integrated over the domain: 20.322 at time: 1.590\n",
+ "J_n integrated over the domain: 21.772 at time: 1.590\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.590\n",
+ "d (def. map) integrated over the domain: 416.965 at time: 1.590\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.590\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.590\n",
+ "\n",
+ "J integrated over the domain: 18.348 at time: 1.600\n",
+ "J_n integrated over the domain: 20.322 at time: 1.600\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.600\n",
+ "d (def. map) integrated over the domain: 340.652 at time: 1.600\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.600\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.600\n",
+ "\n",
+ "J integrated over the domain: 15.976 at time: 1.610\n",
+ "J_n integrated over the domain: 18.348 at time: 1.610\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.610\n",
+ "d (def. map) integrated over the domain: 259.224 at time: 1.610\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.610\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.610\n",
+ "\n",
+ "J integrated over the domain: 13.354 at time: 1.620\n",
+ "J_n integrated over the domain: 15.976 at time: 1.620\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.620\n",
+ "d (def. map) integrated over the domain: 182.319 at time: 1.620\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.620\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.620\n",
+ "\n",
+ "J integrated over the domain: 10.646 at time: 1.630\n",
+ "J_n integrated over the domain: 13.354 at time: 1.630\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.630\n",
+ "d (def. map) integrated over the domain: 117.346 at time: 1.630\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.630\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.630\n",
+ "\n",
+ "J integrated over the domain: 8.024 at time: 1.640\n",
+ "J_n integrated over the domain: 10.646 at time: 1.640\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.640\n",
+ "d (def. map) integrated over the domain: 68.389 at time: 1.640\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.640\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.640\n",
+ "\n",
+ "J integrated over the domain: 5.652 at time: 1.650\n",
+ "J_n integrated over the domain: 8.024 at time: 1.650\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.650\n",
+ "d (def. map) integrated over the domain: 35.944 at time: 1.650\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.650\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.650\n",
+ "\n",
+ "J integrated over the domain: 3.678 at time: 1.660\n",
+ "J_n integrated over the domain: 5.652 at time: 1.660\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.660\n",
+ "d (def. map) integrated over the domain: 17.531 at time: 1.660\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.660\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.660\n",
+ "\n",
+ "J integrated over the domain: 2.228 at time: 1.670\n",
+ "J_n integrated over the domain: 3.678 at time: 1.670\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.670\n",
+ "d (def. map) integrated over the domain: 8.963 at time: 1.670\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.670\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.670\n",
+ "\n",
+ "J integrated over the domain: 1.391 at time: 1.680\n",
+ "J_n integrated over the domain: 2.228 at time: 1.680\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.680\n",
+ "d (def. map) integrated over the domain: 5.936 at time: 1.680\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.680\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.680\n",
+ "\n",
+ "J integrated over the domain: 1.221 at time: 1.690\n",
+ "J_n integrated over the domain: 1.391 at time: 1.690\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.690\n",
+ "d (def. map) integrated over the domain: 5.492 at time: 1.690\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.690\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.690\n",
+ "\n",
+ "J integrated over the domain: 1.729 at time: 1.700\n",
+ "J_n integrated over the domain: 1.221 at time: 1.700\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.700\n",
+ "d (def. map) integrated over the domain: 6.988 at time: 1.700\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.700\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.700\n",
+ "\n",
+ "J integrated over the domain: 2.881 at time: 1.710\n",
+ "J_n integrated over the domain: 1.729 at time: 1.710\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.710\n",
+ "d (def. map) integrated over the domain: 12.302 at time: 1.710\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.710\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.710\n",
+ "\n",
+ "J integrated over the domain: 4.607 at time: 1.720\n",
+ "J_n integrated over the domain: 2.881 at time: 1.720\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.720\n",
+ "d (def. map) integrated over the domain: 25.223 at time: 1.720\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.720\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.720\n",
+ "\n",
+ "J integrated over the domain: 6.797 at time: 1.730\n",
+ "J_n integrated over the domain: 4.607 at time: 1.730\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.730\n",
+ "d (def. map) integrated over the domain: 50.200 at time: 1.730\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.730\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.730\n",
+ "\n",
+ "J integrated over the domain: 9.314 at time: 1.740\n",
+ "J_n integrated over the domain: 6.797 at time: 1.740\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.740\n",
+ "d (def. map) integrated over the domain: 90.753 at time: 1.740\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.740\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.740\n",
+ "\n",
+ "J integrated over the domain: 12.000 at time: 1.750\n",
+ "J_n integrated over the domain: 9.314 at time: 1.750\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.750\n",
+ "d (def. map) integrated over the domain: 148.000 at time: 1.750\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.750\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.750\n",
+ "\n",
+ "J integrated over the domain: 14.686 at time: 1.760\n",
+ "J_n integrated over the domain: 12.000 at time: 1.760\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.760\n",
+ "d (def. map) integrated over the domain: 219.674 at time: 1.760\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.760\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.760\n",
+ "\n",
+ "J integrated over the domain: 17.203 at time: 1.770\n",
+ "J_n integrated over the domain: 14.686 at time: 1.770\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.770\n",
+ "d (def. map) integrated over the domain: 299.941 at time: 1.770\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.770\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.770\n",
+ "\n"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "J integrated over the domain: 19.393 at time: 1.780\n",
+ "J_n integrated over the domain: 17.203 at time: 1.780\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.780\n",
+ "d (def. map) integrated over the domain: 380.093 at time: 1.780\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.780\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.780\n",
+ "\n",
+ "J integrated over the domain: 21.119 at time: 1.790\n",
+ "J_n integrated over the domain: 19.393 at time: 1.790\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.790\n",
+ "d (def. map) integrated over the domain: 450.001 at time: 1.790\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.790\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.790\n",
+ "\n",
+ "J integrated over the domain: 22.271 at time: 1.800\n",
+ "J_n integrated over the domain: 21.119 at time: 1.800\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.800\n",
+ "d (def. map) integrated over the domain: 500.016 at time: 1.800\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.800\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.800\n",
+ "\n",
+ "J integrated over the domain: 22.779 at time: 1.810\n",
+ "J_n integrated over the domain: 22.271 at time: 1.810\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.810\n",
+ "d (def. map) integrated over the domain: 522.869 at time: 1.810\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.810\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.810\n",
+ "\n",
+ "J integrated over the domain: 22.609 at time: 1.820\n",
+ "J_n integrated over the domain: 22.779 at time: 1.820\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.820\n",
+ "d (def. map) integrated over the domain: 515.153 at time: 1.820\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.820\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.820\n",
+ "\n",
+ "J integrated over the domain: 21.772 at time: 1.830\n",
+ "J_n integrated over the domain: 22.609 at time: 1.830\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.830\n",
+ "d (def. map) integrated over the domain: 478.026 at time: 1.830\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.830\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.830\n",
+ "\n",
+ "J integrated over the domain: 20.322 at time: 1.840\n",
+ "J_n integrated over the domain: 21.772 at time: 1.840\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.840\n",
+ "d (def. map) integrated over the domain: 416.965 at time: 1.840\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.840\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.840\n",
+ "\n",
+ "J integrated over the domain: 18.348 at time: 1.850\n",
+ "J_n integrated over the domain: 20.322 at time: 1.850\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.850\n",
+ "d (def. map) integrated over the domain: 340.652 at time: 1.850\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.850\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.850\n",
+ "\n",
+ "J integrated over the domain: 15.976 at time: 1.860\n",
+ "J_n integrated over the domain: 18.348 at time: 1.860\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.860\n",
+ "d (def. map) integrated over the domain: 259.224 at time: 1.860\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.860\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.860\n",
+ "\n",
+ "J integrated over the domain: 13.354 at time: 1.870\n",
+ "J_n integrated over the domain: 15.976 at time: 1.870\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.870\n",
+ "d (def. map) integrated over the domain: 182.319 at time: 1.870\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.870\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.870\n",
+ "\n",
+ "J integrated over the domain: 10.646 at time: 1.880\n",
+ "J_n integrated over the domain: 13.354 at time: 1.880\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.880\n",
+ "d (def. map) integrated over the domain: 117.346 at time: 1.880\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.880\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.880\n",
+ "\n",
+ "J integrated over the domain: 8.024 at time: 1.890\n",
+ "J_n integrated over the domain: 10.646 at time: 1.890\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.890\n",
+ "d (def. map) integrated over the domain: 68.389 at time: 1.890\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.890\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.890\n",
+ "\n",
+ "J integrated over the domain: 5.652 at time: 1.900\n",
+ "J_n integrated over the domain: 8.024 at time: 1.900\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.900\n",
+ "d (def. map) integrated over the domain: 35.944 at time: 1.900\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.900\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.900\n",
+ "\n",
+ "J integrated over the domain: 3.678 at time: 1.910\n",
+ "J_n integrated over the domain: 5.652 at time: 1.910\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.910\n",
+ "d (def. map) integrated over the domain: 17.531 at time: 1.910\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.910\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.910\n",
+ "\n",
+ "J integrated over the domain: 2.228 at time: 1.920\n",
+ "J_n integrated over the domain: 3.678 at time: 1.920\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.920\n",
+ "d (def. map) integrated over the domain: 8.963 at time: 1.920\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.920\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.920\n",
+ "\n",
+ "J integrated over the domain: 1.391 at time: 1.930\n",
+ "J_n integrated over the domain: 2.228 at time: 1.930\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.930\n",
+ "d (def. map) integrated over the domain: 5.936 at time: 1.930\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.930\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.930\n",
+ "\n",
+ "J integrated over the domain: 1.221 at time: 1.940\n",
+ "J_n integrated over the domain: 1.391 at time: 1.940\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.940\n",
+ "d (def. map) integrated over the domain: 5.492 at time: 1.940\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.940\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.940\n",
+ "\n",
+ "J integrated over the domain: 1.729 at time: 1.950\n",
+ "J_n integrated over the domain: 1.221 at time: 1.950\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.950\n",
+ "d (def. map) integrated over the domain: 6.988 at time: 1.950\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.950\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.950\n",
+ "\n",
+ "J integrated over the domain: 2.881 at time: 1.960\n",
+ "J_n integrated over the domain: 1.729 at time: 1.960\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.960\n",
+ "d (def. map) integrated over the domain: 12.302 at time: 1.960\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.960\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.960\n",
+ "\n",
+ "J integrated over the domain: 4.607 at time: 1.970\n",
+ "J_n integrated over the domain: 2.881 at time: 1.970\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.970\n",
+ "d (def. map) integrated over the domain: 25.223 at time: 1.970\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.970\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.970\n",
+ "\n",
+ "J integrated over the domain: 6.797 at time: 1.980\n",
+ "J_n integrated over the domain: 4.607 at time: 1.980\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.980\n",
+ "d (def. map) integrated over the domain: 50.200 at time: 1.980\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.980\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.980\n",
+ "\n",
+ "J integrated over the domain: 9.314 at time: 1.990\n",
+ "J_n integrated over the domain: 6.797 at time: 1.990\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.990\n",
+ "d (def. map) integrated over the domain: 90.753 at time: 1.990\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.990\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.990\n",
+ "\n",
+ "J integrated over the domain: 12.000 at time: 2.000\n",
+ "J_n integrated over the domain: 9.314 at time: 2.000\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 2.000\n",
+ "d (def. map) integrated over the domain: 148.000 at time: 2.000\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 2.000\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 2.000\n",
+ "\n",
+ "DoF for Velocity Space (U): 3298\n",
+ "DoF for Pressure Space (P): 1649\n",
+ "Solution Computed in 36.019 seconds\n",
+ "\n",
+ "----------------Computation Completed!----------------\n",
+ "\n",
+ "\n",
+ "Initializing iNSE problem with Deformation type: High_Osc_con\n",
+ "\n",
+ "\n",
+ "Setup with initial condition: True\n",
+ "Using a non-zero initial condition (2D-Gaussian) for the velocity field!\n",
+ "Defining forms associated to Chorin-Temam scheme...\n",
+ "Using LU Solver...\n",
+ "Starting iteration over time...\n"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "E (Energy) of initial t. velocity: 0.01648 at time 0.000\n",
+ "\n",
+ "J integrated over the domain: 9.314 at time: 0.010\n",
+ "J_n integrated over the domain: 12.000 at time: 0.010\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.010\n",
+ "d (def. map) integrated over the domain: 90.753 at time: 0.010\n",
+ "Strain energy E( eps(|u|^2) ): 0.00041 at time 0.010\n",
+ "Residual of scheme -> 'delta' value: 0.00012 at time 0.010\n",
+ "\n",
+ "J integrated over the domain: 6.797 at time: 0.020\n",
+ "J_n integrated over the domain: 9.314 at time: 0.020\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.020\n",
+ "d (def. map) integrated over the domain: 50.200 at time: 0.020\n",
+ "Strain energy E( eps(|u|^2) ): 0.00045 at time 0.020\n",
+ "Residual of scheme -> 'delta' value: -0.00017 at time 0.020\n",
+ "\n",
+ "J integrated over the domain: 4.607 at time: 0.030\n",
+ "J_n integrated over the domain: 6.797 at time: 0.030\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.030\n",
+ "d (def. map) integrated over the domain: 25.223 at time: 0.030\n",
+ "Strain energy E( eps(|u|^2) ): 0.00029 at time 0.030\n",
+ "Residual of scheme -> 'delta' value: -0.00023 at time 0.030\n",
+ "\n",
+ "J integrated over the domain: 2.881 at time: 0.040\n",
+ "J_n integrated over the domain: 4.607 at time: 0.040\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.040\n",
+ "d (def. map) integrated over the domain: 12.302 at time: 0.040\n",
+ "Strain energy E( eps(|u|^2) ): 0.00010 at time 0.040\n",
+ "Residual of scheme -> 'delta' value: -0.00015 at time 0.040\n",
+ "\n",
+ "J integrated over the domain: 1.729 at time: 0.050\n",
+ "J_n integrated over the domain: 2.881 at time: 0.050\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.050\n",
+ "d (def. map) integrated over the domain: 6.988 at time: 0.050\n",
+ "Strain energy E( eps(|u|^2) ): 0.00002 at time 0.050\n",
+ "Residual of scheme -> 'delta' value: -0.00005 at time 0.050\n",
+ "\n",
+ "J integrated over the domain: 1.221 at time: 0.060\n",
+ "J_n integrated over the domain: 1.729 at time: 0.060\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.060\n",
+ "d (def. map) integrated over the domain: 5.492 at time: 0.060\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.060\n",
+ "Residual of scheme -> 'delta' value: -0.00001 at time 0.060\n",
+ "\n",
+ "J integrated over the domain: 1.391 at time: 0.070\n",
+ "J_n integrated over the domain: 1.221 at time: 0.070\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.070\n",
+ "d (def. map) integrated over the domain: 5.936 at time: 0.070\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.070\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.070\n",
+ "\n",
+ "J integrated over the domain: 2.228 at time: 0.080\n",
+ "J_n integrated over the domain: 1.391 at time: 0.080\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.080\n",
+ "d (def. map) integrated over the domain: 8.963 at time: 0.080\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.080\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.080\n",
+ "\n",
+ "J integrated over the domain: 3.678 at time: 0.090\n",
+ "J_n integrated over the domain: 2.228 at time: 0.090\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.090\n",
+ "d (def. map) integrated over the domain: 17.531 at time: 0.090\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.090\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.090\n",
+ "\n",
+ "J integrated over the domain: 5.652 at time: 0.100\n",
+ "J_n integrated over the domain: 3.678 at time: 0.100\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.100\n",
+ "d (def. map) integrated over the domain: 35.944 at time: 0.100\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.100\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.100\n",
+ "\n",
+ "J integrated over the domain: 8.024 at time: 0.110\n",
+ "J_n integrated over the domain: 5.652 at time: 0.110\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.110\n",
+ "d (def. map) integrated over the domain: 68.389 at time: 0.110\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.110\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.110\n",
+ "\n",
+ "J integrated over the domain: 10.646 at time: 0.120\n",
+ "J_n integrated over the domain: 8.024 at time: 0.120\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.120\n",
+ "d (def. map) integrated over the domain: 117.346 at time: 0.120\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.120\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.120\n",
+ "\n",
+ "J integrated over the domain: 13.354 at time: 0.130\n",
+ "J_n integrated over the domain: 10.646 at time: 0.130\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.130\n",
+ "d (def. map) integrated over the domain: 182.319 at time: 0.130\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.130\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.130\n",
+ "\n",
+ "J integrated over the domain: 15.976 at time: 0.140\n",
+ "J_n integrated over the domain: 13.354 at time: 0.140\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.140\n",
+ "d (def. map) integrated over the domain: 259.224 at time: 0.140\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.140\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.140\n",
+ "\n",
+ "J integrated over the domain: 18.348 at time: 0.150\n",
+ "J_n integrated over the domain: 15.976 at time: 0.150\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.150\n",
+ "d (def. map) integrated over the domain: 340.652 at time: 0.150\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.150\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.150\n",
+ "\n",
+ "J integrated over the domain: 20.322 at time: 0.160\n",
+ "J_n integrated over the domain: 18.348 at time: 0.160\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.160\n",
+ "d (def. map) integrated over the domain: 416.965 at time: 0.160\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.160\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.160\n",
+ "\n",
+ "J integrated over the domain: 21.772 at time: 0.170\n",
+ "J_n integrated over the domain: 20.322 at time: 0.170\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.170\n",
+ "d (def. map) integrated over the domain: 478.026 at time: 0.170\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.170\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.170\n",
+ "\n",
+ "J integrated over the domain: 22.609 at time: 0.180\n",
+ "J_n integrated over the domain: 21.772 at time: 0.180\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.180\n",
+ "d (def. map) integrated over the domain: 515.153 at time: 0.180\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.180\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.180\n",
+ "\n",
+ "J integrated over the domain: 22.779 at time: 0.190\n",
+ "J_n integrated over the domain: 22.609 at time: 0.190\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.190\n",
+ "d (def. map) integrated over the domain: 522.869 at time: 0.190\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.190\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.190\n",
+ "\n",
+ "J integrated over the domain: 22.271 at time: 0.200\n",
+ "J_n integrated over the domain: 22.779 at time: 0.200\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.200\n",
+ "d (def. map) integrated over the domain: 500.016 at time: 0.200\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.200\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.200\n",
+ "\n",
+ "J integrated over the domain: 21.119 at time: 0.210\n",
+ "J_n integrated over the domain: 22.271 at time: 0.210\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.210\n",
+ "d (def. map) integrated over the domain: 450.001 at time: 0.210\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.210\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.210\n",
+ "\n",
+ "J integrated over the domain: 19.393 at time: 0.220\n",
+ "J_n integrated over the domain: 21.119 at time: 0.220\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.220\n",
+ "d (def. map) integrated over the domain: 380.093 at time: 0.220\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.220\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.220\n",
+ "\n",
+ "J integrated over the domain: 17.203 at time: 0.230\n",
+ "J_n integrated over the domain: 19.393 at time: 0.230\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.230\n",
+ "d (def. map) integrated over the domain: 299.941 at time: 0.230\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.230\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.230\n",
+ "\n",
+ "J integrated over the domain: 14.686 at time: 0.240\n",
+ "J_n integrated over the domain: 17.203 at time: 0.240\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.240\n",
+ "d (def. map) integrated over the domain: 219.674 at time: 0.240\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.240\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.240\n",
+ "\n"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "J integrated over the domain: 12.000 at time: 0.250\n",
+ "J_n integrated over the domain: 14.686 at time: 0.250\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.250\n",
+ "d (def. map) integrated over the domain: 148.000 at time: 0.250\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.250\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.250\n",
+ "\n",
+ "J integrated over the domain: 9.314 at time: 0.260\n",
+ "J_n integrated over the domain: 12.000 at time: 0.260\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.260\n",
+ "d (def. map) integrated over the domain: 90.753 at time: 0.260\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.260\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.260\n",
+ "\n",
+ "J integrated over the domain: 6.797 at time: 0.270\n",
+ "J_n integrated over the domain: 9.314 at time: 0.270\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.270\n",
+ "d (def. map) integrated over the domain: 50.200 at time: 0.270\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.270\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.270\n",
+ "\n",
+ "J integrated over the domain: 4.607 at time: 0.280\n",
+ "J_n integrated over the domain: 6.797 at time: 0.280\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.280\n",
+ "d (def. map) integrated over the domain: 25.223 at time: 0.280\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.280\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.280\n",
+ "\n",
+ "J integrated over the domain: 2.881 at time: 0.290\n",
+ "J_n integrated over the domain: 4.607 at time: 0.290\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.290\n",
+ "d (def. map) integrated over the domain: 12.302 at time: 0.290\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.290\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.290\n",
+ "\n",
+ "J integrated over the domain: 1.729 at time: 0.300\n",
+ "J_n integrated over the domain: 2.881 at time: 0.300\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.300\n",
+ "d (def. map) integrated over the domain: 6.988 at time: 0.300\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.300\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.300\n",
+ "\n",
+ "J integrated over the domain: 1.221 at time: 0.310\n",
+ "J_n integrated over the domain: 1.729 at time: 0.310\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.310\n",
+ "d (def. map) integrated over the domain: 5.492 at time: 0.310\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.310\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.310\n",
+ "\n",
+ "J integrated over the domain: 1.391 at time: 0.320\n",
+ "J_n integrated over the domain: 1.221 at time: 0.320\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.320\n",
+ "d (def. map) integrated over the domain: 5.936 at time: 0.320\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.320\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.320\n",
+ "\n",
+ "J integrated over the domain: 2.228 at time: 0.330\n",
+ "J_n integrated over the domain: 1.391 at time: 0.330\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.330\n",
+ "d (def. map) integrated over the domain: 8.963 at time: 0.330\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.330\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.330\n",
+ "\n",
+ "J integrated over the domain: 3.678 at time: 0.340\n",
+ "J_n integrated over the domain: 2.228 at time: 0.340\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.340\n",
+ "d (def. map) integrated over the domain: 17.531 at time: 0.340\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.340\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.340\n",
+ "\n",
+ "J integrated over the domain: 5.652 at time: 0.350\n",
+ "J_n integrated over the domain: 3.678 at time: 0.350\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.350\n",
+ "d (def. map) integrated over the domain: 35.944 at time: 0.350\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.350\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.350\n",
+ "\n",
+ "J integrated over the domain: 8.024 at time: 0.360\n",
+ "J_n integrated over the domain: 5.652 at time: 0.360\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.360\n",
+ "d (def. map) integrated over the domain: 68.389 at time: 0.360\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.360\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.360\n",
+ "\n",
+ "J integrated over the domain: 10.646 at time: 0.370\n",
+ "J_n integrated over the domain: 8.024 at time: 0.370\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.370\n",
+ "d (def. map) integrated over the domain: 117.346 at time: 0.370\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.370\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.370\n",
+ "\n",
+ "J integrated over the domain: 13.354 at time: 0.380\n",
+ "J_n integrated over the domain: 10.646 at time: 0.380\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.380\n",
+ "d (def. map) integrated over the domain: 182.319 at time: 0.380\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.380\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.380\n",
+ "\n",
+ "J integrated over the domain: 15.976 at time: 0.390\n",
+ "J_n integrated over the domain: 13.354 at time: 0.390\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.390\n",
+ "d (def. map) integrated over the domain: 259.224 at time: 0.390\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.390\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.390\n",
+ "\n",
+ "J integrated over the domain: 18.348 at time: 0.400\n",
+ "J_n integrated over the domain: 15.976 at time: 0.400\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.400\n",
+ "d (def. map) integrated over the domain: 340.652 at time: 0.400\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.400\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.400\n",
+ "\n",
+ "J integrated over the domain: 20.322 at time: 0.410\n",
+ "J_n integrated over the domain: 18.348 at time: 0.410\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.410\n",
+ "d (def. map) integrated over the domain: 416.965 at time: 0.410\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.410\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.410\n",
+ "\n",
+ "J integrated over the domain: 21.772 at time: 0.420\n",
+ "J_n integrated over the domain: 20.322 at time: 0.420\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.420\n",
+ "d (def. map) integrated over the domain: 478.026 at time: 0.420\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.420\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.420\n",
+ "\n",
+ "J integrated over the domain: 22.609 at time: 0.430\n",
+ "J_n integrated over the domain: 21.772 at time: 0.430\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.430\n",
+ "d (def. map) integrated over the domain: 515.153 at time: 0.430\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.430\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.430\n",
+ "\n",
+ "J integrated over the domain: 22.779 at time: 0.440\n",
+ "J_n integrated over the domain: 22.609 at time: 0.440\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.440\n",
+ "d (def. map) integrated over the domain: 522.869 at time: 0.440\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.440\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.440\n",
+ "\n",
+ "J integrated over the domain: 22.271 at time: 0.450\n",
+ "J_n integrated over the domain: 22.779 at time: 0.450\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.450\n",
+ "d (def. map) integrated over the domain: 500.016 at time: 0.450\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.450\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.450\n",
+ "\n",
+ "J integrated over the domain: 21.119 at time: 0.460\n",
+ "J_n integrated over the domain: 22.271 at time: 0.460\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.460\n",
+ "d (def. map) integrated over the domain: 450.001 at time: 0.460\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.460\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.460\n",
+ "\n",
+ "J integrated over the domain: 19.393 at time: 0.470\n",
+ "J_n integrated over the domain: 21.119 at time: 0.470\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.470\n",
+ "d (def. map) integrated over the domain: 380.093 at time: 0.470\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.470\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.470\n",
+ "\n",
+ "J integrated over the domain: 17.203 at time: 0.480\n",
+ "J_n integrated over the domain: 19.393 at time: 0.480\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.480\n",
+ "d (def. map) integrated over the domain: 299.941 at time: 0.480\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.480\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.480\n",
+ "\n",
+ "J integrated over the domain: 14.686 at time: 0.490\n",
+ "J_n integrated over the domain: 17.203 at time: 0.490\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.490\n",
+ "d (def. map) integrated over the domain: 219.674 at time: 0.490\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.490\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.490\n",
+ "\n"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "J integrated over the domain: 12.000 at time: 0.500\n",
+ "J_n integrated over the domain: 14.686 at time: 0.500\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.500\n",
+ "d (def. map) integrated over the domain: 148.000 at time: 0.500\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.500\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.500\n",
+ "\n",
+ "J integrated over the domain: 9.314 at time: 0.510\n",
+ "J_n integrated over the domain: 12.000 at time: 0.510\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.510\n",
+ "d (def. map) integrated over the domain: 90.753 at time: 0.510\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.510\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.510\n",
+ "\n",
+ "J integrated over the domain: 6.797 at time: 0.520\n",
+ "J_n integrated over the domain: 9.314 at time: 0.520\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.520\n",
+ "d (def. map) integrated over the domain: 50.200 at time: 0.520\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.520\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.520\n",
+ "\n",
+ "J integrated over the domain: 4.607 at time: 0.530\n",
+ "J_n integrated over the domain: 6.797 at time: 0.530\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.530\n",
+ "d (def. map) integrated over the domain: 25.223 at time: 0.530\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.530\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.530\n",
+ "\n",
+ "J integrated over the domain: 2.881 at time: 0.540\n",
+ "J_n integrated over the domain: 4.607 at time: 0.540\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.540\n",
+ "d (def. map) integrated over the domain: 12.302 at time: 0.540\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.540\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.540\n",
+ "\n",
+ "J integrated over the domain: 1.729 at time: 0.550\n",
+ "J_n integrated over the domain: 2.881 at time: 0.550\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.550\n",
+ "d (def. map) integrated over the domain: 6.988 at time: 0.550\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.550\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.550\n",
+ "\n",
+ "J integrated over the domain: 1.221 at time: 0.560\n",
+ "J_n integrated over the domain: 1.729 at time: 0.560\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.560\n",
+ "d (def. map) integrated over the domain: 5.492 at time: 0.560\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.560\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.560\n",
+ "\n",
+ "J integrated over the domain: 1.391 at time: 0.570\n",
+ "J_n integrated over the domain: 1.221 at time: 0.570\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.570\n",
+ "d (def. map) integrated over the domain: 5.936 at time: 0.570\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.570\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.570\n",
+ "\n",
+ "J integrated over the domain: 2.228 at time: 0.580\n",
+ "J_n integrated over the domain: 1.391 at time: 0.580\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.580\n",
+ "d (def. map) integrated over the domain: 8.963 at time: 0.580\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.580\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.580\n",
+ "\n",
+ "J integrated over the domain: 3.678 at time: 0.590\n",
+ "J_n integrated over the domain: 2.228 at time: 0.590\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.590\n",
+ "d (def. map) integrated over the domain: 17.531 at time: 0.590\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.590\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.590\n",
+ "\n",
+ "J integrated over the domain: 5.652 at time: 0.600\n",
+ "J_n integrated over the domain: 3.678 at time: 0.600\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.600\n",
+ "d (def. map) integrated over the domain: 35.944 at time: 0.600\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.600\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.600\n",
+ "\n",
+ "J integrated over the domain: 8.024 at time: 0.610\n",
+ "J_n integrated over the domain: 5.652 at time: 0.610\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.610\n",
+ "d (def. map) integrated over the domain: 68.389 at time: 0.610\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.610\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.610\n",
+ "\n",
+ "J integrated over the domain: 10.646 at time: 0.620\n",
+ "J_n integrated over the domain: 8.024 at time: 0.620\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.620\n",
+ "d (def. map) integrated over the domain: 117.346 at time: 0.620\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.620\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.620\n",
+ "\n",
+ "J integrated over the domain: 13.354 at time: 0.630\n",
+ "J_n integrated over the domain: 10.646 at time: 0.630\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.630\n",
+ "d (def. map) integrated over the domain: 182.319 at time: 0.630\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.630\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.630\n",
+ "\n",
+ "J integrated over the domain: 15.976 at time: 0.640\n",
+ "J_n integrated over the domain: 13.354 at time: 0.640\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.640\n",
+ "d (def. map) integrated over the domain: 259.224 at time: 0.640\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.640\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.640\n",
+ "\n",
+ "J integrated over the domain: 18.348 at time: 0.650\n",
+ "J_n integrated over the domain: 15.976 at time: 0.650\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.650\n",
+ "d (def. map) integrated over the domain: 340.652 at time: 0.650\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.650\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.650\n",
+ "\n",
+ "J integrated over the domain: 20.322 at time: 0.660\n",
+ "J_n integrated over the domain: 18.348 at time: 0.660\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.660\n",
+ "d (def. map) integrated over the domain: 416.965 at time: 0.660\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.660\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.660\n",
+ "\n",
+ "J integrated over the domain: 21.772 at time: 0.670\n",
+ "J_n integrated over the domain: 20.322 at time: 0.670\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.670\n",
+ "d (def. map) integrated over the domain: 478.026 at time: 0.670\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.670\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.670\n",
+ "\n",
+ "J integrated over the domain: 22.609 at time: 0.680\n",
+ "J_n integrated over the domain: 21.772 at time: 0.680\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.680\n",
+ "d (def. map) integrated over the domain: 515.153 at time: 0.680\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.680\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.680\n",
+ "\n",
+ "J integrated over the domain: 22.779 at time: 0.690\n",
+ "J_n integrated over the domain: 22.609 at time: 0.690\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.690\n",
+ "d (def. map) integrated over the domain: 522.869 at time: 0.690\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.690\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.690\n",
+ "\n",
+ "J integrated over the domain: 22.271 at time: 0.700\n",
+ "J_n integrated over the domain: 22.779 at time: 0.700\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.700\n",
+ "d (def. map) integrated over the domain: 500.016 at time: 0.700\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.700\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.700\n",
+ "\n",
+ "J integrated over the domain: 21.119 at time: 0.710\n",
+ "J_n integrated over the domain: 22.271 at time: 0.710\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.710\n",
+ "d (def. map) integrated over the domain: 450.001 at time: 0.710\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.710\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.710\n",
+ "\n",
+ "J integrated over the domain: 19.393 at time: 0.720\n",
+ "J_n integrated over the domain: 21.119 at time: 0.720\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.720\n",
+ "d (def. map) integrated over the domain: 380.093 at time: 0.720\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.720\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.720\n",
+ "\n",
+ "J integrated over the domain: 17.203 at time: 0.730\n",
+ "J_n integrated over the domain: 19.393 at time: 0.730\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.730\n",
+ "d (def. map) integrated over the domain: 299.941 at time: 0.730\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.730\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.730\n",
+ "\n",
+ "J integrated over the domain: 14.686 at time: 0.740\n",
+ "J_n integrated over the domain: 17.203 at time: 0.740\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.740\n",
+ "d (def. map) integrated over the domain: 219.674 at time: 0.740\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.740\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.740\n",
+ "\n"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "J integrated over the domain: 12.000 at time: 0.750\n",
+ "J_n integrated over the domain: 14.686 at time: 0.750\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.750\n",
+ "d (def. map) integrated over the domain: 148.000 at time: 0.750\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.750\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.750\n",
+ "\n",
+ "J integrated over the domain: 9.314 at time: 0.760\n",
+ "J_n integrated over the domain: 12.000 at time: 0.760\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.760\n",
+ "d (def. map) integrated over the domain: 90.753 at time: 0.760\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.760\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.760\n",
+ "\n",
+ "J integrated over the domain: 6.797 at time: 0.770\n",
+ "J_n integrated over the domain: 9.314 at time: 0.770\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.770\n",
+ "d (def. map) integrated over the domain: 50.200 at time: 0.770\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.770\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.770\n",
+ "\n",
+ "J integrated over the domain: 4.607 at time: 0.780\n",
+ "J_n integrated over the domain: 6.797 at time: 0.780\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.780\n",
+ "d (def. map) integrated over the domain: 25.223 at time: 0.780\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.780\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.780\n",
+ "\n",
+ "J integrated over the domain: 2.881 at time: 0.790\n",
+ "J_n integrated over the domain: 4.607 at time: 0.790\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.790\n",
+ "d (def. map) integrated over the domain: 12.302 at time: 0.790\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.790\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.790\n",
+ "\n",
+ "J integrated over the domain: 1.729 at time: 0.800\n",
+ "J_n integrated over the domain: 2.881 at time: 0.800\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.800\n",
+ "d (def. map) integrated over the domain: 6.988 at time: 0.800\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.800\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.800\n",
+ "\n",
+ "J integrated over the domain: 1.221 at time: 0.810\n",
+ "J_n integrated over the domain: 1.729 at time: 0.810\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.810\n",
+ "d (def. map) integrated over the domain: 5.492 at time: 0.810\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.810\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.810\n",
+ "\n",
+ "J integrated over the domain: 1.391 at time: 0.820\n",
+ "J_n integrated over the domain: 1.221 at time: 0.820\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.820\n",
+ "d (def. map) integrated over the domain: 5.936 at time: 0.820\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.820\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.820\n",
+ "\n",
+ "J integrated over the domain: 2.228 at time: 0.830\n",
+ "J_n integrated over the domain: 1.391 at time: 0.830\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.830\n",
+ "d (def. map) integrated over the domain: 8.963 at time: 0.830\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.830\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.830\n",
+ "\n",
+ "J integrated over the domain: 3.678 at time: 0.840\n",
+ "J_n integrated over the domain: 2.228 at time: 0.840\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.840\n",
+ "d (def. map) integrated over the domain: 17.531 at time: 0.840\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.840\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.840\n",
+ "\n",
+ "J integrated over the domain: 5.652 at time: 0.850\n",
+ "J_n integrated over the domain: 3.678 at time: 0.850\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.850\n",
+ "d (def. map) integrated over the domain: 35.944 at time: 0.850\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.850\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.850\n",
+ "\n",
+ "J integrated over the domain: 8.024 at time: 0.860\n",
+ "J_n integrated over the domain: 5.652 at time: 0.860\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.860\n",
+ "d (def. map) integrated over the domain: 68.389 at time: 0.860\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.860\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.860\n",
+ "\n",
+ "J integrated over the domain: 10.646 at time: 0.870\n",
+ "J_n integrated over the domain: 8.024 at time: 0.870\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.870\n",
+ "d (def. map) integrated over the domain: 117.346 at time: 0.870\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.870\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.870\n",
+ "\n",
+ "J integrated over the domain: 13.354 at time: 0.880\n",
+ "J_n integrated over the domain: 10.646 at time: 0.880\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.880\n",
+ "d (def. map) integrated over the domain: 182.319 at time: 0.880\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.880\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.880\n",
+ "\n",
+ "J integrated over the domain: 15.976 at time: 0.890\n",
+ "J_n integrated over the domain: 13.354 at time: 0.890\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.890\n",
+ "d (def. map) integrated over the domain: 259.224 at time: 0.890\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.890\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.890\n",
+ "\n",
+ "J integrated over the domain: 18.348 at time: 0.900\n",
+ "J_n integrated over the domain: 15.976 at time: 0.900\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.900\n",
+ "d (def. map) integrated over the domain: 340.652 at time: 0.900\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.900\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.900\n",
+ "\n",
+ "J integrated over the domain: 20.322 at time: 0.910\n",
+ "J_n integrated over the domain: 18.348 at time: 0.910\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.910\n",
+ "d (def. map) integrated over the domain: 416.965 at time: 0.910\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.910\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.910\n",
+ "\n",
+ "J integrated over the domain: 21.772 at time: 0.920\n",
+ "J_n integrated over the domain: 20.322 at time: 0.920\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.920\n",
+ "d (def. map) integrated over the domain: 478.026 at time: 0.920\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.920\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.920\n",
+ "\n",
+ "J integrated over the domain: 22.609 at time: 0.930\n",
+ "J_n integrated over the domain: 21.772 at time: 0.930\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.930\n",
+ "d (def. map) integrated over the domain: 515.153 at time: 0.930\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.930\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.930\n",
+ "\n",
+ "J integrated over the domain: 22.779 at time: 0.940\n",
+ "J_n integrated over the domain: 22.609 at time: 0.940\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.940\n",
+ "d (def. map) integrated over the domain: 522.869 at time: 0.940\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.940\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.940\n",
+ "\n",
+ "J integrated over the domain: 22.271 at time: 0.950\n",
+ "J_n integrated over the domain: 22.779 at time: 0.950\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.950\n",
+ "d (def. map) integrated over the domain: 500.016 at time: 0.950\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.950\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.950\n",
+ "\n",
+ "J integrated over the domain: 21.119 at time: 0.960\n",
+ "J_n integrated over the domain: 22.271 at time: 0.960\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.960\n",
+ "d (def. map) integrated over the domain: 450.001 at time: 0.960\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.960\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.960\n",
+ "\n",
+ "J integrated over the domain: 19.393 at time: 0.970\n",
+ "J_n integrated over the domain: 21.119 at time: 0.970\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.970\n",
+ "d (def. map) integrated over the domain: 380.093 at time: 0.970\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.970\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.970\n",
+ "\n",
+ "J integrated over the domain: 17.203 at time: 0.980\n",
+ "J_n integrated over the domain: 19.393 at time: 0.980\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.980\n",
+ "d (def. map) integrated over the domain: 299.941 at time: 0.980\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.980\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.980\n",
+ "\n"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "J integrated over the domain: 14.686 at time: 0.990\n",
+ "J_n integrated over the domain: 17.203 at time: 0.990\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.990\n",
+ "d (def. map) integrated over the domain: 219.674 at time: 0.990\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.990\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.990\n",
+ "\n",
+ "J integrated over the domain: 12.000 at time: 1.000\n",
+ "J_n integrated over the domain: 14.686 at time: 1.000\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.000\n",
+ "d (def. map) integrated over the domain: 148.000 at time: 1.000\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.000\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.000\n",
+ "\n",
+ "J integrated over the domain: 9.314 at time: 1.010\n",
+ "J_n integrated over the domain: 12.000 at time: 1.010\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.010\n",
+ "d (def. map) integrated over the domain: 90.753 at time: 1.010\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.010\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.010\n",
+ "\n",
+ "J integrated over the domain: 6.797 at time: 1.020\n",
+ "J_n integrated over the domain: 9.314 at time: 1.020\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.020\n",
+ "d (def. map) integrated over the domain: 50.200 at time: 1.020\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.020\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.020\n",
+ "\n",
+ "J integrated over the domain: 4.607 at time: 1.030\n",
+ "J_n integrated over the domain: 6.797 at time: 1.030\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.030\n",
+ "d (def. map) integrated over the domain: 25.223 at time: 1.030\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.030\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.030\n",
+ "\n",
+ "J integrated over the domain: 2.881 at time: 1.040\n",
+ "J_n integrated over the domain: 4.607 at time: 1.040\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.040\n",
+ "d (def. map) integrated over the domain: 12.302 at time: 1.040\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.040\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.040\n",
+ "\n",
+ "J integrated over the domain: 1.729 at time: 1.050\n",
+ "J_n integrated over the domain: 2.881 at time: 1.050\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.050\n",
+ "d (def. map) integrated over the domain: 6.988 at time: 1.050\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.050\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.050\n",
+ "\n",
+ "J integrated over the domain: 1.221 at time: 1.060\n",
+ "J_n integrated over the domain: 1.729 at time: 1.060\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.060\n",
+ "d (def. map) integrated over the domain: 5.492 at time: 1.060\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.060\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.060\n",
+ "\n",
+ "J integrated over the domain: 1.391 at time: 1.070\n",
+ "J_n integrated over the domain: 1.221 at time: 1.070\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.070\n",
+ "d (def. map) integrated over the domain: 5.936 at time: 1.070\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.070\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.070\n",
+ "\n",
+ "J integrated over the domain: 2.228 at time: 1.080\n",
+ "J_n integrated over the domain: 1.391 at time: 1.080\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.080\n",
+ "d (def. map) integrated over the domain: 8.963 at time: 1.080\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.080\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.080\n",
+ "\n",
+ "J integrated over the domain: 3.678 at time: 1.090\n",
+ "J_n integrated over the domain: 2.228 at time: 1.090\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.090\n",
+ "d (def. map) integrated over the domain: 17.531 at time: 1.090\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.090\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.090\n",
+ "\n",
+ "J integrated over the domain: 5.652 at time: 1.100\n",
+ "J_n integrated over the domain: 3.678 at time: 1.100\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.100\n",
+ "d (def. map) integrated over the domain: 35.944 at time: 1.100\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.100\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.100\n",
+ "\n",
+ "J integrated over the domain: 8.024 at time: 1.110\n",
+ "J_n integrated over the domain: 5.652 at time: 1.110\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.110\n",
+ "d (def. map) integrated over the domain: 68.389 at time: 1.110\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.110\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.110\n",
+ "\n",
+ "J integrated over the domain: 10.646 at time: 1.120\n",
+ "J_n integrated over the domain: 8.024 at time: 1.120\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.120\n",
+ "d (def. map) integrated over the domain: 117.346 at time: 1.120\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.120\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.120\n",
+ "\n",
+ "J integrated over the domain: 13.354 at time: 1.130\n",
+ "J_n integrated over the domain: 10.646 at time: 1.130\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.130\n",
+ "d (def. map) integrated over the domain: 182.319 at time: 1.130\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.130\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.130\n",
+ "\n",
+ "J integrated over the domain: 15.976 at time: 1.140\n",
+ "J_n integrated over the domain: 13.354 at time: 1.140\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.140\n",
+ "d (def. map) integrated over the domain: 259.224 at time: 1.140\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.140\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.140\n",
+ "\n",
+ "J integrated over the domain: 18.348 at time: 1.150\n",
+ "J_n integrated over the domain: 15.976 at time: 1.150\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.150\n",
+ "d (def. map) integrated over the domain: 340.652 at time: 1.150\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.150\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.150\n",
+ "\n",
+ "J integrated over the domain: 20.322 at time: 1.160\n",
+ "J_n integrated over the domain: 18.348 at time: 1.160\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.160\n",
+ "d (def. map) integrated over the domain: 416.965 at time: 1.160\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.160\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.160\n",
+ "\n",
+ "J integrated over the domain: 21.772 at time: 1.170\n",
+ "J_n integrated over the domain: 20.322 at time: 1.170\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.170\n",
+ "d (def. map) integrated over the domain: 478.026 at time: 1.170\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.170\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.170\n",
+ "\n",
+ "J integrated over the domain: 22.609 at time: 1.180\n",
+ "J_n integrated over the domain: 21.772 at time: 1.180\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.180\n",
+ "d (def. map) integrated over the domain: 515.153 at time: 1.180\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.180\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.180\n",
+ "\n",
+ "J integrated over the domain: 22.779 at time: 1.190\n",
+ "J_n integrated over the domain: 22.609 at time: 1.190\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.190\n",
+ "d (def. map) integrated over the domain: 522.869 at time: 1.190\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.190\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.190\n",
+ "\n",
+ "J integrated over the domain: 22.271 at time: 1.200\n",
+ "J_n integrated over the domain: 22.779 at time: 1.200\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.200\n",
+ "d (def. map) integrated over the domain: 500.016 at time: 1.200\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.200\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.200\n",
+ "\n",
+ "J integrated over the domain: 21.119 at time: 1.210\n",
+ "J_n integrated over the domain: 22.271 at time: 1.210\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.210\n",
+ "d (def. map) integrated over the domain: 450.001 at time: 1.210\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.210\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.210\n",
+ "\n",
+ "J integrated over the domain: 19.393 at time: 1.220\n",
+ "J_n integrated over the domain: 21.119 at time: 1.220\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.220\n",
+ "d (def. map) integrated over the domain: 380.093 at time: 1.220\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.220\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.220\n",
+ "\n"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "J integrated over the domain: 17.203 at time: 1.230\n",
+ "J_n integrated over the domain: 19.393 at time: 1.230\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.230\n",
+ "d (def. map) integrated over the domain: 299.941 at time: 1.230\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.230\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.230\n",
+ "\n",
+ "J integrated over the domain: 14.686 at time: 1.240\n",
+ "J_n integrated over the domain: 17.203 at time: 1.240\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.240\n",
+ "d (def. map) integrated over the domain: 219.674 at time: 1.240\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.240\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.240\n",
+ "\n",
+ "J integrated over the domain: 12.000 at time: 1.250\n",
+ "J_n integrated over the domain: 14.686 at time: 1.250\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.250\n",
+ "d (def. map) integrated over the domain: 148.000 at time: 1.250\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.250\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.250\n",
+ "\n",
+ "J integrated over the domain: 9.314 at time: 1.260\n",
+ "J_n integrated over the domain: 12.000 at time: 1.260\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.260\n",
+ "d (def. map) integrated over the domain: 90.753 at time: 1.260\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.260\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.260\n",
+ "\n",
+ "J integrated over the domain: 6.797 at time: 1.270\n",
+ "J_n integrated over the domain: 9.314 at time: 1.270\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.270\n",
+ "d (def. map) integrated over the domain: 50.200 at time: 1.270\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.270\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.270\n",
+ "\n",
+ "J integrated over the domain: 4.607 at time: 1.280\n",
+ "J_n integrated over the domain: 6.797 at time: 1.280\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.280\n",
+ "d (def. map) integrated over the domain: 25.223 at time: 1.280\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.280\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.280\n",
+ "\n",
+ "J integrated over the domain: 2.881 at time: 1.290\n",
+ "J_n integrated over the domain: 4.607 at time: 1.290\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.290\n",
+ "d (def. map) integrated over the domain: 12.302 at time: 1.290\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.290\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.290\n",
+ "\n",
+ "J integrated over the domain: 1.729 at time: 1.300\n",
+ "J_n integrated over the domain: 2.881 at time: 1.300\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.300\n",
+ "d (def. map) integrated over the domain: 6.988 at time: 1.300\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.300\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.300\n",
+ "\n",
+ "J integrated over the domain: 1.221 at time: 1.310\n",
+ "J_n integrated over the domain: 1.729 at time: 1.310\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.310\n",
+ "d (def. map) integrated over the domain: 5.492 at time: 1.310\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.310\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.310\n",
+ "\n",
+ "J integrated over the domain: 1.391 at time: 1.320\n",
+ "J_n integrated over the domain: 1.221 at time: 1.320\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.320\n",
+ "d (def. map) integrated over the domain: 5.936 at time: 1.320\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.320\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.320\n",
+ "\n",
+ "J integrated over the domain: 2.228 at time: 1.330\n",
+ "J_n integrated over the domain: 1.391 at time: 1.330\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.330\n",
+ "d (def. map) integrated over the domain: 8.963 at time: 1.330\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.330\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.330\n",
+ "\n",
+ "J integrated over the domain: 3.678 at time: 1.340\n",
+ "J_n integrated over the domain: 2.228 at time: 1.340\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.340\n",
+ "d (def. map) integrated over the domain: 17.531 at time: 1.340\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.340\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.340\n",
+ "\n",
+ "J integrated over the domain: 5.652 at time: 1.350\n",
+ "J_n integrated over the domain: 3.678 at time: 1.350\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.350\n",
+ "d (def. map) integrated over the domain: 35.944 at time: 1.350\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.350\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.350\n",
+ "\n",
+ "J integrated over the domain: 8.024 at time: 1.360\n",
+ "J_n integrated over the domain: 5.652 at time: 1.360\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.360\n",
+ "d (def. map) integrated over the domain: 68.389 at time: 1.360\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.360\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.360\n",
+ "\n",
+ "J integrated over the domain: 10.646 at time: 1.370\n",
+ "J_n integrated over the domain: 8.024 at time: 1.370\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.370\n",
+ "d (def. map) integrated over the domain: 117.346 at time: 1.370\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.370\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.370\n",
+ "\n",
+ "J integrated over the domain: 13.354 at time: 1.380\n",
+ "J_n integrated over the domain: 10.646 at time: 1.380\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.380\n",
+ "d (def. map) integrated over the domain: 182.319 at time: 1.380\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.380\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.380\n",
+ "\n",
+ "J integrated over the domain: 15.976 at time: 1.390\n",
+ "J_n integrated over the domain: 13.354 at time: 1.390\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.390\n",
+ "d (def. map) integrated over the domain: 259.224 at time: 1.390\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.390\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.390\n",
+ "\n",
+ "J integrated over the domain: 18.348 at time: 1.400\n",
+ "J_n integrated over the domain: 15.976 at time: 1.400\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.400\n",
+ "d (def. map) integrated over the domain: 340.652 at time: 1.400\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.400\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.400\n",
+ "\n",
+ "J integrated over the domain: 20.322 at time: 1.410\n",
+ "J_n integrated over the domain: 18.348 at time: 1.410\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.410\n",
+ "d (def. map) integrated over the domain: 416.965 at time: 1.410\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.410\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.410\n",
+ "\n",
+ "J integrated over the domain: 21.772 at time: 1.420\n",
+ "J_n integrated over the domain: 20.322 at time: 1.420\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.420\n",
+ "d (def. map) integrated over the domain: 478.026 at time: 1.420\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.420\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.420\n",
+ "\n",
+ "J integrated over the domain: 22.609 at time: 1.430\n",
+ "J_n integrated over the domain: 21.772 at time: 1.430\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.430\n",
+ "d (def. map) integrated over the domain: 515.153 at time: 1.430\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.430\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.430\n",
+ "\n",
+ "J integrated over the domain: 22.779 at time: 1.440\n",
+ "J_n integrated over the domain: 22.609 at time: 1.440\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.440\n",
+ "d (def. map) integrated over the domain: 522.869 at time: 1.440\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.440\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.440\n",
+ "\n",
+ "J integrated over the domain: 22.271 at time: 1.450\n",
+ "J_n integrated over the domain: 22.779 at time: 1.450\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.450\n",
+ "d (def. map) integrated over the domain: 500.016 at time: 1.450\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.450\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.450\n",
+ "\n",
+ "J integrated over the domain: 21.119 at time: 1.460\n",
+ "J_n integrated over the domain: 22.271 at time: 1.460\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.460\n",
+ "d (def. map) integrated over the domain: 450.001 at time: 1.460\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.460\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.460\n",
+ "\n"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "J integrated over the domain: 19.393 at time: 1.470\n",
+ "J_n integrated over the domain: 21.119 at time: 1.470\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.470\n",
+ "d (def. map) integrated over the domain: 380.093 at time: 1.470\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.470\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.470\n",
+ "\n",
+ "J integrated over the domain: 17.203 at time: 1.480\n",
+ "J_n integrated over the domain: 19.393 at time: 1.480\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.480\n",
+ "d (def. map) integrated over the domain: 299.941 at time: 1.480\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.480\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.480\n",
+ "\n",
+ "J integrated over the domain: 14.686 at time: 1.490\n",
+ "J_n integrated over the domain: 17.203 at time: 1.490\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.490\n",
+ "d (def. map) integrated over the domain: 219.674 at time: 1.490\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.490\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.490\n",
+ "\n",
+ "J integrated over the domain: 12.000 at time: 1.500\n",
+ "J_n integrated over the domain: 14.686 at time: 1.500\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.500\n",
+ "d (def. map) integrated over the domain: 148.000 at time: 1.500\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.500\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.500\n",
+ "\n",
+ "J integrated over the domain: 9.314 at time: 1.510\n",
+ "J_n integrated over the domain: 12.000 at time: 1.510\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.510\n",
+ "d (def. map) integrated over the domain: 90.753 at time: 1.510\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.510\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.510\n",
+ "\n",
+ "J integrated over the domain: 6.797 at time: 1.520\n",
+ "J_n integrated over the domain: 9.314 at time: 1.520\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.520\n",
+ "d (def. map) integrated over the domain: 50.200 at time: 1.520\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.520\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.520\n",
+ "\n",
+ "J integrated over the domain: 4.607 at time: 1.530\n",
+ "J_n integrated over the domain: 6.797 at time: 1.530\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.530\n",
+ "d (def. map) integrated over the domain: 25.223 at time: 1.530\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.530\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.530\n",
+ "\n",
+ "J integrated over the domain: 2.881 at time: 1.540\n",
+ "J_n integrated over the domain: 4.607 at time: 1.540\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.540\n",
+ "d (def. map) integrated over the domain: 12.302 at time: 1.540\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.540\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.540\n",
+ "\n",
+ "J integrated over the domain: 1.729 at time: 1.550\n",
+ "J_n integrated over the domain: 2.881 at time: 1.550\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.550\n",
+ "d (def. map) integrated over the domain: 6.988 at time: 1.550\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.550\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.550\n",
+ "\n",
+ "J integrated over the domain: 1.221 at time: 1.560\n",
+ "J_n integrated over the domain: 1.729 at time: 1.560\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.560\n",
+ "d (def. map) integrated over the domain: 5.492 at time: 1.560\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.560\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.560\n",
+ "\n",
+ "J integrated over the domain: 1.391 at time: 1.570\n",
+ "J_n integrated over the domain: 1.221 at time: 1.570\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.570\n",
+ "d (def. map) integrated over the domain: 5.936 at time: 1.570\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.570\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.570\n",
+ "\n",
+ "J integrated over the domain: 2.228 at time: 1.580\n",
+ "J_n integrated over the domain: 1.391 at time: 1.580\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.580\n",
+ "d (def. map) integrated over the domain: 8.963 at time: 1.580\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.580\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.580\n",
+ "\n",
+ "J integrated over the domain: 3.678 at time: 1.590\n",
+ "J_n integrated over the domain: 2.228 at time: 1.590\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.590\n",
+ "d (def. map) integrated over the domain: 17.531 at time: 1.590\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.590\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.590\n",
+ "\n",
+ "J integrated over the domain: 5.652 at time: 1.600\n",
+ "J_n integrated over the domain: 3.678 at time: 1.600\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.600\n",
+ "d (def. map) integrated over the domain: 35.944 at time: 1.600\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.600\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.600\n",
+ "\n",
+ "J integrated over the domain: 8.024 at time: 1.610\n",
+ "J_n integrated over the domain: 5.652 at time: 1.610\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.610\n",
+ "d (def. map) integrated over the domain: 68.389 at time: 1.610\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.610\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.610\n",
+ "\n",
+ "J integrated over the domain: 10.646 at time: 1.620\n",
+ "J_n integrated over the domain: 8.024 at time: 1.620\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.620\n",
+ "d (def. map) integrated over the domain: 117.346 at time: 1.620\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.620\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.620\n",
+ "\n",
+ "J integrated over the domain: 13.354 at time: 1.630\n",
+ "J_n integrated over the domain: 10.646 at time: 1.630\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.630\n",
+ "d (def. map) integrated over the domain: 182.319 at time: 1.630\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.630\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.630\n",
+ "\n",
+ "J integrated over the domain: 15.976 at time: 1.640\n",
+ "J_n integrated over the domain: 13.354 at time: 1.640\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.640\n",
+ "d (def. map) integrated over the domain: 259.224 at time: 1.640\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.640\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.640\n",
+ "\n",
+ "J integrated over the domain: 18.348 at time: 1.650\n",
+ "J_n integrated over the domain: 15.976 at time: 1.650\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.650\n",
+ "d (def. map) integrated over the domain: 340.652 at time: 1.650\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.650\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.650\n",
+ "\n",
+ "J integrated over the domain: 20.322 at time: 1.660\n",
+ "J_n integrated over the domain: 18.348 at time: 1.660\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.660\n",
+ "d (def. map) integrated over the domain: 416.965 at time: 1.660\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.660\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.660\n",
+ "\n",
+ "J integrated over the domain: 21.772 at time: 1.670\n",
+ "J_n integrated over the domain: 20.322 at time: 1.670\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.670\n",
+ "d (def. map) integrated over the domain: 478.026 at time: 1.670\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.670\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.670\n",
+ "\n",
+ "J integrated over the domain: 22.609 at time: 1.680\n",
+ "J_n integrated over the domain: 21.772 at time: 1.680\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.680\n",
+ "d (def. map) integrated over the domain: 515.153 at time: 1.680\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.680\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.680\n",
+ "\n",
+ "J integrated over the domain: 22.779 at time: 1.690\n",
+ "J_n integrated over the domain: 22.609 at time: 1.690\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.690\n",
+ "d (def. map) integrated over the domain: 522.869 at time: 1.690\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.690\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.690\n",
+ "\n",
+ "J integrated over the domain: 22.271 at time: 1.700\n",
+ "J_n integrated over the domain: 22.779 at time: 1.700\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.700\n",
+ "d (def. map) integrated over the domain: 500.016 at time: 1.700\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.700\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.700\n",
+ "\n",
+ "J integrated over the domain: 21.119 at time: 1.710\n",
+ "J_n integrated over the domain: 22.271 at time: 1.710\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.710\n",
+ "d (def. map) integrated over the domain: 450.001 at time: 1.710\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.710\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.710\n",
+ "\n"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "J integrated over the domain: 19.393 at time: 1.720\n",
+ "J_n integrated over the domain: 21.119 at time: 1.720\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.720\n",
+ "d (def. map) integrated over the domain: 380.093 at time: 1.720\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.720\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.720\n",
+ "\n",
+ "J integrated over the domain: 17.203 at time: 1.730\n",
+ "J_n integrated over the domain: 19.393 at time: 1.730\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.730\n",
+ "d (def. map) integrated over the domain: 299.941 at time: 1.730\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.730\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.730\n",
+ "\n",
+ "J integrated over the domain: 14.686 at time: 1.740\n",
+ "J_n integrated over the domain: 17.203 at time: 1.740\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.740\n",
+ "d (def. map) integrated over the domain: 219.674 at time: 1.740\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.740\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.740\n",
+ "\n",
+ "J integrated over the domain: 12.000 at time: 1.750\n",
+ "J_n integrated over the domain: 14.686 at time: 1.750\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.750\n",
+ "d (def. map) integrated over the domain: 148.000 at time: 1.750\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.750\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.750\n",
+ "\n",
+ "J integrated over the domain: 9.314 at time: 1.760\n",
+ "J_n integrated over the domain: 12.000 at time: 1.760\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.760\n",
+ "d (def. map) integrated over the domain: 90.753 at time: 1.760\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.760\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.760\n",
+ "\n",
+ "J integrated over the domain: 6.797 at time: 1.770\n",
+ "J_n integrated over the domain: 9.314 at time: 1.770\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.770\n",
+ "d (def. map) integrated over the domain: 50.200 at time: 1.770\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.770\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.770\n",
+ "\n",
+ "J integrated over the domain: 4.607 at time: 1.780\n",
+ "J_n integrated over the domain: 6.797 at time: 1.780\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.780\n",
+ "d (def. map) integrated over the domain: 25.223 at time: 1.780\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.780\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.780\n",
+ "\n",
+ "J integrated over the domain: 2.881 at time: 1.790\n",
+ "J_n integrated over the domain: 4.607 at time: 1.790\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.790\n",
+ "d (def. map) integrated over the domain: 12.302 at time: 1.790\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.790\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.790\n",
+ "\n",
+ "J integrated over the domain: 1.729 at time: 1.800\n",
+ "J_n integrated over the domain: 2.881 at time: 1.800\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.800\n",
+ "d (def. map) integrated over the domain: 6.988 at time: 1.800\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.800\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.800\n",
+ "\n",
+ "J integrated over the domain: 1.221 at time: 1.810\n",
+ "J_n integrated over the domain: 1.729 at time: 1.810\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.810\n",
+ "d (def. map) integrated over the domain: 5.492 at time: 1.810\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.810\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.810\n",
+ "\n",
+ "J integrated over the domain: 1.391 at time: 1.820\n",
+ "J_n integrated over the domain: 1.221 at time: 1.820\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.820\n",
+ "d (def. map) integrated over the domain: 5.936 at time: 1.820\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.820\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.820\n",
+ "\n",
+ "J integrated over the domain: 2.228 at time: 1.830\n",
+ "J_n integrated over the domain: 1.391 at time: 1.830\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.830\n",
+ "d (def. map) integrated over the domain: 8.963 at time: 1.830\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.830\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.830\n",
+ "\n",
+ "J integrated over the domain: 3.678 at time: 1.840\n",
+ "J_n integrated over the domain: 2.228 at time: 1.840\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.840\n",
+ "d (def. map) integrated over the domain: 17.531 at time: 1.840\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.840\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.840\n",
+ "\n",
+ "J integrated over the domain: 5.652 at time: 1.850\n",
+ "J_n integrated over the domain: 3.678 at time: 1.850\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.850\n",
+ "d (def. map) integrated over the domain: 35.944 at time: 1.850\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.850\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.850\n",
+ "\n",
+ "J integrated over the domain: 8.024 at time: 1.860\n",
+ "J_n integrated over the domain: 5.652 at time: 1.860\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.860\n",
+ "d (def. map) integrated over the domain: 68.389 at time: 1.860\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.860\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.860\n",
+ "\n",
+ "J integrated over the domain: 10.646 at time: 1.870\n",
+ "J_n integrated over the domain: 8.024 at time: 1.870\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.870\n",
+ "d (def. map) integrated over the domain: 117.346 at time: 1.870\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.870\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.870\n",
+ "\n",
+ "J integrated over the domain: 13.354 at time: 1.880\n",
+ "J_n integrated over the domain: 10.646 at time: 1.880\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.880\n",
+ "d (def. map) integrated over the domain: 182.319 at time: 1.880\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.880\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.880\n",
+ "\n",
+ "J integrated over the domain: 15.976 at time: 1.890\n",
+ "J_n integrated over the domain: 13.354 at time: 1.890\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.890\n",
+ "d (def. map) integrated over the domain: 259.224 at time: 1.890\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.890\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.890\n",
+ "\n",
+ "J integrated over the domain: 18.348 at time: 1.900\n",
+ "J_n integrated over the domain: 15.976 at time: 1.900\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.900\n",
+ "d (def. map) integrated over the domain: 340.652 at time: 1.900\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.900\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.900\n",
+ "\n",
+ "J integrated over the domain: 20.322 at time: 1.910\n",
+ "J_n integrated over the domain: 18.348 at time: 1.910\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.910\n",
+ "d (def. map) integrated over the domain: 416.965 at time: 1.910\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.910\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.910\n",
+ "\n",
+ "J integrated over the domain: 21.772 at time: 1.920\n",
+ "J_n integrated over the domain: 20.322 at time: 1.920\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.920\n",
+ "d (def. map) integrated over the domain: 478.026 at time: 1.920\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.920\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.920\n",
+ "\n",
+ "J integrated over the domain: 22.609 at time: 1.930\n",
+ "J_n integrated over the domain: 21.772 at time: 1.930\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.930\n",
+ "d (def. map) integrated over the domain: 515.153 at time: 1.930\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.930\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.930\n",
+ "\n",
+ "J integrated over the domain: 22.779 at time: 1.940\n",
+ "J_n integrated over the domain: 22.609 at time: 1.940\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.940\n",
+ "d (def. map) integrated over the domain: 522.869 at time: 1.940\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.940\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.940\n",
+ "\n",
+ "J integrated over the domain: 22.271 at time: 1.950\n",
+ "J_n integrated over the domain: 22.779 at time: 1.950\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.950\n",
+ "d (def. map) integrated over the domain: 500.016 at time: 1.950\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.950\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.950\n",
+ "\n"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "J integrated over the domain: 21.119 at time: 1.960\n",
+ "J_n integrated over the domain: 22.271 at time: 1.960\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.960\n",
+ "d (def. map) integrated over the domain: 450.001 at time: 1.960\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.960\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.960\n",
+ "\n",
+ "J integrated over the domain: 19.393 at time: 1.970\n",
+ "J_n integrated over the domain: 21.119 at time: 1.970\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.970\n",
+ "d (def. map) integrated over the domain: 380.093 at time: 1.970\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.970\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.970\n",
+ "\n",
+ "J integrated over the domain: 17.203 at time: 1.980\n",
+ "J_n integrated over the domain: 19.393 at time: 1.980\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.980\n",
+ "d (def. map) integrated over the domain: 299.941 at time: 1.980\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.980\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.980\n",
+ "\n",
+ "J integrated over the domain: 14.686 at time: 1.990\n",
+ "J_n integrated over the domain: 17.203 at time: 1.990\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.990\n",
+ "d (def. map) integrated over the domain: 219.674 at time: 1.990\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.990\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.990\n",
+ "\n",
+ "J integrated over the domain: 12.000 at time: 2.000\n",
+ "J_n integrated over the domain: 14.686 at time: 2.000\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 2.000\n",
+ "d (def. map) integrated over the domain: 148.000 at time: 2.000\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 2.000\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 2.000\n",
+ "\n",
+ "DoF for Velocity Space (U): 3298\n",
+ "DoF for Pressure Space (P): 1649\n",
+ "Solution Computed in 36.944 seconds\n",
+ "\n",
+ "----------------Computation Completed!----------------\n",
+ "\n",
+ "\n",
+ "----------------Simulations Done!----------------.\n",
+ "\n",
+ "Initializing testing of two deformation cases with input parameters:\n",
+ " Solver to use -solver_to_use- : LU\n",
+ " GCL-stabilization term -gcl_stab- : True\n",
+ " Evaluation of jacobian at n in time-derivate term -jac_at_n- : True\n",
+ " \n",
+ "\n",
+ "Initializing iNSE problem with Deformation type: High_Osc_exp\n",
+ "\n",
+ "\n",
+ "Setup with initial condition: True\n",
+ "Using a non-zero initial condition (2D-Gaussian) for the velocity field!\n",
+ "Using time-derivative term approximated with Jacobian at n...\n",
+ "Using LU Solver...\n",
+ "Starting iteration over time...\n",
+ "E (Energy) of initial velocity field: 0.01659 at time 0.000\n",
+ "\n",
+ "J integrated over the domain: 14.686 at time: 0.010\n",
+ "J_n integrated over the domain: 12.000 at time: 0.010\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.010\n",
+ "d (def. map) integrated over the domain: 219.674 at time: 0.010\n",
+ "Strain energy E( eps(|u|^2) ): 0.00013 at time 0.010\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.010\n",
+ "\n",
+ "J integrated over the domain: 17.203 at time: 0.020\n",
+ "J_n integrated over the domain: 14.686 at time: 0.020\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.020\n",
+ "d (def. map) integrated over the domain: 299.941 at time: 0.020\n",
+ "Strain energy E( eps(|u|^2) ): 0.00010 at time 0.020\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.020\n",
+ "\n",
+ "J integrated over the domain: 19.393 at time: 0.030\n",
+ "J_n integrated over the domain: 17.203 at time: 0.030\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.030\n",
+ "d (def. map) integrated over the domain: 380.093 at time: 0.030\n",
+ "Strain energy E( eps(|u|^2) ): 0.00008 at time 0.030\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.030\n",
+ "\n",
+ "J integrated over the domain: 21.119 at time: 0.040\n",
+ "J_n integrated over the domain: 19.393 at time: 0.040\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.040\n",
+ "d (def. map) integrated over the domain: 450.001 at time: 0.040\n",
+ "Strain energy E( eps(|u|^2) ): 0.00006 at time 0.040\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.040\n",
+ "\n",
+ "J integrated over the domain: 22.271 at time: 0.050\n",
+ "J_n integrated over the domain: 21.119 at time: 0.050\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.050\n",
+ "d (def. map) integrated over the domain: 500.016 at time: 0.050\n",
+ "Strain energy E( eps(|u|^2) ): 0.00006 at time 0.050\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.050\n",
+ "\n",
+ "J integrated over the domain: 22.779 at time: 0.060\n",
+ "J_n integrated over the domain: 22.271 at time: 0.060\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.060\n",
+ "d (def. map) integrated over the domain: 522.869 at time: 0.060\n",
+ "Strain energy E( eps(|u|^2) ): 0.00005 at time 0.060\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.060\n",
+ "\n",
+ "J integrated over the domain: 22.609 at time: 0.070\n",
+ "J_n integrated over the domain: 22.779 at time: 0.070\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.070\n",
+ "d (def. map) integrated over the domain: 515.153 at time: 0.070\n",
+ "Strain energy E( eps(|u|^2) ): 0.00005 at time 0.070\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.070\n",
+ "\n",
+ "J integrated over the domain: 21.772 at time: 0.080\n",
+ "J_n integrated over the domain: 22.609 at time: 0.080\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.080\n",
+ "d (def. map) integrated over the domain: 478.026 at time: 0.080\n",
+ "Strain energy E( eps(|u|^2) ): 0.00004 at time 0.080\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.080\n",
+ "\n",
+ "J integrated over the domain: 20.322 at time: 0.090\n",
+ "J_n integrated over the domain: 21.772 at time: 0.090\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.090\n",
+ "d (def. map) integrated over the domain: 416.965 at time: 0.090\n",
+ "Strain energy E( eps(|u|^2) ): 0.00004 at time 0.090\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.090\n",
+ "\n",
+ "J integrated over the domain: 18.348 at time: 0.100\n",
+ "J_n integrated over the domain: 20.322 at time: 0.100\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.100\n",
+ "d (def. map) integrated over the domain: 340.652 at time: 0.100\n",
+ "Strain energy E( eps(|u|^2) ): 0.00004 at time 0.100\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.100\n",
+ "\n",
+ "J integrated over the domain: 15.976 at time: 0.110\n",
+ "J_n integrated over the domain: 18.348 at time: 0.110\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.110\n",
+ "d (def. map) integrated over the domain: 259.224 at time: 0.110\n",
+ "Strain energy E( eps(|u|^2) ): 0.00004 at time 0.110\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.110\n",
+ "\n",
+ "J integrated over the domain: 13.354 at time: 0.120\n",
+ "J_n integrated over the domain: 15.976 at time: 0.120\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.120\n",
+ "d (def. map) integrated over the domain: 182.319 at time: 0.120\n",
+ "Strain energy E( eps(|u|^2) ): 0.00005 at time 0.120\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.120\n",
+ "\n",
+ "J integrated over the domain: 10.646 at time: 0.130\n",
+ "J_n integrated over the domain: 13.354 at time: 0.130\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.130\n",
+ "d (def. map) integrated over the domain: 117.346 at time: 0.130\n",
+ "Strain energy E( eps(|u|^2) ): 0.00012 at time 0.130\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.130\n",
+ "\n",
+ "J integrated over the domain: 8.024 at time: 0.140\n",
+ "J_n integrated over the domain: 10.646 at time: 0.140\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.140\n",
+ "d (def. map) integrated over the domain: 68.389 at time: 0.140\n",
+ "Strain energy E( eps(|u|^2) ): 0.00023 at time 0.140\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.140\n",
+ "\n",
+ "J integrated over the domain: 5.652 at time: 0.150\n",
+ "J_n integrated over the domain: 8.024 at time: 0.150\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.150\n",
+ "d (def. map) integrated over the domain: 35.944 at time: 0.150\n",
+ "Strain energy E( eps(|u|^2) ): 0.00030 at time 0.150\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.150\n",
+ "\n",
+ "J integrated over the domain: 3.678 at time: 0.160\n",
+ "J_n integrated over the domain: 5.652 at time: 0.160\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.160\n",
+ "d (def. map) integrated over the domain: 17.531 at time: 0.160\n",
+ "Strain energy E( eps(|u|^2) ): 0.00025 at time 0.160\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.160\n",
+ "\n",
+ "J integrated over the domain: 2.228 at time: 0.170\n",
+ "J_n integrated over the domain: 3.678 at time: 0.170\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.170\n",
+ "d (def. map) integrated over the domain: 8.963 at time: 0.170\n",
+ "Strain energy E( eps(|u|^2) ): 0.00012 at time 0.170\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.170\n",
+ "\n"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "J integrated over the domain: 1.391 at time: 0.180\n",
+ "J_n integrated over the domain: 2.228 at time: 0.180\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.180\n",
+ "d (def. map) integrated over the domain: 5.936 at time: 0.180\n",
+ "Strain energy E( eps(|u|^2) ): 0.00004 at time 0.180\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.180\n",
+ "\n",
+ "J integrated over the domain: 1.221 at time: 0.190\n",
+ "J_n integrated over the domain: 1.391 at time: 0.190\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.190\n",
+ "d (def. map) integrated over the domain: 5.492 at time: 0.190\n",
+ "Strain energy E( eps(|u|^2) ): 0.00001 at time 0.190\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.190\n",
+ "\n",
+ "J integrated over the domain: 1.729 at time: 0.200\n",
+ "J_n integrated over the domain: 1.221 at time: 0.200\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.200\n",
+ "d (def. map) integrated over the domain: 6.988 at time: 0.200\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.200\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.200\n",
+ "\n",
+ "J integrated over the domain: 2.881 at time: 0.210\n",
+ "J_n integrated over the domain: 1.729 at time: 0.210\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.210\n",
+ "d (def. map) integrated over the domain: 12.302 at time: 0.210\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.210\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.210\n",
+ "\n",
+ "J integrated over the domain: 4.607 at time: 0.220\n",
+ "J_n integrated over the domain: 2.881 at time: 0.220\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.220\n",
+ "d (def. map) integrated over the domain: 25.223 at time: 0.220\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.220\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.220\n",
+ "\n",
+ "J integrated over the domain: 6.797 at time: 0.230\n",
+ "J_n integrated over the domain: 4.607 at time: 0.230\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.230\n",
+ "d (def. map) integrated over the domain: 50.200 at time: 0.230\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.230\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.230\n",
+ "\n",
+ "J integrated over the domain: 9.314 at time: 0.240\n",
+ "J_n integrated over the domain: 6.797 at time: 0.240\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.240\n",
+ "d (def. map) integrated over the domain: 90.753 at time: 0.240\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.240\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.240\n",
+ "\n",
+ "J integrated over the domain: 12.000 at time: 0.250\n",
+ "J_n integrated over the domain: 9.314 at time: 0.250\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.250\n",
+ "d (def. map) integrated over the domain: 148.000 at time: 0.250\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.250\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.250\n",
+ "\n",
+ "J integrated over the domain: 14.686 at time: 0.260\n",
+ "J_n integrated over the domain: 12.000 at time: 0.260\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.260\n",
+ "d (def. map) integrated over the domain: 219.674 at time: 0.260\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.260\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.260\n",
+ "\n",
+ "J integrated over the domain: 17.203 at time: 0.270\n",
+ "J_n integrated over the domain: 14.686 at time: 0.270\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.270\n",
+ "d (def. map) integrated over the domain: 299.941 at time: 0.270\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.270\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.270\n",
+ "\n",
+ "J integrated over the domain: 19.393 at time: 0.280\n",
+ "J_n integrated over the domain: 17.203 at time: 0.280\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.280\n",
+ "d (def. map) integrated over the domain: 380.093 at time: 0.280\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.280\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.280\n",
+ "\n",
+ "J integrated over the domain: 21.119 at time: 0.290\n",
+ "J_n integrated over the domain: 19.393 at time: 0.290\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.290\n",
+ "d (def. map) integrated over the domain: 450.001 at time: 0.290\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.290\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.290\n",
+ "\n",
+ "J integrated over the domain: 22.271 at time: 0.300\n",
+ "J_n integrated over the domain: 21.119 at time: 0.300\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.300\n",
+ "d (def. map) integrated over the domain: 500.016 at time: 0.300\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.300\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.300\n",
+ "\n",
+ "J integrated over the domain: 22.779 at time: 0.310\n",
+ "J_n integrated over the domain: 22.271 at time: 0.310\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.310\n",
+ "d (def. map) integrated over the domain: 522.869 at time: 0.310\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.310\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.310\n",
+ "\n",
+ "J integrated over the domain: 22.609 at time: 0.320\n",
+ "J_n integrated over the domain: 22.779 at time: 0.320\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.320\n",
+ "d (def. map) integrated over the domain: 515.153 at time: 0.320\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.320\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.320\n",
+ "\n",
+ "J integrated over the domain: 21.772 at time: 0.330\n",
+ "J_n integrated over the domain: 22.609 at time: 0.330\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.330\n",
+ "d (def. map) integrated over the domain: 478.026 at time: 0.330\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.330\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.330\n",
+ "\n",
+ "J integrated over the domain: 20.322 at time: 0.340\n",
+ "J_n integrated over the domain: 21.772 at time: 0.340\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.340\n",
+ "d (def. map) integrated over the domain: 416.965 at time: 0.340\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.340\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.340\n",
+ "\n",
+ "J integrated over the domain: 18.348 at time: 0.350\n",
+ "J_n integrated over the domain: 20.322 at time: 0.350\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.350\n",
+ "d (def. map) integrated over the domain: 340.652 at time: 0.350\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.350\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.350\n",
+ "\n",
+ "J integrated over the domain: 15.976 at time: 0.360\n",
+ "J_n integrated over the domain: 18.348 at time: 0.360\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.360\n",
+ "d (def. map) integrated over the domain: 259.224 at time: 0.360\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.360\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.360\n",
+ "\n",
+ "J integrated over the domain: 13.354 at time: 0.370\n",
+ "J_n integrated over the domain: 15.976 at time: 0.370\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.370\n",
+ "d (def. map) integrated over the domain: 182.319 at time: 0.370\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.370\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.370\n",
+ "\n",
+ "J integrated over the domain: 10.646 at time: 0.380\n",
+ "J_n integrated over the domain: 13.354 at time: 0.380\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.380\n",
+ "d (def. map) integrated over the domain: 117.346 at time: 0.380\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.380\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.380\n",
+ "\n",
+ "J integrated over the domain: 8.024 at time: 0.390\n",
+ "J_n integrated over the domain: 10.646 at time: 0.390\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.390\n",
+ "d (def. map) integrated over the domain: 68.389 at time: 0.390\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.390\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.390\n",
+ "\n",
+ "J integrated over the domain: 5.652 at time: 0.400\n",
+ "J_n integrated over the domain: 8.024 at time: 0.400\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.400\n",
+ "d (def. map) integrated over the domain: 35.944 at time: 0.400\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.400\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.400\n",
+ "\n",
+ "J integrated over the domain: 3.678 at time: 0.410\n",
+ "J_n integrated over the domain: 5.652 at time: 0.410\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.410\n",
+ "d (def. map) integrated over the domain: 17.531 at time: 0.410\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.410\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.410\n",
+ "\n"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "J integrated over the domain: 2.228 at time: 0.420\n",
+ "J_n integrated over the domain: 3.678 at time: 0.420\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.420\n",
+ "d (def. map) integrated over the domain: 8.963 at time: 0.420\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.420\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.420\n",
+ "\n",
+ "J integrated over the domain: 1.391 at time: 0.430\n",
+ "J_n integrated over the domain: 2.228 at time: 0.430\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.430\n",
+ "d (def. map) integrated over the domain: 5.936 at time: 0.430\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.430\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.430\n",
+ "\n",
+ "J integrated over the domain: 1.221 at time: 0.440\n",
+ "J_n integrated over the domain: 1.391 at time: 0.440\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.440\n",
+ "d (def. map) integrated over the domain: 5.492 at time: 0.440\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.440\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.440\n",
+ "\n",
+ "J integrated over the domain: 1.729 at time: 0.450\n",
+ "J_n integrated over the domain: 1.221 at time: 0.450\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.450\n",
+ "d (def. map) integrated over the domain: 6.988 at time: 0.450\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.450\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.450\n",
+ "\n",
+ "J integrated over the domain: 2.881 at time: 0.460\n",
+ "J_n integrated over the domain: 1.729 at time: 0.460\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.460\n",
+ "d (def. map) integrated over the domain: 12.302 at time: 0.460\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.460\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.460\n",
+ "\n",
+ "J integrated over the domain: 4.607 at time: 0.470\n",
+ "J_n integrated over the domain: 2.881 at time: 0.470\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.470\n",
+ "d (def. map) integrated over the domain: 25.223 at time: 0.470\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.470\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.470\n",
+ "\n",
+ "J integrated over the domain: 6.797 at time: 0.480\n",
+ "J_n integrated over the domain: 4.607 at time: 0.480\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.480\n",
+ "d (def. map) integrated over the domain: 50.200 at time: 0.480\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.480\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.480\n",
+ "\n",
+ "J integrated over the domain: 9.314 at time: 0.490\n",
+ "J_n integrated over the domain: 6.797 at time: 0.490\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.490\n",
+ "d (def. map) integrated over the domain: 90.753 at time: 0.490\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.490\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.490\n",
+ "\n",
+ "J integrated over the domain: 12.000 at time: 0.500\n",
+ "J_n integrated over the domain: 9.314 at time: 0.500\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.500\n",
+ "d (def. map) integrated over the domain: 148.000 at time: 0.500\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.500\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.500\n",
+ "\n",
+ "J integrated over the domain: 14.686 at time: 0.510\n",
+ "J_n integrated over the domain: 12.000 at time: 0.510\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.510\n",
+ "d (def. map) integrated over the domain: 219.674 at time: 0.510\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.510\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.510\n",
+ "\n",
+ "J integrated over the domain: 17.203 at time: 0.520\n",
+ "J_n integrated over the domain: 14.686 at time: 0.520\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.520\n",
+ "d (def. map) integrated over the domain: 299.941 at time: 0.520\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.520\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.520\n",
+ "\n",
+ "J integrated over the domain: 19.393 at time: 0.530\n",
+ "J_n integrated over the domain: 17.203 at time: 0.530\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.530\n",
+ "d (def. map) integrated over the domain: 380.093 at time: 0.530\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.530\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.530\n",
+ "\n",
+ "J integrated over the domain: 21.119 at time: 0.540\n",
+ "J_n integrated over the domain: 19.393 at time: 0.540\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.540\n",
+ "d (def. map) integrated over the domain: 450.001 at time: 0.540\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.540\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.540\n",
+ "\n",
+ "J integrated over the domain: 22.271 at time: 0.550\n",
+ "J_n integrated over the domain: 21.119 at time: 0.550\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.550\n",
+ "d (def. map) integrated over the domain: 500.016 at time: 0.550\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.550\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.550\n",
+ "\n",
+ "J integrated over the domain: 22.779 at time: 0.560\n",
+ "J_n integrated over the domain: 22.271 at time: 0.560\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.560\n",
+ "d (def. map) integrated over the domain: 522.869 at time: 0.560\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.560\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.560\n",
+ "\n",
+ "J integrated over the domain: 22.609 at time: 0.570\n",
+ "J_n integrated over the domain: 22.779 at time: 0.570\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.570\n",
+ "d (def. map) integrated over the domain: 515.153 at time: 0.570\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.570\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.570\n",
+ "\n",
+ "J integrated over the domain: 21.772 at time: 0.580\n",
+ "J_n integrated over the domain: 22.609 at time: 0.580\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.580\n",
+ "d (def. map) integrated over the domain: 478.026 at time: 0.580\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.580\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.580\n",
+ "\n",
+ "J integrated over the domain: 20.322 at time: 0.590\n",
+ "J_n integrated over the domain: 21.772 at time: 0.590\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.590\n",
+ "d (def. map) integrated over the domain: 416.965 at time: 0.590\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.590\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.590\n",
+ "\n",
+ "J integrated over the domain: 18.348 at time: 0.600\n",
+ "J_n integrated over the domain: 20.322 at time: 0.600\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.600\n",
+ "d (def. map) integrated over the domain: 340.652 at time: 0.600\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.600\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.600\n",
+ "\n",
+ "J integrated over the domain: 15.976 at time: 0.610\n",
+ "J_n integrated over the domain: 18.348 at time: 0.610\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.610\n",
+ "d (def. map) integrated over the domain: 259.224 at time: 0.610\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.610\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.610\n",
+ "\n",
+ "J integrated over the domain: 13.354 at time: 0.620\n",
+ "J_n integrated over the domain: 15.976 at time: 0.620\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.620\n",
+ "d (def. map) integrated over the domain: 182.319 at time: 0.620\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.620\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.620\n",
+ "\n",
+ "J integrated over the domain: 10.646 at time: 0.630\n",
+ "J_n integrated over the domain: 13.354 at time: 0.630\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.630\n",
+ "d (def. map) integrated over the domain: 117.346 at time: 0.630\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.630\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.630\n",
+ "\n",
+ "J integrated over the domain: 8.024 at time: 0.640\n",
+ "J_n integrated over the domain: 10.646 at time: 0.640\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.640\n",
+ "d (def. map) integrated over the domain: 68.389 at time: 0.640\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.640\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.640\n",
+ "\n",
+ "J integrated over the domain: 5.652 at time: 0.650\n",
+ "J_n integrated over the domain: 8.024 at time: 0.650\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.650\n",
+ "d (def. map) integrated over the domain: 35.944 at time: 0.650\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.650\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.650\n",
+ "\n"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "J integrated over the domain: 3.678 at time: 0.660\n",
+ "J_n integrated over the domain: 5.652 at time: 0.660\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.660\n",
+ "d (def. map) integrated over the domain: 17.531 at time: 0.660\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.660\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.660\n",
+ "\n",
+ "J integrated over the domain: 2.228 at time: 0.670\n",
+ "J_n integrated over the domain: 3.678 at time: 0.670\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.670\n",
+ "d (def. map) integrated over the domain: 8.963 at time: 0.670\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.670\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.670\n",
+ "\n",
+ "J integrated over the domain: 1.391 at time: 0.680\n",
+ "J_n integrated over the domain: 2.228 at time: 0.680\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.680\n",
+ "d (def. map) integrated over the domain: 5.936 at time: 0.680\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.680\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.680\n",
+ "\n",
+ "J integrated over the domain: 1.221 at time: 0.690\n",
+ "J_n integrated over the domain: 1.391 at time: 0.690\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.690\n",
+ "d (def. map) integrated over the domain: 5.492 at time: 0.690\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.690\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.690\n",
+ "\n",
+ "J integrated over the domain: 1.729 at time: 0.700\n",
+ "J_n integrated over the domain: 1.221 at time: 0.700\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.700\n",
+ "d (def. map) integrated over the domain: 6.988 at time: 0.700\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.700\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.700\n",
+ "\n",
+ "J integrated over the domain: 2.881 at time: 0.710\n",
+ "J_n integrated over the domain: 1.729 at time: 0.710\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.710\n",
+ "d (def. map) integrated over the domain: 12.302 at time: 0.710\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.710\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.710\n",
+ "\n",
+ "J integrated over the domain: 4.607 at time: 0.720\n",
+ "J_n integrated over the domain: 2.881 at time: 0.720\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.720\n",
+ "d (def. map) integrated over the domain: 25.223 at time: 0.720\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.720\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.720\n",
+ "\n",
+ "J integrated over the domain: 6.797 at time: 0.730\n",
+ "J_n integrated over the domain: 4.607 at time: 0.730\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.730\n",
+ "d (def. map) integrated over the domain: 50.200 at time: 0.730\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.730\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.730\n",
+ "\n",
+ "J integrated over the domain: 9.314 at time: 0.740\n",
+ "J_n integrated over the domain: 6.797 at time: 0.740\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.740\n",
+ "d (def. map) integrated over the domain: 90.753 at time: 0.740\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.740\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.740\n",
+ "\n",
+ "J integrated over the domain: 12.000 at time: 0.750\n",
+ "J_n integrated over the domain: 9.314 at time: 0.750\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.750\n",
+ "d (def. map) integrated over the domain: 148.000 at time: 0.750\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.750\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.750\n",
+ "\n",
+ "J integrated over the domain: 14.686 at time: 0.760\n",
+ "J_n integrated over the domain: 12.000 at time: 0.760\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.760\n",
+ "d (def. map) integrated over the domain: 219.674 at time: 0.760\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.760\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.760\n",
+ "\n",
+ "J integrated over the domain: 17.203 at time: 0.770\n",
+ "J_n integrated over the domain: 14.686 at time: 0.770\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.770\n",
+ "d (def. map) integrated over the domain: 299.941 at time: 0.770\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.770\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.770\n",
+ "\n",
+ "J integrated over the domain: 19.393 at time: 0.780\n",
+ "J_n integrated over the domain: 17.203 at time: 0.780\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.780\n",
+ "d (def. map) integrated over the domain: 380.093 at time: 0.780\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.780\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.780\n",
+ "\n",
+ "J integrated over the domain: 21.119 at time: 0.790\n",
+ "J_n integrated over the domain: 19.393 at time: 0.790\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.790\n",
+ "d (def. map) integrated over the domain: 450.001 at time: 0.790\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.790\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.790\n",
+ "\n",
+ "J integrated over the domain: 22.271 at time: 0.800\n",
+ "J_n integrated over the domain: 21.119 at time: 0.800\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.800\n",
+ "d (def. map) integrated over the domain: 500.016 at time: 0.800\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.800\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.800\n",
+ "\n",
+ "J integrated over the domain: 22.779 at time: 0.810\n",
+ "J_n integrated over the domain: 22.271 at time: 0.810\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.810\n",
+ "d (def. map) integrated over the domain: 522.869 at time: 0.810\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.810\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.810\n",
+ "\n",
+ "J integrated over the domain: 22.609 at time: 0.820\n",
+ "J_n integrated over the domain: 22.779 at time: 0.820\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.820\n",
+ "d (def. map) integrated over the domain: 515.153 at time: 0.820\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.820\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.820\n",
+ "\n",
+ "J integrated over the domain: 21.772 at time: 0.830\n",
+ "J_n integrated over the domain: 22.609 at time: 0.830\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.830\n",
+ "d (def. map) integrated over the domain: 478.026 at time: 0.830\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.830\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.830\n",
+ "\n",
+ "J integrated over the domain: 20.322 at time: 0.840\n",
+ "J_n integrated over the domain: 21.772 at time: 0.840\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.840\n",
+ "d (def. map) integrated over the domain: 416.965 at time: 0.840\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.840\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.840\n",
+ "\n",
+ "J integrated over the domain: 18.348 at time: 0.850\n",
+ "J_n integrated over the domain: 20.322 at time: 0.850\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.850\n",
+ "d (def. map) integrated over the domain: 340.652 at time: 0.850\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.850\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.850\n",
+ "\n",
+ "J integrated over the domain: 15.976 at time: 0.860\n",
+ "J_n integrated over the domain: 18.348 at time: 0.860\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.860\n",
+ "d (def. map) integrated over the domain: 259.224 at time: 0.860\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.860\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.860\n",
+ "\n",
+ "J integrated over the domain: 13.354 at time: 0.870\n",
+ "J_n integrated over the domain: 15.976 at time: 0.870\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.870\n",
+ "d (def. map) integrated over the domain: 182.319 at time: 0.870\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.870\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.870\n",
+ "\n",
+ "J integrated over the domain: 10.646 at time: 0.880\n",
+ "J_n integrated over the domain: 13.354 at time: 0.880\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.880\n",
+ "d (def. map) integrated over the domain: 117.346 at time: 0.880\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.880\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.880\n",
+ "\n",
+ "J integrated over the domain: 8.024 at time: 0.890\n",
+ "J_n integrated over the domain: 10.646 at time: 0.890\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.890\n",
+ "d (def. map) integrated over the domain: 68.389 at time: 0.890\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.890\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.890\n",
+ "\n"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "J integrated over the domain: 5.652 at time: 0.900\n",
+ "J_n integrated over the domain: 8.024 at time: 0.900\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.900\n",
+ "d (def. map) integrated over the domain: 35.944 at time: 0.900\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.900\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.900\n",
+ "\n",
+ "J integrated over the domain: 3.678 at time: 0.910\n",
+ "J_n integrated over the domain: 5.652 at time: 0.910\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.910\n",
+ "d (def. map) integrated over the domain: 17.531 at time: 0.910\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.910\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.910\n",
+ "\n",
+ "J integrated over the domain: 2.228 at time: 0.920\n",
+ "J_n integrated over the domain: 3.678 at time: 0.920\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.920\n",
+ "d (def. map) integrated over the domain: 8.963 at time: 0.920\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.920\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.920\n",
+ "\n",
+ "J integrated over the domain: 1.391 at time: 0.930\n",
+ "J_n integrated over the domain: 2.228 at time: 0.930\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.930\n",
+ "d (def. map) integrated over the domain: 5.936 at time: 0.930\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.930\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.930\n",
+ "\n",
+ "J integrated over the domain: 1.221 at time: 0.940\n",
+ "J_n integrated over the domain: 1.391 at time: 0.940\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.940\n",
+ "d (def. map) integrated over the domain: 5.492 at time: 0.940\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.940\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.940\n",
+ "\n",
+ "J integrated over the domain: 1.729 at time: 0.950\n",
+ "J_n integrated over the domain: 1.221 at time: 0.950\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.950\n",
+ "d (def. map) integrated over the domain: 6.988 at time: 0.950\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.950\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.950\n",
+ "\n",
+ "J integrated over the domain: 2.881 at time: 0.960\n",
+ "J_n integrated over the domain: 1.729 at time: 0.960\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.960\n",
+ "d (def. map) integrated over the domain: 12.302 at time: 0.960\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.960\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.960\n",
+ "\n",
+ "J integrated over the domain: 4.607 at time: 0.970\n",
+ "J_n integrated over the domain: 2.881 at time: 0.970\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.970\n",
+ "d (def. map) integrated over the domain: 25.223 at time: 0.970\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.970\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.970\n",
+ "\n",
+ "J integrated over the domain: 6.797 at time: 0.980\n",
+ "J_n integrated over the domain: 4.607 at time: 0.980\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.980\n",
+ "d (def. map) integrated over the domain: 50.200 at time: 0.980\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.980\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.980\n",
+ "\n",
+ "J integrated over the domain: 9.314 at time: 0.990\n",
+ "J_n integrated over the domain: 6.797 at time: 0.990\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.990\n",
+ "d (def. map) integrated over the domain: 90.753 at time: 0.990\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.990\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.990\n",
+ "\n",
+ "J integrated over the domain: 12.000 at time: 1.000\n",
+ "J_n integrated over the domain: 9.314 at time: 1.000\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.000\n",
+ "d (def. map) integrated over the domain: 148.000 at time: 1.000\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.000\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.000\n",
+ "\n",
+ "J integrated over the domain: 14.686 at time: 1.010\n",
+ "J_n integrated over the domain: 12.000 at time: 1.010\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.010\n",
+ "d (def. map) integrated over the domain: 219.674 at time: 1.010\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.010\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.010\n",
+ "\n",
+ "J integrated over the domain: 17.203 at time: 1.020\n",
+ "J_n integrated over the domain: 14.686 at time: 1.020\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.020\n",
+ "d (def. map) integrated over the domain: 299.941 at time: 1.020\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.020\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.020\n",
+ "\n",
+ "J integrated over the domain: 19.393 at time: 1.030\n",
+ "J_n integrated over the domain: 17.203 at time: 1.030\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.030\n",
+ "d (def. map) integrated over the domain: 380.093 at time: 1.030\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.030\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.030\n",
+ "\n",
+ "J integrated over the domain: 21.119 at time: 1.040\n",
+ "J_n integrated over the domain: 19.393 at time: 1.040\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.040\n",
+ "d (def. map) integrated over the domain: 450.001 at time: 1.040\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.040\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.040\n",
+ "\n",
+ "J integrated over the domain: 22.271 at time: 1.050\n",
+ "J_n integrated over the domain: 21.119 at time: 1.050\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.050\n",
+ "d (def. map) integrated over the domain: 500.016 at time: 1.050\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.050\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.050\n",
+ "\n",
+ "J integrated over the domain: 22.779 at time: 1.060\n",
+ "J_n integrated over the domain: 22.271 at time: 1.060\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.060\n",
+ "d (def. map) integrated over the domain: 522.869 at time: 1.060\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.060\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.060\n",
+ "\n",
+ "J integrated over the domain: 22.609 at time: 1.070\n",
+ "J_n integrated over the domain: 22.779 at time: 1.070\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.070\n",
+ "d (def. map) integrated over the domain: 515.153 at time: 1.070\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.070\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.070\n",
+ "\n",
+ "J integrated over the domain: 21.772 at time: 1.080\n",
+ "J_n integrated over the domain: 22.609 at time: 1.080\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.080\n",
+ "d (def. map) integrated over the domain: 478.026 at time: 1.080\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.080\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.080\n",
+ "\n",
+ "J integrated over the domain: 20.322 at time: 1.090\n",
+ "J_n integrated over the domain: 21.772 at time: 1.090\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.090\n",
+ "d (def. map) integrated over the domain: 416.965 at time: 1.090\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.090\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.090\n",
+ "\n",
+ "J integrated over the domain: 18.348 at time: 1.100\n",
+ "J_n integrated over the domain: 20.322 at time: 1.100\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.100\n",
+ "d (def. map) integrated over the domain: 340.652 at time: 1.100\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.100\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.100\n",
+ "\n",
+ "J integrated over the domain: 15.976 at time: 1.110\n",
+ "J_n integrated over the domain: 18.348 at time: 1.110\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.110\n",
+ "d (def. map) integrated over the domain: 259.224 at time: 1.110\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.110\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.110\n",
+ "\n",
+ "J integrated over the domain: 13.354 at time: 1.120\n",
+ "J_n integrated over the domain: 15.976 at time: 1.120\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.120\n",
+ "d (def. map) integrated over the domain: 182.319 at time: 1.120\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.120\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.120\n",
+ "\n",
+ "J integrated over the domain: 10.646 at time: 1.130\n",
+ "J_n integrated over the domain: 13.354 at time: 1.130\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.130\n",
+ "d (def. map) integrated over the domain: 117.346 at time: 1.130\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.130\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.130\n",
+ "\n"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "J integrated over the domain: 8.024 at time: 1.140\n",
+ "J_n integrated over the domain: 10.646 at time: 1.140\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.140\n",
+ "d (def. map) integrated over the domain: 68.389 at time: 1.140\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.140\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.140\n",
+ "\n",
+ "J integrated over the domain: 5.652 at time: 1.150\n",
+ "J_n integrated over the domain: 8.024 at time: 1.150\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.150\n",
+ "d (def. map) integrated over the domain: 35.944 at time: 1.150\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.150\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.150\n",
+ "\n",
+ "J integrated over the domain: 3.678 at time: 1.160\n",
+ "J_n integrated over the domain: 5.652 at time: 1.160\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.160\n",
+ "d (def. map) integrated over the domain: 17.531 at time: 1.160\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.160\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.160\n",
+ "\n",
+ "J integrated over the domain: 2.228 at time: 1.170\n",
+ "J_n integrated over the domain: 3.678 at time: 1.170\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.170\n",
+ "d (def. map) integrated over the domain: 8.963 at time: 1.170\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.170\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.170\n",
+ "\n",
+ "J integrated over the domain: 1.391 at time: 1.180\n",
+ "J_n integrated over the domain: 2.228 at time: 1.180\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.180\n",
+ "d (def. map) integrated over the domain: 5.936 at time: 1.180\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.180\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.180\n",
+ "\n",
+ "J integrated over the domain: 1.221 at time: 1.190\n",
+ "J_n integrated over the domain: 1.391 at time: 1.190\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.190\n",
+ "d (def. map) integrated over the domain: 5.492 at time: 1.190\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.190\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.190\n",
+ "\n",
+ "J integrated over the domain: 1.729 at time: 1.200\n",
+ "J_n integrated over the domain: 1.221 at time: 1.200\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.200\n",
+ "d (def. map) integrated over the domain: 6.988 at time: 1.200\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.200\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.200\n",
+ "\n",
+ "J integrated over the domain: 2.881 at time: 1.210\n",
+ "J_n integrated over the domain: 1.729 at time: 1.210\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.210\n",
+ "d (def. map) integrated over the domain: 12.302 at time: 1.210\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.210\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.210\n",
+ "\n",
+ "J integrated over the domain: 4.607 at time: 1.220\n",
+ "J_n integrated over the domain: 2.881 at time: 1.220\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.220\n",
+ "d (def. map) integrated over the domain: 25.223 at time: 1.220\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.220\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.220\n",
+ "\n",
+ "J integrated over the domain: 6.797 at time: 1.230\n",
+ "J_n integrated over the domain: 4.607 at time: 1.230\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.230\n",
+ "d (def. map) integrated over the domain: 50.200 at time: 1.230\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.230\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.230\n",
+ "\n",
+ "J integrated over the domain: 9.314 at time: 1.240\n",
+ "J_n integrated over the domain: 6.797 at time: 1.240\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.240\n",
+ "d (def. map) integrated over the domain: 90.753 at time: 1.240\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.240\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.240\n",
+ "\n",
+ "J integrated over the domain: 12.000 at time: 1.250\n",
+ "J_n integrated over the domain: 9.314 at time: 1.250\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.250\n",
+ "d (def. map) integrated over the domain: 148.000 at time: 1.250\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.250\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.250\n",
+ "\n",
+ "J integrated over the domain: 14.686 at time: 1.260\n",
+ "J_n integrated over the domain: 12.000 at time: 1.260\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.260\n",
+ "d (def. map) integrated over the domain: 219.674 at time: 1.260\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.260\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.260\n",
+ "\n",
+ "J integrated over the domain: 17.203 at time: 1.270\n",
+ "J_n integrated over the domain: 14.686 at time: 1.270\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.270\n",
+ "d (def. map) integrated over the domain: 299.941 at time: 1.270\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.270\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.270\n",
+ "\n",
+ "J integrated over the domain: 19.393 at time: 1.280\n",
+ "J_n integrated over the domain: 17.203 at time: 1.280\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.280\n",
+ "d (def. map) integrated over the domain: 380.093 at time: 1.280\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.280\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.280\n",
+ "\n",
+ "J integrated over the domain: 21.119 at time: 1.290\n",
+ "J_n integrated over the domain: 19.393 at time: 1.290\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.290\n",
+ "d (def. map) integrated over the domain: 450.001 at time: 1.290\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.290\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.290\n",
+ "\n",
+ "J integrated over the domain: 22.271 at time: 1.300\n",
+ "J_n integrated over the domain: 21.119 at time: 1.300\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.300\n",
+ "d (def. map) integrated over the domain: 500.016 at time: 1.300\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.300\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.300\n",
+ "\n",
+ "J integrated over the domain: 22.779 at time: 1.310\n",
+ "J_n integrated over the domain: 22.271 at time: 1.310\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.310\n",
+ "d (def. map) integrated over the domain: 522.869 at time: 1.310\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.310\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.310\n",
+ "\n",
+ "J integrated over the domain: 22.609 at time: 1.320\n",
+ "J_n integrated over the domain: 22.779 at time: 1.320\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.320\n",
+ "d (def. map) integrated over the domain: 515.153 at time: 1.320\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.320\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.320\n",
+ "\n",
+ "J integrated over the domain: 21.772 at time: 1.330\n",
+ "J_n integrated over the domain: 22.609 at time: 1.330\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.330\n",
+ "d (def. map) integrated over the domain: 478.026 at time: 1.330\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.330\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.330\n",
+ "\n",
+ "J integrated over the domain: 20.322 at time: 1.340\n",
+ "J_n integrated over the domain: 21.772 at time: 1.340\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.340\n",
+ "d (def. map) integrated over the domain: 416.965 at time: 1.340\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.340\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.340\n",
+ "\n",
+ "J integrated over the domain: 18.348 at time: 1.350\n",
+ "J_n integrated over the domain: 20.322 at time: 1.350\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.350\n",
+ "d (def. map) integrated over the domain: 340.652 at time: 1.350\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.350\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.350\n",
+ "\n",
+ "J integrated over the domain: 15.976 at time: 1.360\n",
+ "J_n integrated over the domain: 18.348 at time: 1.360\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.360\n",
+ "d (def. map) integrated over the domain: 259.224 at time: 1.360\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.360\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.360\n",
+ "\n",
+ "J integrated over the domain: 13.354 at time: 1.370\n",
+ "J_n integrated over the domain: 15.976 at time: 1.370\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.370\n",
+ "d (def. map) integrated over the domain: 182.319 at time: 1.370\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.370\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.370\n",
+ "\n"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "J integrated over the domain: 10.646 at time: 1.380\n",
+ "J_n integrated over the domain: 13.354 at time: 1.380\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.380\n",
+ "d (def. map) integrated over the domain: 117.346 at time: 1.380\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.380\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.380\n",
+ "\n",
+ "J integrated over the domain: 8.024 at time: 1.390\n",
+ "J_n integrated over the domain: 10.646 at time: 1.390\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.390\n",
+ "d (def. map) integrated over the domain: 68.389 at time: 1.390\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.390\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.390\n",
+ "\n",
+ "J integrated over the domain: 5.652 at time: 1.400\n",
+ "J_n integrated over the domain: 8.024 at time: 1.400\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.400\n",
+ "d (def. map) integrated over the domain: 35.944 at time: 1.400\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.400\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.400\n",
+ "\n",
+ "J integrated over the domain: 3.678 at time: 1.410\n",
+ "J_n integrated over the domain: 5.652 at time: 1.410\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.410\n",
+ "d (def. map) integrated over the domain: 17.531 at time: 1.410\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.410\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.410\n",
+ "\n",
+ "J integrated over the domain: 2.228 at time: 1.420\n",
+ "J_n integrated over the domain: 3.678 at time: 1.420\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.420\n",
+ "d (def. map) integrated over the domain: 8.963 at time: 1.420\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.420\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.420\n",
+ "\n",
+ "J integrated over the domain: 1.391 at time: 1.430\n",
+ "J_n integrated over the domain: 2.228 at time: 1.430\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.430\n",
+ "d (def. map) integrated over the domain: 5.936 at time: 1.430\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.430\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.430\n",
+ "\n",
+ "J integrated over the domain: 1.221 at time: 1.440\n",
+ "J_n integrated over the domain: 1.391 at time: 1.440\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.440\n",
+ "d (def. map) integrated over the domain: 5.492 at time: 1.440\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.440\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.440\n",
+ "\n",
+ "J integrated over the domain: 1.729 at time: 1.450\n",
+ "J_n integrated over the domain: 1.221 at time: 1.450\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.450\n",
+ "d (def. map) integrated over the domain: 6.988 at time: 1.450\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.450\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.450\n",
+ "\n",
+ "J integrated over the domain: 2.881 at time: 1.460\n",
+ "J_n integrated over the domain: 1.729 at time: 1.460\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.460\n",
+ "d (def. map) integrated over the domain: 12.302 at time: 1.460\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.460\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.460\n",
+ "\n",
+ "J integrated over the domain: 4.607 at time: 1.470\n",
+ "J_n integrated over the domain: 2.881 at time: 1.470\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.470\n",
+ "d (def. map) integrated over the domain: 25.223 at time: 1.470\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.470\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.470\n",
+ "\n",
+ "J integrated over the domain: 6.797 at time: 1.480\n",
+ "J_n integrated over the domain: 4.607 at time: 1.480\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.480\n",
+ "d (def. map) integrated over the domain: 50.200 at time: 1.480\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.480\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.480\n",
+ "\n",
+ "J integrated over the domain: 9.314 at time: 1.490\n",
+ "J_n integrated over the domain: 6.797 at time: 1.490\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.490\n",
+ "d (def. map) integrated over the domain: 90.753 at time: 1.490\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.490\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.490\n",
+ "\n",
+ "J integrated over the domain: 12.000 at time: 1.500\n",
+ "J_n integrated over the domain: 9.314 at time: 1.500\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.500\n",
+ "d (def. map) integrated over the domain: 148.000 at time: 1.500\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.500\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.500\n",
+ "\n",
+ "J integrated over the domain: 14.686 at time: 1.510\n",
+ "J_n integrated over the domain: 12.000 at time: 1.510\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.510\n",
+ "d (def. map) integrated over the domain: 219.674 at time: 1.510\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.510\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.510\n",
+ "\n",
+ "J integrated over the domain: 17.203 at time: 1.520\n",
+ "J_n integrated over the domain: 14.686 at time: 1.520\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.520\n",
+ "d (def. map) integrated over the domain: 299.941 at time: 1.520\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.520\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.520\n",
+ "\n",
+ "J integrated over the domain: 19.393 at time: 1.530\n",
+ "J_n integrated over the domain: 17.203 at time: 1.530\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.530\n",
+ "d (def. map) integrated over the domain: 380.093 at time: 1.530\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.530\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.530\n",
+ "\n",
+ "J integrated over the domain: 21.119 at time: 1.540\n",
+ "J_n integrated over the domain: 19.393 at time: 1.540\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.540\n",
+ "d (def. map) integrated over the domain: 450.001 at time: 1.540\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.540\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.540\n",
+ "\n",
+ "J integrated over the domain: 22.271 at time: 1.550\n",
+ "J_n integrated over the domain: 21.119 at time: 1.550\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.550\n",
+ "d (def. map) integrated over the domain: 500.016 at time: 1.550\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.550\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.550\n",
+ "\n",
+ "J integrated over the domain: 22.779 at time: 1.560\n",
+ "J_n integrated over the domain: 22.271 at time: 1.560\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.560\n",
+ "d (def. map) integrated over the domain: 522.869 at time: 1.560\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.560\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.560\n",
+ "\n",
+ "J integrated over the domain: 22.609 at time: 1.570\n",
+ "J_n integrated over the domain: 22.779 at time: 1.570\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.570\n",
+ "d (def. map) integrated over the domain: 515.153 at time: 1.570\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.570\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.570\n",
+ "\n",
+ "J integrated over the domain: 21.772 at time: 1.580\n",
+ "J_n integrated over the domain: 22.609 at time: 1.580\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.580\n",
+ "d (def. map) integrated over the domain: 478.026 at time: 1.580\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.580\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.580\n",
+ "\n",
+ "J integrated over the domain: 20.322 at time: 1.590\n",
+ "J_n integrated over the domain: 21.772 at time: 1.590\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.590\n",
+ "d (def. map) integrated over the domain: 416.965 at time: 1.590\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.590\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.590\n",
+ "\n",
+ "J integrated over the domain: 18.348 at time: 1.600\n",
+ "J_n integrated over the domain: 20.322 at time: 1.600\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.600\n",
+ "d (def. map) integrated over the domain: 340.652 at time: 1.600\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.600\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.600\n",
+ "\n",
+ "J integrated over the domain: 15.976 at time: 1.610\n",
+ "J_n integrated over the domain: 18.348 at time: 1.610\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.610\n",
+ "d (def. map) integrated over the domain: 259.224 at time: 1.610\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.610\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.610\n",
+ "\n"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "J integrated over the domain: 13.354 at time: 1.620\n",
+ "J_n integrated over the domain: 15.976 at time: 1.620\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.620\n",
+ "d (def. map) integrated over the domain: 182.319 at time: 1.620\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.620\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.620\n",
+ "\n",
+ "J integrated over the domain: 10.646 at time: 1.630\n",
+ "J_n integrated over the domain: 13.354 at time: 1.630\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.630\n",
+ "d (def. map) integrated over the domain: 117.346 at time: 1.630\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.630\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.630\n",
+ "\n",
+ "J integrated over the domain: 8.024 at time: 1.640\n",
+ "J_n integrated over the domain: 10.646 at time: 1.640\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.640\n",
+ "d (def. map) integrated over the domain: 68.389 at time: 1.640\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.640\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.640\n",
+ "\n",
+ "J integrated over the domain: 5.652 at time: 1.650\n",
+ "J_n integrated over the domain: 8.024 at time: 1.650\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.650\n",
+ "d (def. map) integrated over the domain: 35.944 at time: 1.650\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.650\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.650\n",
+ "\n",
+ "J integrated over the domain: 3.678 at time: 1.660\n",
+ "J_n integrated over the domain: 5.652 at time: 1.660\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.660\n",
+ "d (def. map) integrated over the domain: 17.531 at time: 1.660\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.660\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.660\n",
+ "\n",
+ "J integrated over the domain: 2.228 at time: 1.670\n",
+ "J_n integrated over the domain: 3.678 at time: 1.670\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.670\n",
+ "d (def. map) integrated over the domain: 8.963 at time: 1.670\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.670\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.670\n",
+ "\n",
+ "J integrated over the domain: 1.391 at time: 1.680\n",
+ "J_n integrated over the domain: 2.228 at time: 1.680\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.680\n",
+ "d (def. map) integrated over the domain: 5.936 at time: 1.680\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.680\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.680\n",
+ "\n",
+ "J integrated over the domain: 1.221 at time: 1.690\n",
+ "J_n integrated over the domain: 1.391 at time: 1.690\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.690\n",
+ "d (def. map) integrated over the domain: 5.492 at time: 1.690\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.690\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.690\n",
+ "\n",
+ "J integrated over the domain: 1.729 at time: 1.700\n",
+ "J_n integrated over the domain: 1.221 at time: 1.700\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.700\n",
+ "d (def. map) integrated over the domain: 6.988 at time: 1.700\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.700\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.700\n",
+ "\n",
+ "J integrated over the domain: 2.881 at time: 1.710\n",
+ "J_n integrated over the domain: 1.729 at time: 1.710\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.710\n",
+ "d (def. map) integrated over the domain: 12.302 at time: 1.710\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.710\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.710\n",
+ "\n",
+ "J integrated over the domain: 4.607 at time: 1.720\n",
+ "J_n integrated over the domain: 2.881 at time: 1.720\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.720\n",
+ "d (def. map) integrated over the domain: 25.223 at time: 1.720\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.720\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.720\n",
+ "\n",
+ "J integrated over the domain: 6.797 at time: 1.730\n",
+ "J_n integrated over the domain: 4.607 at time: 1.730\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.730\n",
+ "d (def. map) integrated over the domain: 50.200 at time: 1.730\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.730\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.730\n",
+ "\n",
+ "J integrated over the domain: 9.314 at time: 1.740\n",
+ "J_n integrated over the domain: 6.797 at time: 1.740\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.740\n",
+ "d (def. map) integrated over the domain: 90.753 at time: 1.740\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.740\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.740\n",
+ "\n",
+ "J integrated over the domain: 12.000 at time: 1.750\n",
+ "J_n integrated over the domain: 9.314 at time: 1.750\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.750\n",
+ "d (def. map) integrated over the domain: 148.000 at time: 1.750\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.750\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.750\n",
+ "\n",
+ "J integrated over the domain: 14.686 at time: 1.760\n",
+ "J_n integrated over the domain: 12.000 at time: 1.760\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.760\n",
+ "d (def. map) integrated over the domain: 219.674 at time: 1.760\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.760\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.760\n",
+ "\n",
+ "J integrated over the domain: 17.203 at time: 1.770\n",
+ "J_n integrated over the domain: 14.686 at time: 1.770\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.770\n",
+ "d (def. map) integrated over the domain: 299.941 at time: 1.770\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.770\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.770\n",
+ "\n",
+ "J integrated over the domain: 19.393 at time: 1.780\n",
+ "J_n integrated over the domain: 17.203 at time: 1.780\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.780\n",
+ "d (def. map) integrated over the domain: 380.093 at time: 1.780\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.780\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.780\n",
+ "\n",
+ "J integrated over the domain: 21.119 at time: 1.790\n",
+ "J_n integrated over the domain: 19.393 at time: 1.790\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.790\n",
+ "d (def. map) integrated over the domain: 450.001 at time: 1.790\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.790\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.790\n",
+ "\n",
+ "J integrated over the domain: 22.271 at time: 1.800\n",
+ "J_n integrated over the domain: 21.119 at time: 1.800\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.800\n",
+ "d (def. map) integrated over the domain: 500.016 at time: 1.800\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.800\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.800\n",
+ "\n",
+ "J integrated over the domain: 22.779 at time: 1.810\n",
+ "J_n integrated over the domain: 22.271 at time: 1.810\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.810\n",
+ "d (def. map) integrated over the domain: 522.869 at time: 1.810\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.810\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.810\n",
+ "\n",
+ "J integrated over the domain: 22.609 at time: 1.820\n",
+ "J_n integrated over the domain: 22.779 at time: 1.820\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.820\n",
+ "d (def. map) integrated over the domain: 515.153 at time: 1.820\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.820\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.820\n",
+ "\n",
+ "J integrated over the domain: 21.772 at time: 1.830\n",
+ "J_n integrated over the domain: 22.609 at time: 1.830\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.830\n",
+ "d (def. map) integrated over the domain: 478.026 at time: 1.830\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.830\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.830\n",
+ "\n",
+ "J integrated over the domain: 20.322 at time: 1.840\n",
+ "J_n integrated over the domain: 21.772 at time: 1.840\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.840\n",
+ "d (def. map) integrated over the domain: 416.965 at time: 1.840\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.840\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.840\n",
+ "\n",
+ "J integrated over the domain: 18.348 at time: 1.850\n",
+ "J_n integrated over the domain: 20.322 at time: 1.850\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.850\n",
+ "d (def. map) integrated over the domain: 340.652 at time: 1.850\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.850\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.850\n",
+ "\n"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "J integrated over the domain: 15.976 at time: 1.860\n",
+ "J_n integrated over the domain: 18.348 at time: 1.860\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.860\n",
+ "d (def. map) integrated over the domain: 259.224 at time: 1.860\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.860\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.860\n",
+ "\n",
+ "J integrated over the domain: 13.354 at time: 1.870\n",
+ "J_n integrated over the domain: 15.976 at time: 1.870\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.870\n",
+ "d (def. map) integrated over the domain: 182.319 at time: 1.870\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.870\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.870\n",
+ "\n",
+ "J integrated over the domain: 10.646 at time: 1.880\n",
+ "J_n integrated over the domain: 13.354 at time: 1.880\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.880\n",
+ "d (def. map) integrated over the domain: 117.346 at time: 1.880\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.880\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.880\n",
+ "\n",
+ "J integrated over the domain: 8.024 at time: 1.890\n",
+ "J_n integrated over the domain: 10.646 at time: 1.890\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.890\n",
+ "d (def. map) integrated over the domain: 68.389 at time: 1.890\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.890\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.890\n",
+ "\n",
+ "J integrated over the domain: 5.652 at time: 1.900\n",
+ "J_n integrated over the domain: 8.024 at time: 1.900\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.900\n",
+ "d (def. map) integrated over the domain: 35.944 at time: 1.900\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.900\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.900\n",
+ "\n",
+ "J integrated over the domain: 3.678 at time: 1.910\n",
+ "J_n integrated over the domain: 5.652 at time: 1.910\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.910\n",
+ "d (def. map) integrated over the domain: 17.531 at time: 1.910\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.910\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.910\n",
+ "\n",
+ "J integrated over the domain: 2.228 at time: 1.920\n",
+ "J_n integrated over the domain: 3.678 at time: 1.920\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.920\n",
+ "d (def. map) integrated over the domain: 8.963 at time: 1.920\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.920\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.920\n",
+ "\n",
+ "J integrated over the domain: 1.391 at time: 1.930\n",
+ "J_n integrated over the domain: 2.228 at time: 1.930\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.930\n",
+ "d (def. map) integrated over the domain: 5.936 at time: 1.930\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.930\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.930\n",
+ "\n",
+ "J integrated over the domain: 1.221 at time: 1.940\n",
+ "J_n integrated over the domain: 1.391 at time: 1.940\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.940\n",
+ "d (def. map) integrated over the domain: 5.492 at time: 1.940\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.940\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.940\n",
+ "\n",
+ "J integrated over the domain: 1.729 at time: 1.950\n",
+ "J_n integrated over the domain: 1.221 at time: 1.950\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.950\n",
+ "d (def. map) integrated over the domain: 6.988 at time: 1.950\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.950\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.950\n",
+ "\n",
+ "J integrated over the domain: 2.881 at time: 1.960\n",
+ "J_n integrated over the domain: 1.729 at time: 1.960\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.960\n",
+ "d (def. map) integrated over the domain: 12.302 at time: 1.960\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.960\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.960\n",
+ "\n",
+ "J integrated over the domain: 4.607 at time: 1.970\n",
+ "J_n integrated over the domain: 2.881 at time: 1.970\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.970\n",
+ "d (def. map) integrated over the domain: 25.223 at time: 1.970\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.970\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.970\n",
+ "\n",
+ "J integrated over the domain: 6.797 at time: 1.980\n",
+ "J_n integrated over the domain: 4.607 at time: 1.980\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.980\n",
+ "d (def. map) integrated over the domain: 50.200 at time: 1.980\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.980\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.980\n",
+ "\n",
+ "J integrated over the domain: 9.314 at time: 1.990\n",
+ "J_n integrated over the domain: 6.797 at time: 1.990\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.990\n",
+ "d (def. map) integrated over the domain: 90.753 at time: 1.990\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.990\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.990\n",
+ "\n",
+ "J integrated over the domain: 12.000 at time: 2.000\n",
+ "J_n integrated over the domain: 9.314 at time: 2.000\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 2.000\n",
+ "d (def. map) integrated over the domain: 148.000 at time: 2.000\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 2.000\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 2.000\n",
+ "\n",
+ "Number of degrees of freedom: 14387\n",
+ "Solution Computed in 103.99 seconds\n",
+ "\n",
+ "----------------Computation Completed!----------------\n",
+ "\n",
+ "\n",
+ "Initializing iNSE problem with Deformation type: High_Osc_con\n",
+ "\n",
+ "\n",
+ "Setup with initial condition: True\n",
+ "Using a non-zero initial condition (2D-Gaussian) for the velocity field!\n",
+ "Using time-derivative term approximated with Jacobian at n...\n",
+ "Using LU Solver...\n",
+ "Starting iteration over time...\n",
+ "E (Energy) of initial velocity field: 0.01659 at time 0.000\n",
+ "\n",
+ "J integrated over the domain: 9.314 at time: 0.010\n",
+ "J_n integrated over the domain: 12.000 at time: 0.010\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.010\n",
+ "d (def. map) integrated over the domain: 90.753 at time: 0.010\n",
+ "Strain energy E( eps(|u|^2) ): 0.00045 at time 0.010\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.010\n",
+ "\n",
+ "J integrated over the domain: 6.797 at time: 0.020\n",
+ "J_n integrated over the domain: 9.314 at time: 0.020\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.020\n",
+ "d (def. map) integrated over the domain: 50.200 at time: 0.020\n",
+ "Strain energy E( eps(|u|^2) ): 0.00068 at time 0.020\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.020\n",
+ "\n",
+ "J integrated over the domain: 4.607 at time: 0.030\n",
+ "J_n integrated over the domain: 6.797 at time: 0.030\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.030\n",
+ "d (def. map) integrated over the domain: 25.223 at time: 0.030\n",
+ "Strain energy E( eps(|u|^2) ): 0.00058 at time 0.030\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.030\n",
+ "\n",
+ "J integrated over the domain: 2.881 at time: 0.040\n",
+ "J_n integrated over the domain: 4.607 at time: 0.040\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.040\n",
+ "d (def. map) integrated over the domain: 12.302 at time: 0.040\n",
+ "Strain energy E( eps(|u|^2) ): 0.00030 at time 0.040\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.040\n",
+ "\n",
+ "J integrated over the domain: 1.729 at time: 0.050\n",
+ "J_n integrated over the domain: 2.881 at time: 0.050\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.050\n",
+ "d (def. map) integrated over the domain: 6.988 at time: 0.050\n",
+ "Strain energy E( eps(|u|^2) ): 0.00010 at time 0.050\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.050\n",
+ "\n",
+ "J integrated over the domain: 1.221 at time: 0.060\n",
+ "J_n integrated over the domain: 1.729 at time: 0.060\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.060\n",
+ "d (def. map) integrated over the domain: 5.492 at time: 0.060\n",
+ "Strain energy E( eps(|u|^2) ): 0.00002 at time 0.060\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.060\n",
+ "\n",
+ "J integrated over the domain: 1.391 at time: 0.070\n",
+ "J_n integrated over the domain: 1.221 at time: 0.070\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.070\n",
+ "d (def. map) integrated over the domain: 5.936 at time: 0.070\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.070\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.070\n",
+ "\n",
+ "J integrated over the domain: 2.228 at time: 0.080\n",
+ "J_n integrated over the domain: 1.391 at time: 0.080\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.080\n",
+ "d (def. map) integrated over the domain: 8.963 at time: 0.080\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.080\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.080\n",
+ "\n"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "J integrated over the domain: 3.678 at time: 0.090\n",
+ "J_n integrated over the domain: 2.228 at time: 0.090\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.090\n",
+ "d (def. map) integrated over the domain: 17.531 at time: 0.090\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.090\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.090\n",
+ "\n",
+ "J integrated over the domain: 5.652 at time: 0.100\n",
+ "J_n integrated over the domain: 3.678 at time: 0.100\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.100\n",
+ "d (def. map) integrated over the domain: 35.944 at time: 0.100\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.100\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.100\n",
+ "\n",
+ "J integrated over the domain: 8.024 at time: 0.110\n",
+ "J_n integrated over the domain: 5.652 at time: 0.110\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.110\n",
+ "d (def. map) integrated over the domain: 68.389 at time: 0.110\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.110\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.110\n",
+ "\n",
+ "J integrated over the domain: 10.646 at time: 0.120\n",
+ "J_n integrated over the domain: 8.024 at time: 0.120\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.120\n",
+ "d (def. map) integrated over the domain: 117.346 at time: 0.120\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.120\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.120\n",
+ "\n",
+ "J integrated over the domain: 13.354 at time: 0.130\n",
+ "J_n integrated over the domain: 10.646 at time: 0.130\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.130\n",
+ "d (def. map) integrated over the domain: 182.319 at time: 0.130\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.130\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.130\n",
+ "\n",
+ "J integrated over the domain: 15.976 at time: 0.140\n",
+ "J_n integrated over the domain: 13.354 at time: 0.140\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.140\n",
+ "d (def. map) integrated over the domain: 259.224 at time: 0.140\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.140\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.140\n",
+ "\n",
+ "J integrated over the domain: 18.348 at time: 0.150\n",
+ "J_n integrated over the domain: 15.976 at time: 0.150\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.150\n",
+ "d (def. map) integrated over the domain: 340.652 at time: 0.150\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.150\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.150\n",
+ "\n",
+ "J integrated over the domain: 20.322 at time: 0.160\n",
+ "J_n integrated over the domain: 18.348 at time: 0.160\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.160\n",
+ "d (def. map) integrated over the domain: 416.965 at time: 0.160\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.160\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.160\n",
+ "\n",
+ "J integrated over the domain: 21.772 at time: 0.170\n",
+ "J_n integrated over the domain: 20.322 at time: 0.170\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.170\n",
+ "d (def. map) integrated over the domain: 478.026 at time: 0.170\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.170\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.170\n",
+ "\n",
+ "J integrated over the domain: 22.609 at time: 0.180\n",
+ "J_n integrated over the domain: 21.772 at time: 0.180\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.180\n",
+ "d (def. map) integrated over the domain: 515.153 at time: 0.180\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.180\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.180\n",
+ "\n",
+ "J integrated over the domain: 22.779 at time: 0.190\n",
+ "J_n integrated over the domain: 22.609 at time: 0.190\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.190\n",
+ "d (def. map) integrated over the domain: 522.869 at time: 0.190\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.190\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.190\n",
+ "\n",
+ "J integrated over the domain: 22.271 at time: 0.200\n",
+ "J_n integrated over the domain: 22.779 at time: 0.200\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.200\n",
+ "d (def. map) integrated over the domain: 500.016 at time: 0.200\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.200\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.200\n",
+ "\n",
+ "J integrated over the domain: 21.119 at time: 0.210\n",
+ "J_n integrated over the domain: 22.271 at time: 0.210\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.210\n",
+ "d (def. map) integrated over the domain: 450.001 at time: 0.210\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.210\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.210\n",
+ "\n",
+ "J integrated over the domain: 19.393 at time: 0.220\n",
+ "J_n integrated over the domain: 21.119 at time: 0.220\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.220\n",
+ "d (def. map) integrated over the domain: 380.093 at time: 0.220\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.220\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.220\n",
+ "\n",
+ "J integrated over the domain: 17.203 at time: 0.230\n",
+ "J_n integrated over the domain: 19.393 at time: 0.230\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.230\n",
+ "d (def. map) integrated over the domain: 299.941 at time: 0.230\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.230\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.230\n",
+ "\n",
+ "J integrated over the domain: 14.686 at time: 0.240\n",
+ "J_n integrated over the domain: 17.203 at time: 0.240\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.240\n",
+ "d (def. map) integrated over the domain: 219.674 at time: 0.240\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.240\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.240\n",
+ "\n",
+ "J integrated over the domain: 12.000 at time: 0.250\n",
+ "J_n integrated over the domain: 14.686 at time: 0.250\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.250\n",
+ "d (def. map) integrated over the domain: 148.000 at time: 0.250\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.250\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.250\n",
+ "\n",
+ "J integrated over the domain: 9.314 at time: 0.260\n",
+ "J_n integrated over the domain: 12.000 at time: 0.260\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.260\n",
+ "d (def. map) integrated over the domain: 90.753 at time: 0.260\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.260\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.260\n",
+ "\n",
+ "J integrated over the domain: 6.797 at time: 0.270\n",
+ "J_n integrated over the domain: 9.314 at time: 0.270\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.270\n",
+ "d (def. map) integrated over the domain: 50.200 at time: 0.270\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.270\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.270\n",
+ "\n",
+ "J integrated over the domain: 4.607 at time: 0.280\n",
+ "J_n integrated over the domain: 6.797 at time: 0.280\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.280\n",
+ "d (def. map) integrated over the domain: 25.223 at time: 0.280\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.280\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.280\n",
+ "\n",
+ "J integrated over the domain: 2.881 at time: 0.290\n",
+ "J_n integrated over the domain: 4.607 at time: 0.290\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.290\n",
+ "d (def. map) integrated over the domain: 12.302 at time: 0.290\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.290\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.290\n",
+ "\n",
+ "J integrated over the domain: 1.729 at time: 0.300\n",
+ "J_n integrated over the domain: 2.881 at time: 0.300\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.300\n",
+ "d (def. map) integrated over the domain: 6.988 at time: 0.300\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.300\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.300\n",
+ "\n",
+ "J integrated over the domain: 1.221 at time: 0.310\n",
+ "J_n integrated over the domain: 1.729 at time: 0.310\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.310\n",
+ "d (def. map) integrated over the domain: 5.492 at time: 0.310\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.310\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.310\n",
+ "\n",
+ "J integrated over the domain: 1.391 at time: 0.320\n",
+ "J_n integrated over the domain: 1.221 at time: 0.320\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.320\n",
+ "d (def. map) integrated over the domain: 5.936 at time: 0.320\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.320\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.320\n",
+ "\n"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "J integrated over the domain: 2.228 at time: 0.330\n",
+ "J_n integrated over the domain: 1.391 at time: 0.330\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.330\n",
+ "d (def. map) integrated over the domain: 8.963 at time: 0.330\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.330\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.330\n",
+ "\n",
+ "J integrated over the domain: 3.678 at time: 0.340\n",
+ "J_n integrated over the domain: 2.228 at time: 0.340\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.340\n",
+ "d (def. map) integrated over the domain: 17.531 at time: 0.340\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.340\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.340\n",
+ "\n",
+ "J integrated over the domain: 5.652 at time: 0.350\n",
+ "J_n integrated over the domain: 3.678 at time: 0.350\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.350\n",
+ "d (def. map) integrated over the domain: 35.944 at time: 0.350\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.350\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.350\n",
+ "\n",
+ "J integrated over the domain: 8.024 at time: 0.360\n",
+ "J_n integrated over the domain: 5.652 at time: 0.360\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.360\n",
+ "d (def. map) integrated over the domain: 68.389 at time: 0.360\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.360\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.360\n",
+ "\n",
+ "J integrated over the domain: 10.646 at time: 0.370\n",
+ "J_n integrated over the domain: 8.024 at time: 0.370\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.370\n",
+ "d (def. map) integrated over the domain: 117.346 at time: 0.370\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.370\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.370\n",
+ "\n",
+ "J integrated over the domain: 13.354 at time: 0.380\n",
+ "J_n integrated over the domain: 10.646 at time: 0.380\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.380\n",
+ "d (def. map) integrated over the domain: 182.319 at time: 0.380\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.380\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.380\n",
+ "\n",
+ "J integrated over the domain: 15.976 at time: 0.390\n",
+ "J_n integrated over the domain: 13.354 at time: 0.390\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.390\n",
+ "d (def. map) integrated over the domain: 259.224 at time: 0.390\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.390\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.390\n",
+ "\n",
+ "J integrated over the domain: 18.348 at time: 0.400\n",
+ "J_n integrated over the domain: 15.976 at time: 0.400\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.400\n",
+ "d (def. map) integrated over the domain: 340.652 at time: 0.400\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.400\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.400\n",
+ "\n",
+ "J integrated over the domain: 20.322 at time: 0.410\n",
+ "J_n integrated over the domain: 18.348 at time: 0.410\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.410\n",
+ "d (def. map) integrated over the domain: 416.965 at time: 0.410\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.410\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.410\n",
+ "\n",
+ "J integrated over the domain: 21.772 at time: 0.420\n",
+ "J_n integrated over the domain: 20.322 at time: 0.420\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.420\n",
+ "d (def. map) integrated over the domain: 478.026 at time: 0.420\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.420\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.420\n",
+ "\n",
+ "J integrated over the domain: 22.609 at time: 0.430\n",
+ "J_n integrated over the domain: 21.772 at time: 0.430\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.430\n",
+ "d (def. map) integrated over the domain: 515.153 at time: 0.430\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.430\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.430\n",
+ "\n",
+ "J integrated over the domain: 22.779 at time: 0.440\n",
+ "J_n integrated over the domain: 22.609 at time: 0.440\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.440\n",
+ "d (def. map) integrated over the domain: 522.869 at time: 0.440\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.440\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.440\n",
+ "\n",
+ "J integrated over the domain: 22.271 at time: 0.450\n",
+ "J_n integrated over the domain: 22.779 at time: 0.450\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.450\n",
+ "d (def. map) integrated over the domain: 500.016 at time: 0.450\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.450\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.450\n",
+ "\n",
+ "J integrated over the domain: 21.119 at time: 0.460\n",
+ "J_n integrated over the domain: 22.271 at time: 0.460\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.460\n",
+ "d (def. map) integrated over the domain: 450.001 at time: 0.460\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.460\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.460\n",
+ "\n",
+ "J integrated over the domain: 19.393 at time: 0.470\n",
+ "J_n integrated over the domain: 21.119 at time: 0.470\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.470\n",
+ "d (def. map) integrated over the domain: 380.093 at time: 0.470\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.470\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.470\n",
+ "\n",
+ "J integrated over the domain: 17.203 at time: 0.480\n",
+ "J_n integrated over the domain: 19.393 at time: 0.480\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.480\n",
+ "d (def. map) integrated over the domain: 299.941 at time: 0.480\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.480\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.480\n",
+ "\n",
+ "J integrated over the domain: 14.686 at time: 0.490\n",
+ "J_n integrated over the domain: 17.203 at time: 0.490\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.490\n",
+ "d (def. map) integrated over the domain: 219.674 at time: 0.490\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.490\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.490\n",
+ "\n",
+ "J integrated over the domain: 12.000 at time: 0.500\n",
+ "J_n integrated over the domain: 14.686 at time: 0.500\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.500\n",
+ "d (def. map) integrated over the domain: 148.000 at time: 0.500\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.500\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.500\n",
+ "\n",
+ "J integrated over the domain: 9.314 at time: 0.510\n",
+ "J_n integrated over the domain: 12.000 at time: 0.510\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.510\n",
+ "d (def. map) integrated over the domain: 90.753 at time: 0.510\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.510\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.510\n",
+ "\n",
+ "J integrated over the domain: 6.797 at time: 0.520\n",
+ "J_n integrated over the domain: 9.314 at time: 0.520\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.520\n",
+ "d (def. map) integrated over the domain: 50.200 at time: 0.520\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.520\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.520\n",
+ "\n",
+ "J integrated over the domain: 4.607 at time: 0.530\n",
+ "J_n integrated over the domain: 6.797 at time: 0.530\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.530\n",
+ "d (def. map) integrated over the domain: 25.223 at time: 0.530\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.530\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.530\n",
+ "\n",
+ "J integrated over the domain: 2.881 at time: 0.540\n",
+ "J_n integrated over the domain: 4.607 at time: 0.540\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.540\n",
+ "d (def. map) integrated over the domain: 12.302 at time: 0.540\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.540\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.540\n",
+ "\n",
+ "J integrated over the domain: 1.729 at time: 0.550\n",
+ "J_n integrated over the domain: 2.881 at time: 0.550\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.550\n",
+ "d (def. map) integrated over the domain: 6.988 at time: 0.550\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.550\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.550\n",
+ "\n",
+ "J integrated over the domain: 1.221 at time: 0.560\n",
+ "J_n integrated over the domain: 1.729 at time: 0.560\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.560\n",
+ "d (def. map) integrated over the domain: 5.492 at time: 0.560\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.560\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.560\n",
+ "\n"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "J integrated over the domain: 1.391 at time: 0.570\n",
+ "J_n integrated over the domain: 1.221 at time: 0.570\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.570\n",
+ "d (def. map) integrated over the domain: 5.936 at time: 0.570\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.570\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.570\n",
+ "\n",
+ "J integrated over the domain: 2.228 at time: 0.580\n",
+ "J_n integrated over the domain: 1.391 at time: 0.580\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.580\n",
+ "d (def. map) integrated over the domain: 8.963 at time: 0.580\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.580\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.580\n",
+ "\n",
+ "J integrated over the domain: 3.678 at time: 0.590\n",
+ "J_n integrated over the domain: 2.228 at time: 0.590\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.590\n",
+ "d (def. map) integrated over the domain: 17.531 at time: 0.590\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.590\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.590\n",
+ "\n",
+ "J integrated over the domain: 5.652 at time: 0.600\n",
+ "J_n integrated over the domain: 3.678 at time: 0.600\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.600\n",
+ "d (def. map) integrated over the domain: 35.944 at time: 0.600\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.600\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.600\n",
+ "\n",
+ "J integrated over the domain: 8.024 at time: 0.610\n",
+ "J_n integrated over the domain: 5.652 at time: 0.610\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.610\n",
+ "d (def. map) integrated over the domain: 68.389 at time: 0.610\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.610\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.610\n",
+ "\n",
+ "J integrated over the domain: 10.646 at time: 0.620\n",
+ "J_n integrated over the domain: 8.024 at time: 0.620\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.620\n",
+ "d (def. map) integrated over the domain: 117.346 at time: 0.620\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.620\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.620\n",
+ "\n",
+ "J integrated over the domain: 13.354 at time: 0.630\n",
+ "J_n integrated over the domain: 10.646 at time: 0.630\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.630\n",
+ "d (def. map) integrated over the domain: 182.319 at time: 0.630\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.630\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.630\n",
+ "\n",
+ "J integrated over the domain: 15.976 at time: 0.640\n",
+ "J_n integrated over the domain: 13.354 at time: 0.640\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.640\n",
+ "d (def. map) integrated over the domain: 259.224 at time: 0.640\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.640\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.640\n",
+ "\n",
+ "J integrated over the domain: 18.348 at time: 0.650\n",
+ "J_n integrated over the domain: 15.976 at time: 0.650\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.650\n",
+ "d (def. map) integrated over the domain: 340.652 at time: 0.650\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.650\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.650\n",
+ "\n",
+ "J integrated over the domain: 20.322 at time: 0.660\n",
+ "J_n integrated over the domain: 18.348 at time: 0.660\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.660\n",
+ "d (def. map) integrated over the domain: 416.965 at time: 0.660\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.660\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.660\n",
+ "\n",
+ "J integrated over the domain: 21.772 at time: 0.670\n",
+ "J_n integrated over the domain: 20.322 at time: 0.670\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.670\n",
+ "d (def. map) integrated over the domain: 478.026 at time: 0.670\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.670\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.670\n",
+ "\n",
+ "J integrated over the domain: 22.609 at time: 0.680\n",
+ "J_n integrated over the domain: 21.772 at time: 0.680\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.680\n",
+ "d (def. map) integrated over the domain: 515.153 at time: 0.680\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.680\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.680\n",
+ "\n",
+ "J integrated over the domain: 22.779 at time: 0.690\n",
+ "J_n integrated over the domain: 22.609 at time: 0.690\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.690\n",
+ "d (def. map) integrated over the domain: 522.869 at time: 0.690\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.690\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.690\n",
+ "\n",
+ "J integrated over the domain: 22.271 at time: 0.700\n",
+ "J_n integrated over the domain: 22.779 at time: 0.700\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.700\n",
+ "d (def. map) integrated over the domain: 500.016 at time: 0.700\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.700\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.700\n",
+ "\n",
+ "J integrated over the domain: 21.119 at time: 0.710\n",
+ "J_n integrated over the domain: 22.271 at time: 0.710\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.710\n",
+ "d (def. map) integrated over the domain: 450.001 at time: 0.710\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.710\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.710\n",
+ "\n",
+ "J integrated over the domain: 19.393 at time: 0.720\n",
+ "J_n integrated over the domain: 21.119 at time: 0.720\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.720\n",
+ "d (def. map) integrated over the domain: 380.093 at time: 0.720\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.720\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.720\n",
+ "\n",
+ "J integrated over the domain: 17.203 at time: 0.730\n",
+ "J_n integrated over the domain: 19.393 at time: 0.730\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.730\n",
+ "d (def. map) integrated over the domain: 299.941 at time: 0.730\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.730\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.730\n",
+ "\n",
+ "J integrated over the domain: 14.686 at time: 0.740\n",
+ "J_n integrated over the domain: 17.203 at time: 0.740\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.740\n",
+ "d (def. map) integrated over the domain: 219.674 at time: 0.740\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.740\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.740\n",
+ "\n",
+ "J integrated over the domain: 12.000 at time: 0.750\n",
+ "J_n integrated over the domain: 14.686 at time: 0.750\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.750\n",
+ "d (def. map) integrated over the domain: 148.000 at time: 0.750\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.750\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.750\n",
+ "\n",
+ "J integrated over the domain: 9.314 at time: 0.760\n",
+ "J_n integrated over the domain: 12.000 at time: 0.760\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.760\n",
+ "d (def. map) integrated over the domain: 90.753 at time: 0.760\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.760\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.760\n",
+ "\n",
+ "J integrated over the domain: 6.797 at time: 0.770\n",
+ "J_n integrated over the domain: 9.314 at time: 0.770\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.770\n",
+ "d (def. map) integrated over the domain: 50.200 at time: 0.770\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.770\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.770\n",
+ "\n",
+ "J integrated over the domain: 4.607 at time: 0.780\n",
+ "J_n integrated over the domain: 6.797 at time: 0.780\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.780\n",
+ "d (def. map) integrated over the domain: 25.223 at time: 0.780\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.780\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.780\n",
+ "\n",
+ "J integrated over the domain: 2.881 at time: 0.790\n",
+ "J_n integrated over the domain: 4.607 at time: 0.790\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.790\n",
+ "d (def. map) integrated over the domain: 12.302 at time: 0.790\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.790\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.790\n",
+ "\n",
+ "J integrated over the domain: 1.729 at time: 0.800\n",
+ "J_n integrated over the domain: 2.881 at time: 0.800\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.800\n",
+ "d (def. map) integrated over the domain: 6.988 at time: 0.800\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.800\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.800\n",
+ "\n"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "J integrated over the domain: 1.221 at time: 0.810\n",
+ "J_n integrated over the domain: 1.729 at time: 0.810\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.810\n",
+ "d (def. map) integrated over the domain: 5.492 at time: 0.810\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.810\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.810\n",
+ "\n",
+ "J integrated over the domain: 1.391 at time: 0.820\n",
+ "J_n integrated over the domain: 1.221 at time: 0.820\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.820\n",
+ "d (def. map) integrated over the domain: 5.936 at time: 0.820\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.820\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.820\n",
+ "\n",
+ "J integrated over the domain: 2.228 at time: 0.830\n",
+ "J_n integrated over the domain: 1.391 at time: 0.830\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.830\n",
+ "d (def. map) integrated over the domain: 8.963 at time: 0.830\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.830\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.830\n",
+ "\n",
+ "J integrated over the domain: 3.678 at time: 0.840\n",
+ "J_n integrated over the domain: 2.228 at time: 0.840\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.840\n",
+ "d (def. map) integrated over the domain: 17.531 at time: 0.840\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.840\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.840\n",
+ "\n",
+ "J integrated over the domain: 5.652 at time: 0.850\n",
+ "J_n integrated over the domain: 3.678 at time: 0.850\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.850\n",
+ "d (def. map) integrated over the domain: 35.944 at time: 0.850\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.850\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.850\n",
+ "\n",
+ "J integrated over the domain: 8.024 at time: 0.860\n",
+ "J_n integrated over the domain: 5.652 at time: 0.860\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.860\n",
+ "d (def. map) integrated over the domain: 68.389 at time: 0.860\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.860\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.860\n",
+ "\n",
+ "J integrated over the domain: 10.646 at time: 0.870\n",
+ "J_n integrated over the domain: 8.024 at time: 0.870\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.870\n",
+ "d (def. map) integrated over the domain: 117.346 at time: 0.870\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.870\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.870\n",
+ "\n",
+ "J integrated over the domain: 13.354 at time: 0.880\n",
+ "J_n integrated over the domain: 10.646 at time: 0.880\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.880\n",
+ "d (def. map) integrated over the domain: 182.319 at time: 0.880\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.880\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.880\n",
+ "\n",
+ "J integrated over the domain: 15.976 at time: 0.890\n",
+ "J_n integrated over the domain: 13.354 at time: 0.890\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.890\n",
+ "d (def. map) integrated over the domain: 259.224 at time: 0.890\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.890\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.890\n",
+ "\n",
+ "J integrated over the domain: 18.348 at time: 0.900\n",
+ "J_n integrated over the domain: 15.976 at time: 0.900\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.900\n",
+ "d (def. map) integrated over the domain: 340.652 at time: 0.900\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.900\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.900\n",
+ "\n",
+ "J integrated over the domain: 20.322 at time: 0.910\n",
+ "J_n integrated over the domain: 18.348 at time: 0.910\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.910\n",
+ "d (def. map) integrated over the domain: 416.965 at time: 0.910\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.910\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.910\n",
+ "\n",
+ "J integrated over the domain: 21.772 at time: 0.920\n",
+ "J_n integrated over the domain: 20.322 at time: 0.920\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.920\n",
+ "d (def. map) integrated over the domain: 478.026 at time: 0.920\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.920\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.920\n",
+ "\n",
+ "J integrated over the domain: 22.609 at time: 0.930\n",
+ "J_n integrated over the domain: 21.772 at time: 0.930\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.930\n",
+ "d (def. map) integrated over the domain: 515.153 at time: 0.930\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.930\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.930\n",
+ "\n",
+ "J integrated over the domain: 22.779 at time: 0.940\n",
+ "J_n integrated over the domain: 22.609 at time: 0.940\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.940\n",
+ "d (def. map) integrated over the domain: 522.869 at time: 0.940\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.940\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.940\n",
+ "\n",
+ "J integrated over the domain: 22.271 at time: 0.950\n",
+ "J_n integrated over the domain: 22.779 at time: 0.950\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.950\n",
+ "d (def. map) integrated over the domain: 500.016 at time: 0.950\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.950\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.950\n",
+ "\n",
+ "J integrated over the domain: 21.119 at time: 0.960\n",
+ "J_n integrated over the domain: 22.271 at time: 0.960\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.960\n",
+ "d (def. map) integrated over the domain: 450.001 at time: 0.960\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.960\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.960\n",
+ "\n",
+ "J integrated over the domain: 19.393 at time: 0.970\n",
+ "J_n integrated over the domain: 21.119 at time: 0.970\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.970\n",
+ "d (def. map) integrated over the domain: 380.093 at time: 0.970\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.970\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.970\n",
+ "\n",
+ "J integrated over the domain: 17.203 at time: 0.980\n",
+ "J_n integrated over the domain: 19.393 at time: 0.980\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.980\n",
+ "d (def. map) integrated over the domain: 299.941 at time: 0.980\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.980\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 0.980\n",
+ "\n",
+ "J integrated over the domain: 14.686 at time: 0.990\n",
+ "J_n integrated over the domain: 17.203 at time: 0.990\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.990\n",
+ "d (def. map) integrated over the domain: 219.674 at time: 0.990\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.990\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.990\n",
+ "\n",
+ "J integrated over the domain: 12.000 at time: 1.000\n",
+ "J_n integrated over the domain: 14.686 at time: 1.000\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.000\n",
+ "d (def. map) integrated over the domain: 148.000 at time: 1.000\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.000\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.000\n",
+ "\n",
+ "J integrated over the domain: 9.314 at time: 1.010\n",
+ "J_n integrated over the domain: 12.000 at time: 1.010\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.010\n",
+ "d (def. map) integrated over the domain: 90.753 at time: 1.010\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.010\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.010\n",
+ "\n",
+ "J integrated over the domain: 6.797 at time: 1.020\n",
+ "J_n integrated over the domain: 9.314 at time: 1.020\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.020\n",
+ "d (def. map) integrated over the domain: 50.200 at time: 1.020\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.020\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.020\n",
+ "\n",
+ "J integrated over the domain: 4.607 at time: 1.030\n",
+ "J_n integrated over the domain: 6.797 at time: 1.030\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.030\n",
+ "d (def. map) integrated over the domain: 25.223 at time: 1.030\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.030\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.030\n",
+ "\n",
+ "J integrated over the domain: 2.881 at time: 1.040\n",
+ "J_n integrated over the domain: 4.607 at time: 1.040\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.040\n",
+ "d (def. map) integrated over the domain: 12.302 at time: 1.040\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.040\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.040\n",
+ "\n",
+ "J integrated over the domain: 1.729 at time: 1.050\n",
+ "J_n integrated over the domain: 2.881 at time: 1.050\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.050\n",
+ "d (def. map) integrated over the domain: 6.988 at time: 1.050\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.050\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.050\n",
+ "\n"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "J integrated over the domain: 1.221 at time: 1.060\n",
+ "J_n integrated over the domain: 1.729 at time: 1.060\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.060\n",
+ "d (def. map) integrated over the domain: 5.492 at time: 1.060\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.060\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.060\n",
+ "\n",
+ "J integrated over the domain: 1.391 at time: 1.070\n",
+ "J_n integrated over the domain: 1.221 at time: 1.070\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.070\n",
+ "d (def. map) integrated over the domain: 5.936 at time: 1.070\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.070\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.070\n",
+ "\n",
+ "J integrated over the domain: 2.228 at time: 1.080\n",
+ "J_n integrated over the domain: 1.391 at time: 1.080\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.080\n",
+ "d (def. map) integrated over the domain: 8.963 at time: 1.080\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.080\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.080\n",
+ "\n",
+ "J integrated over the domain: 3.678 at time: 1.090\n",
+ "J_n integrated over the domain: 2.228 at time: 1.090\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.090\n",
+ "d (def. map) integrated over the domain: 17.531 at time: 1.090\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.090\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.090\n",
+ "\n",
+ "J integrated over the domain: 5.652 at time: 1.100\n",
+ "J_n integrated over the domain: 3.678 at time: 1.100\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.100\n",
+ "d (def. map) integrated over the domain: 35.944 at time: 1.100\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.100\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.100\n",
+ "\n",
+ "J integrated over the domain: 8.024 at time: 1.110\n",
+ "J_n integrated over the domain: 5.652 at time: 1.110\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.110\n",
+ "d (def. map) integrated over the domain: 68.389 at time: 1.110\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.110\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.110\n",
+ "\n",
+ "J integrated over the domain: 10.646 at time: 1.120\n",
+ "J_n integrated over the domain: 8.024 at time: 1.120\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.120\n",
+ "d (def. map) integrated over the domain: 117.346 at time: 1.120\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.120\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.120\n",
+ "\n",
+ "J integrated over the domain: 13.354 at time: 1.130\n",
+ "J_n integrated over the domain: 10.646 at time: 1.130\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.130\n",
+ "d (def. map) integrated over the domain: 182.319 at time: 1.130\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.130\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.130\n",
+ "\n",
+ "J integrated over the domain: 15.976 at time: 1.140\n",
+ "J_n integrated over the domain: 13.354 at time: 1.140\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.140\n",
+ "d (def. map) integrated over the domain: 259.224 at time: 1.140\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.140\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.140\n",
+ "\n",
+ "J integrated over the domain: 18.348 at time: 1.150\n",
+ "J_n integrated over the domain: 15.976 at time: 1.150\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.150\n",
+ "d (def. map) integrated over the domain: 340.652 at time: 1.150\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.150\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.150\n",
+ "\n",
+ "J integrated over the domain: 20.322 at time: 1.160\n",
+ "J_n integrated over the domain: 18.348 at time: 1.160\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.160\n",
+ "d (def. map) integrated over the domain: 416.965 at time: 1.160\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.160\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.160\n",
+ "\n",
+ "J integrated over the domain: 21.772 at time: 1.170\n",
+ "J_n integrated over the domain: 20.322 at time: 1.170\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.170\n",
+ "d (def. map) integrated over the domain: 478.026 at time: 1.170\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.170\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.170\n",
+ "\n",
+ "J integrated over the domain: 22.609 at time: 1.180\n",
+ "J_n integrated over the domain: 21.772 at time: 1.180\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.180\n",
+ "d (def. map) integrated over the domain: 515.153 at time: 1.180\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.180\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.180\n",
+ "\n",
+ "J integrated over the domain: 22.779 at time: 1.190\n",
+ "J_n integrated over the domain: 22.609 at time: 1.190\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.190\n",
+ "d (def. map) integrated over the domain: 522.869 at time: 1.190\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.190\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.190\n",
+ "\n",
+ "J integrated over the domain: 22.271 at time: 1.200\n",
+ "J_n integrated over the domain: 22.779 at time: 1.200\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.200\n",
+ "d (def. map) integrated over the domain: 500.016 at time: 1.200\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.200\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.200\n",
+ "\n",
+ "J integrated over the domain: 21.119 at time: 1.210\n",
+ "J_n integrated over the domain: 22.271 at time: 1.210\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.210\n",
+ "d (def. map) integrated over the domain: 450.001 at time: 1.210\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.210\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.210\n",
+ "\n",
+ "J integrated over the domain: 19.393 at time: 1.220\n",
+ "J_n integrated over the domain: 21.119 at time: 1.220\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.220\n",
+ "d (def. map) integrated over the domain: 380.093 at time: 1.220\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.220\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.220\n",
+ "\n",
+ "J integrated over the domain: 17.203 at time: 1.230\n",
+ "J_n integrated over the domain: 19.393 at time: 1.230\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.230\n",
+ "d (def. map) integrated over the domain: 299.941 at time: 1.230\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.230\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.230\n",
+ "\n",
+ "J integrated over the domain: 14.686 at time: 1.240\n",
+ "J_n integrated over the domain: 17.203 at time: 1.240\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.240\n",
+ "d (def. map) integrated over the domain: 219.674 at time: 1.240\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.240\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.240\n",
+ "\n",
+ "J integrated over the domain: 12.000 at time: 1.250\n",
+ "J_n integrated over the domain: 14.686 at time: 1.250\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.250\n",
+ "d (def. map) integrated over the domain: 148.000 at time: 1.250\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.250\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.250\n",
+ "\n",
+ "J integrated over the domain: 9.314 at time: 1.260\n",
+ "J_n integrated over the domain: 12.000 at time: 1.260\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.260\n",
+ "d (def. map) integrated over the domain: 90.753 at time: 1.260\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.260\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.260\n",
+ "\n",
+ "J integrated over the domain: 6.797 at time: 1.270\n",
+ "J_n integrated over the domain: 9.314 at time: 1.270\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.270\n",
+ "d (def. map) integrated over the domain: 50.200 at time: 1.270\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.270\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.270\n",
+ "\n",
+ "J integrated over the domain: 4.607 at time: 1.280\n",
+ "J_n integrated over the domain: 6.797 at time: 1.280\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.280\n",
+ "d (def. map) integrated over the domain: 25.223 at time: 1.280\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.280\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.280\n",
+ "\n",
+ "J integrated over the domain: 2.881 at time: 1.290\n",
+ "J_n integrated over the domain: 4.607 at time: 1.290\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.290\n",
+ "d (def. map) integrated over the domain: 12.302 at time: 1.290\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.290\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.290\n",
+ "\n"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "J integrated over the domain: 1.729 at time: 1.300\n",
+ "J_n integrated over the domain: 2.881 at time: 1.300\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.300\n",
+ "d (def. map) integrated over the domain: 6.988 at time: 1.300\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.300\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.300\n",
+ "\n",
+ "J integrated over the domain: 1.221 at time: 1.310\n",
+ "J_n integrated over the domain: 1.729 at time: 1.310\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.310\n",
+ "d (def. map) integrated over the domain: 5.492 at time: 1.310\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.310\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.310\n",
+ "\n",
+ "J integrated over the domain: 1.391 at time: 1.320\n",
+ "J_n integrated over the domain: 1.221 at time: 1.320\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.320\n",
+ "d (def. map) integrated over the domain: 5.936 at time: 1.320\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.320\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.320\n",
+ "\n",
+ "J integrated over the domain: 2.228 at time: 1.330\n",
+ "J_n integrated over the domain: 1.391 at time: 1.330\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.330\n",
+ "d (def. map) integrated over the domain: 8.963 at time: 1.330\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.330\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.330\n",
+ "\n",
+ "J integrated over the domain: 3.678 at time: 1.340\n",
+ "J_n integrated over the domain: 2.228 at time: 1.340\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.340\n",
+ "d (def. map) integrated over the domain: 17.531 at time: 1.340\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.340\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.340\n",
+ "\n",
+ "J integrated over the domain: 5.652 at time: 1.350\n",
+ "J_n integrated over the domain: 3.678 at time: 1.350\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.350\n",
+ "d (def. map) integrated over the domain: 35.944 at time: 1.350\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.350\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.350\n",
+ "\n",
+ "J integrated over the domain: 8.024 at time: 1.360\n",
+ "J_n integrated over the domain: 5.652 at time: 1.360\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.360\n",
+ "d (def. map) integrated over the domain: 68.389 at time: 1.360\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.360\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.360\n",
+ "\n",
+ "J integrated over the domain: 10.646 at time: 1.370\n",
+ "J_n integrated over the domain: 8.024 at time: 1.370\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.370\n",
+ "d (def. map) integrated over the domain: 117.346 at time: 1.370\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.370\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.370\n",
+ "\n",
+ "J integrated over the domain: 13.354 at time: 1.380\n",
+ "J_n integrated over the domain: 10.646 at time: 1.380\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.380\n",
+ "d (def. map) integrated over the domain: 182.319 at time: 1.380\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.380\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.380\n",
+ "\n",
+ "J integrated over the domain: 15.976 at time: 1.390\n",
+ "J_n integrated over the domain: 13.354 at time: 1.390\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.390\n",
+ "d (def. map) integrated over the domain: 259.224 at time: 1.390\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.390\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.390\n",
+ "\n",
+ "J integrated over the domain: 18.348 at time: 1.400\n",
+ "J_n integrated over the domain: 15.976 at time: 1.400\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.400\n",
+ "d (def. map) integrated over the domain: 340.652 at time: 1.400\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.400\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.400\n",
+ "\n",
+ "J integrated over the domain: 20.322 at time: 1.410\n",
+ "J_n integrated over the domain: 18.348 at time: 1.410\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.410\n",
+ "d (def. map) integrated over the domain: 416.965 at time: 1.410\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.410\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.410\n",
+ "\n",
+ "J integrated over the domain: 21.772 at time: 1.420\n",
+ "J_n integrated over the domain: 20.322 at time: 1.420\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.420\n",
+ "d (def. map) integrated over the domain: 478.026 at time: 1.420\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.420\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.420\n",
+ "\n",
+ "J integrated over the domain: 22.609 at time: 1.430\n",
+ "J_n integrated over the domain: 21.772 at time: 1.430\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.430\n",
+ "d (def. map) integrated over the domain: 515.153 at time: 1.430\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.430\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.430\n",
+ "\n",
+ "J integrated over the domain: 22.779 at time: 1.440\n",
+ "J_n integrated over the domain: 22.609 at time: 1.440\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.440\n",
+ "d (def. map) integrated over the domain: 522.869 at time: 1.440\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.440\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.440\n",
+ "\n",
+ "J integrated over the domain: 22.271 at time: 1.450\n",
+ "J_n integrated over the domain: 22.779 at time: 1.450\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.450\n",
+ "d (def. map) integrated over the domain: 500.016 at time: 1.450\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.450\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.450\n",
+ "\n",
+ "J integrated over the domain: 21.119 at time: 1.460\n",
+ "J_n integrated over the domain: 22.271 at time: 1.460\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.460\n",
+ "d (def. map) integrated over the domain: 450.001 at time: 1.460\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.460\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.460\n",
+ "\n",
+ "J integrated over the domain: 19.393 at time: 1.470\n",
+ "J_n integrated over the domain: 21.119 at time: 1.470\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.470\n",
+ "d (def. map) integrated over the domain: 380.093 at time: 1.470\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.470\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.470\n",
+ "\n",
+ "J integrated over the domain: 17.203 at time: 1.480\n",
+ "J_n integrated over the domain: 19.393 at time: 1.480\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.480\n",
+ "d (def. map) integrated over the domain: 299.941 at time: 1.480\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.480\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.480\n",
+ "\n",
+ "J integrated over the domain: 14.686 at time: 1.490\n",
+ "J_n integrated over the domain: 17.203 at time: 1.490\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.490\n",
+ "d (def. map) integrated over the domain: 219.674 at time: 1.490\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.490\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.490\n",
+ "\n",
+ "J integrated over the domain: 12.000 at time: 1.500\n",
+ "J_n integrated over the domain: 14.686 at time: 1.500\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.500\n",
+ "d (def. map) integrated over the domain: 148.000 at time: 1.500\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.500\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.500\n",
+ "\n",
+ "J integrated over the domain: 9.314 at time: 1.510\n",
+ "J_n integrated over the domain: 12.000 at time: 1.510\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.510\n",
+ "d (def. map) integrated over the domain: 90.753 at time: 1.510\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.510\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.510\n",
+ "\n",
+ "J integrated over the domain: 6.797 at time: 1.520\n",
+ "J_n integrated over the domain: 9.314 at time: 1.520\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.520\n",
+ "d (def. map) integrated over the domain: 50.200 at time: 1.520\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.520\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.520\n",
+ "\n",
+ "J integrated over the domain: 4.607 at time: 1.530\n",
+ "J_n integrated over the domain: 6.797 at time: 1.530\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.530\n",
+ "d (def. map) integrated over the domain: 25.223 at time: 1.530\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.530\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.530\n",
+ "\n"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "J integrated over the domain: 2.881 at time: 1.540\n",
+ "J_n integrated over the domain: 4.607 at time: 1.540\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.540\n",
+ "d (def. map) integrated over the domain: 12.302 at time: 1.540\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.540\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.540\n",
+ "\n",
+ "J integrated over the domain: 1.729 at time: 1.550\n",
+ "J_n integrated over the domain: 2.881 at time: 1.550\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.550\n",
+ "d (def. map) integrated over the domain: 6.988 at time: 1.550\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.550\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.550\n",
+ "\n",
+ "J integrated over the domain: 1.221 at time: 1.560\n",
+ "J_n integrated over the domain: 1.729 at time: 1.560\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.560\n",
+ "d (def. map) integrated over the domain: 5.492 at time: 1.560\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.560\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.560\n",
+ "\n",
+ "J integrated over the domain: 1.391 at time: 1.570\n",
+ "J_n integrated over the domain: 1.221 at time: 1.570\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.570\n",
+ "d (def. map) integrated over the domain: 5.936 at time: 1.570\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.570\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.570\n",
+ "\n",
+ "J integrated over the domain: 2.228 at time: 1.580\n",
+ "J_n integrated over the domain: 1.391 at time: 1.580\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.580\n",
+ "d (def. map) integrated over the domain: 8.963 at time: 1.580\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.580\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.580\n",
+ "\n",
+ "J integrated over the domain: 3.678 at time: 1.590\n",
+ "J_n integrated over the domain: 2.228 at time: 1.590\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.590\n",
+ "d (def. map) integrated over the domain: 17.531 at time: 1.590\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.590\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.590\n",
+ "\n",
+ "J integrated over the domain: 5.652 at time: 1.600\n",
+ "J_n integrated over the domain: 3.678 at time: 1.600\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.600\n",
+ "d (def. map) integrated over the domain: 35.944 at time: 1.600\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.600\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.600\n",
+ "\n",
+ "J integrated over the domain: 8.024 at time: 1.610\n",
+ "J_n integrated over the domain: 5.652 at time: 1.610\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.610\n",
+ "d (def. map) integrated over the domain: 68.389 at time: 1.610\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.610\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.610\n",
+ "\n",
+ "J integrated over the domain: 10.646 at time: 1.620\n",
+ "J_n integrated over the domain: 8.024 at time: 1.620\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.620\n",
+ "d (def. map) integrated over the domain: 117.346 at time: 1.620\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.620\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.620\n",
+ "\n",
+ "J integrated over the domain: 13.354 at time: 1.630\n",
+ "J_n integrated over the domain: 10.646 at time: 1.630\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.630\n",
+ "d (def. map) integrated over the domain: 182.319 at time: 1.630\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.630\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.630\n",
+ "\n",
+ "J integrated over the domain: 15.976 at time: 1.640\n",
+ "J_n integrated over the domain: 13.354 at time: 1.640\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.640\n",
+ "d (def. map) integrated over the domain: 259.224 at time: 1.640\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.640\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.640\n",
+ "\n",
+ "J integrated over the domain: 18.348 at time: 1.650\n",
+ "J_n integrated over the domain: 15.976 at time: 1.650\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.650\n",
+ "d (def. map) integrated over the domain: 340.652 at time: 1.650\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.650\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.650\n",
+ "\n",
+ "J integrated over the domain: 20.322 at time: 1.660\n",
+ "J_n integrated over the domain: 18.348 at time: 1.660\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.660\n",
+ "d (def. map) integrated over the domain: 416.965 at time: 1.660\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.660\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.660\n",
+ "\n",
+ "J integrated over the domain: 21.772 at time: 1.670\n",
+ "J_n integrated over the domain: 20.322 at time: 1.670\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.670\n",
+ "d (def. map) integrated over the domain: 478.026 at time: 1.670\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.670\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.670\n",
+ "\n",
+ "J integrated over the domain: 22.609 at time: 1.680\n",
+ "J_n integrated over the domain: 21.772 at time: 1.680\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.680\n",
+ "d (def. map) integrated over the domain: 515.153 at time: 1.680\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.680\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.680\n",
+ "\n",
+ "J integrated over the domain: 22.779 at time: 1.690\n",
+ "J_n integrated over the domain: 22.609 at time: 1.690\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.690\n",
+ "d (def. map) integrated over the domain: 522.869 at time: 1.690\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.690\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.690\n",
+ "\n",
+ "J integrated over the domain: 22.271 at time: 1.700\n",
+ "J_n integrated over the domain: 22.779 at time: 1.700\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.700\n",
+ "d (def. map) integrated over the domain: 500.016 at time: 1.700\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.700\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.700\n",
+ "\n",
+ "J integrated over the domain: 21.119 at time: 1.710\n",
+ "J_n integrated over the domain: 22.271 at time: 1.710\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.710\n",
+ "d (def. map) integrated over the domain: 450.001 at time: 1.710\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.710\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.710\n",
+ "\n",
+ "J integrated over the domain: 19.393 at time: 1.720\n",
+ "J_n integrated over the domain: 21.119 at time: 1.720\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.720\n",
+ "d (def. map) integrated over the domain: 380.093 at time: 1.720\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.720\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.720\n",
+ "\n",
+ "J integrated over the domain: 17.203 at time: 1.730\n",
+ "J_n integrated over the domain: 19.393 at time: 1.730\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.730\n",
+ "d (def. map) integrated over the domain: 299.941 at time: 1.730\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.730\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.730\n",
+ "\n",
+ "J integrated over the domain: 14.686 at time: 1.740\n",
+ "J_n integrated over the domain: 17.203 at time: 1.740\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.740\n",
+ "d (def. map) integrated over the domain: 219.674 at time: 1.740\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.740\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.740\n",
+ "\n",
+ "J integrated over the domain: 12.000 at time: 1.750\n",
+ "J_n integrated over the domain: 14.686 at time: 1.750\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.750\n",
+ "d (def. map) integrated over the domain: 148.000 at time: 1.750\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.750\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.750\n",
+ "\n",
+ "J integrated over the domain: 9.314 at time: 1.760\n",
+ "J_n integrated over the domain: 12.000 at time: 1.760\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.760\n",
+ "d (def. map) integrated over the domain: 90.753 at time: 1.760\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.760\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.760\n",
+ "\n",
+ "J integrated over the domain: 6.797 at time: 1.770\n",
+ "J_n integrated over the domain: 9.314 at time: 1.770\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.770\n",
+ "d (def. map) integrated over the domain: 50.200 at time: 1.770\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.770\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.770\n",
+ "\n"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "J integrated over the domain: 4.607 at time: 1.780\n",
+ "J_n integrated over the domain: 6.797 at time: 1.780\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.780\n",
+ "d (def. map) integrated over the domain: 25.223 at time: 1.780\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.780\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.780\n",
+ "\n",
+ "J integrated over the domain: 2.881 at time: 1.790\n",
+ "J_n integrated over the domain: 4.607 at time: 1.790\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.790\n",
+ "d (def. map) integrated over the domain: 12.302 at time: 1.790\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.790\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.790\n",
+ "\n",
+ "J integrated over the domain: 1.729 at time: 1.800\n",
+ "J_n integrated over the domain: 2.881 at time: 1.800\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.800\n",
+ "d (def. map) integrated over the domain: 6.988 at time: 1.800\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.800\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.800\n",
+ "\n",
+ "J integrated over the domain: 1.221 at time: 1.810\n",
+ "J_n integrated over the domain: 1.729 at time: 1.810\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.810\n",
+ "d (def. map) integrated over the domain: 5.492 at time: 1.810\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.810\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.810\n",
+ "\n",
+ "J integrated over the domain: 1.391 at time: 1.820\n",
+ "J_n integrated over the domain: 1.221 at time: 1.820\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.820\n",
+ "d (def. map) integrated over the domain: 5.936 at time: 1.820\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.820\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.820\n",
+ "\n",
+ "J integrated over the domain: 2.228 at time: 1.830\n",
+ "J_n integrated over the domain: 1.391 at time: 1.830\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.830\n",
+ "d (def. map) integrated over the domain: 8.963 at time: 1.830\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.830\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.830\n",
+ "\n",
+ "J integrated over the domain: 3.678 at time: 1.840\n",
+ "J_n integrated over the domain: 2.228 at time: 1.840\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.840\n",
+ "d (def. map) integrated over the domain: 17.531 at time: 1.840\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.840\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.840\n",
+ "\n",
+ "J integrated over the domain: 5.652 at time: 1.850\n",
+ "J_n integrated over the domain: 3.678 at time: 1.850\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.850\n",
+ "d (def. map) integrated over the domain: 35.944 at time: 1.850\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.850\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.850\n",
+ "\n",
+ "J integrated over the domain: 8.024 at time: 1.860\n",
+ "J_n integrated over the domain: 5.652 at time: 1.860\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.860\n",
+ "d (def. map) integrated over the domain: 68.389 at time: 1.860\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.860\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.860\n",
+ "\n",
+ "J integrated over the domain: 10.646 at time: 1.870\n",
+ "J_n integrated over the domain: 8.024 at time: 1.870\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.870\n",
+ "d (def. map) integrated over the domain: 117.346 at time: 1.870\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.870\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.870\n",
+ "\n",
+ "J integrated over the domain: 13.354 at time: 1.880\n",
+ "J_n integrated over the domain: 10.646 at time: 1.880\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.880\n",
+ "d (def. map) integrated over the domain: 182.319 at time: 1.880\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.880\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.880\n",
+ "\n",
+ "J integrated over the domain: 15.976 at time: 1.890\n",
+ "J_n integrated over the domain: 13.354 at time: 1.890\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.890\n",
+ "d (def. map) integrated over the domain: 259.224 at time: 1.890\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.890\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.890\n",
+ "\n",
+ "J integrated over the domain: 18.348 at time: 1.900\n",
+ "J_n integrated over the domain: 15.976 at time: 1.900\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.900\n",
+ "d (def. map) integrated over the domain: 340.652 at time: 1.900\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.900\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.900\n",
+ "\n",
+ "J integrated over the domain: 20.322 at time: 1.910\n",
+ "J_n integrated over the domain: 18.348 at time: 1.910\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.910\n",
+ "d (def. map) integrated over the domain: 416.965 at time: 1.910\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.910\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.910\n",
+ "\n",
+ "J integrated over the domain: 21.772 at time: 1.920\n",
+ "J_n integrated over the domain: 20.322 at time: 1.920\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.920\n",
+ "d (def. map) integrated over the domain: 478.026 at time: 1.920\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.920\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.920\n",
+ "\n",
+ "J integrated over the domain: 22.609 at time: 1.930\n",
+ "J_n integrated over the domain: 21.772 at time: 1.930\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.930\n",
+ "d (def. map) integrated over the domain: 515.153 at time: 1.930\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.930\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.930\n",
+ "\n",
+ "J integrated over the domain: 22.779 at time: 1.940\n",
+ "J_n integrated over the domain: 22.609 at time: 1.940\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.940\n",
+ "d (def. map) integrated over the domain: 522.869 at time: 1.940\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.940\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.940\n",
+ "\n",
+ "J integrated over the domain: 22.271 at time: 1.950\n",
+ "J_n integrated over the domain: 22.779 at time: 1.950\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.950\n",
+ "d (def. map) integrated over the domain: 500.016 at time: 1.950\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.950\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.950\n",
+ "\n",
+ "J integrated over the domain: 21.119 at time: 1.960\n",
+ "J_n integrated over the domain: 22.271 at time: 1.960\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.960\n",
+ "d (def. map) integrated over the domain: 450.001 at time: 1.960\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.960\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.960\n",
+ "\n",
+ "J integrated over the domain: 19.393 at time: 1.970\n",
+ "J_n integrated over the domain: 21.119 at time: 1.970\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.970\n",
+ "d (def. map) integrated over the domain: 380.093 at time: 1.970\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.970\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.970\n",
+ "\n",
+ "J integrated over the domain: 17.203 at time: 1.980\n",
+ "J_n integrated over the domain: 19.393 at time: 1.980\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.980\n",
+ "d (def. map) integrated over the domain: 299.941 at time: 1.980\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.980\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.980\n",
+ "\n",
+ "J integrated over the domain: 14.686 at time: 1.990\n",
+ "J_n integrated over the domain: 17.203 at time: 1.990\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.990\n",
+ "d (def. map) integrated over the domain: 219.674 at time: 1.990\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.990\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 1.990\n",
+ "\n",
+ "J integrated over the domain: 12.000 at time: 2.000\n",
+ "J_n integrated over the domain: 14.686 at time: 2.000\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 2.000\n",
+ "d (def. map) integrated over the domain: 148.000 at time: 2.000\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 2.000\n",
+ "Residual of scheme -> 'delta' value: 0.00000 at time 2.000\n",
+ "\n",
+ "Number of degrees of freedom: 14387\n",
+ "Solution Computed in 103.93 seconds\n",
+ "\n",
+ "----------------Computation Completed!----------------\n",
+ "\n",
+ "\n",
+ "----------------Simulations Done!----------------.\n",
+ "\n",
+ "Initializing testing of two deformation cases with input parameters:\n",
+ " Solver to use -solver_to_use- : LU\n",
+ " \n",
+ "\n",
+ "Initializing iNSE problem with Deformation type: High_Osc_exp\n",
+ "\n",
+ "\n",
+ "Setup with initial condition: True\n",
+ "Using a non-zero initial condition (2D-Gaussian) for the velocity field!\n",
+ "Defining forms associated to Chorin-Temam scheme...\n"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Using LU Solver...\n",
+ "Starting iteration over time...\n",
+ "E (Energy) of initial t. velocity: 0.01648 at time 0.000\n",
+ "\n",
+ "J integrated over the domain: 14.686 at time: 0.010\n",
+ "J_n integrated over the domain: 12.000 at time: 0.010\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.010\n",
+ "d (def. map) integrated over the domain: 219.674 at time: 0.010\n",
+ "Strain energy E( eps(|u|^2) ): 0.00007 at time 0.010\n",
+ "Residual of scheme -> 'delta' value: -0.00069 at time 0.010\n",
+ "\n",
+ "J integrated over the domain: 17.203 at time: 0.020\n",
+ "J_n integrated over the domain: 14.686 at time: 0.020\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.020\n",
+ "d (def. map) integrated over the domain: 299.941 at time: 0.020\n",
+ "Strain energy E( eps(|u|^2) ): 0.00006 at time 0.020\n",
+ "Residual of scheme -> 'delta' value: -0.00010 at time 0.020\n",
+ "\n",
+ "J integrated over the domain: 19.393 at time: 0.030\n",
+ "J_n integrated over the domain: 17.203 at time: 0.030\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.030\n",
+ "d (def. map) integrated over the domain: 380.093 at time: 0.030\n",
+ "Strain energy E( eps(|u|^2) ): 0.00006 at time 0.030\n",
+ "Residual of scheme -> 'delta' value: -0.00005 at time 0.030\n",
+ "\n",
+ "J integrated over the domain: 21.119 at time: 0.040\n",
+ "J_n integrated over the domain: 19.393 at time: 0.040\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.040\n",
+ "d (def. map) integrated over the domain: 450.001 at time: 0.040\n",
+ "Strain energy E( eps(|u|^2) ): 0.00005 at time 0.040\n",
+ "Residual of scheme -> 'delta' value: -0.00002 at time 0.040\n",
+ "\n",
+ "J integrated over the domain: 22.271 at time: 0.050\n",
+ "J_n integrated over the domain: 21.119 at time: 0.050\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.050\n",
+ "d (def. map) integrated over the domain: 500.016 at time: 0.050\n",
+ "Strain energy E( eps(|u|^2) ): 0.00005 at time 0.050\n",
+ "Residual of scheme -> 'delta' value: -0.00001 at time 0.050\n",
+ "\n",
+ "J integrated over the domain: 22.779 at time: 0.060\n",
+ "J_n integrated over the domain: 22.271 at time: 0.060\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.060\n",
+ "d (def. map) integrated over the domain: 522.869 at time: 0.060\n",
+ "Strain energy E( eps(|u|^2) ): 0.00004 at time 0.060\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.060\n",
+ "\n",
+ "J integrated over the domain: 22.609 at time: 0.070\n",
+ "J_n integrated over the domain: 22.779 at time: 0.070\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.070\n",
+ "d (def. map) integrated over the domain: 515.153 at time: 0.070\n",
+ "Strain energy E( eps(|u|^2) ): 0.00004 at time 0.070\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.070\n",
+ "\n",
+ "J integrated over the domain: 21.772 at time: 0.080\n",
+ "J_n integrated over the domain: 22.609 at time: 0.080\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.080\n",
+ "d (def. map) integrated over the domain: 478.026 at time: 0.080\n",
+ "Strain energy E( eps(|u|^2) ): 0.00004 at time 0.080\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.080\n",
+ "\n",
+ "J integrated over the domain: 20.322 at time: 0.090\n",
+ "J_n integrated over the domain: 21.772 at time: 0.090\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.090\n",
+ "d (def. map) integrated over the domain: 416.965 at time: 0.090\n",
+ "Strain energy E( eps(|u|^2) ): 0.00003 at time 0.090\n",
+ "Residual of scheme -> 'delta' value: -0.00001 at time 0.090\n",
+ "\n",
+ "J integrated over the domain: 18.348 at time: 0.100\n",
+ "J_n integrated over the domain: 20.322 at time: 0.100\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.100\n",
+ "d (def. map) integrated over the domain: 340.652 at time: 0.100\n",
+ "Strain energy E( eps(|u|^2) ): 0.00003 at time 0.100\n",
+ "Residual of scheme -> 'delta' value: -0.00002 at time 0.100\n",
+ "\n",
+ "J integrated over the domain: 15.976 at time: 0.110\n",
+ "J_n integrated over the domain: 18.348 at time: 0.110\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.110\n",
+ "d (def. map) integrated over the domain: 259.224 at time: 0.110\n",
+ "Strain energy E( eps(|u|^2) ): 0.00003 at time 0.110\n",
+ "Residual of scheme -> 'delta' value: -0.00003 at time 0.110\n",
+ "\n",
+ "J integrated over the domain: 13.354 at time: 0.120\n",
+ "J_n integrated over the domain: 15.976 at time: 0.120\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.120\n",
+ "d (def. map) integrated over the domain: 182.319 at time: 0.120\n",
+ "Strain energy E( eps(|u|^2) ): 0.00004 at time 0.120\n",
+ "Residual of scheme -> 'delta' value: -0.00005 at time 0.120\n",
+ "\n",
+ "J integrated over the domain: 10.646 at time: 0.130\n",
+ "J_n integrated over the domain: 13.354 at time: 0.130\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.130\n",
+ "d (def. map) integrated over the domain: 117.346 at time: 0.130\n",
+ "Strain energy E( eps(|u|^2) ): 0.00008 at time 0.130\n",
+ "Residual of scheme -> 'delta' value: -0.00005 at time 0.130\n",
+ "\n",
+ "J integrated over the domain: 8.024 at time: 0.140\n",
+ "J_n integrated over the domain: 10.646 at time: 0.140\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.140\n",
+ "d (def. map) integrated over the domain: 68.389 at time: 0.140\n",
+ "Strain energy E( eps(|u|^2) ): 0.00015 at time 0.140\n",
+ "Residual of scheme -> 'delta' value: -0.00005 at time 0.140\n",
+ "\n",
+ "J integrated over the domain: 5.652 at time: 0.150\n",
+ "J_n integrated over the domain: 8.024 at time: 0.150\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.150\n",
+ "d (def. map) integrated over the domain: 35.944 at time: 0.150\n",
+ "Strain energy E( eps(|u|^2) ): 0.00020 at time 0.150\n",
+ "Residual of scheme -> 'delta' value: -0.00005 at time 0.150\n",
+ "\n",
+ "J integrated over the domain: 3.678 at time: 0.160\n",
+ "J_n integrated over the domain: 5.652 at time: 0.160\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.160\n",
+ "d (def. map) integrated over the domain: 17.531 at time: 0.160\n",
+ "Strain energy E( eps(|u|^2) ): 0.00016 at time 0.160\n",
+ "Residual of scheme -> 'delta' value: -0.00005 at time 0.160\n",
+ "\n",
+ "J integrated over the domain: 2.228 at time: 0.170\n",
+ "J_n integrated over the domain: 3.678 at time: 0.170\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.170\n",
+ "d (def. map) integrated over the domain: 8.963 at time: 0.170\n",
+ "Strain energy E( eps(|u|^2) ): 0.00008 at time 0.170\n",
+ "Residual of scheme -> 'delta' value: -0.00004 at time 0.170\n",
+ "\n",
+ "J integrated over the domain: 1.391 at time: 0.180\n",
+ "J_n integrated over the domain: 2.228 at time: 0.180\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.180\n",
+ "d (def. map) integrated over the domain: 5.936 at time: 0.180\n",
+ "Strain energy E( eps(|u|^2) ): 0.00002 at time 0.180\n",
+ "Residual of scheme -> 'delta' value: -0.00002 at time 0.180\n",
+ "\n",
+ "J integrated over the domain: 1.221 at time: 0.190\n",
+ "J_n integrated over the domain: 1.391 at time: 0.190\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.190\n",
+ "d (def. map) integrated over the domain: 5.492 at time: 0.190\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.190\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.190\n",
+ "\n",
+ "J integrated over the domain: 1.729 at time: 0.200\n",
+ "J_n integrated over the domain: 1.221 at time: 0.200\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.200\n",
+ "d (def. map) integrated over the domain: 6.988 at time: 0.200\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.200\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.200\n",
+ "\n",
+ "J integrated over the domain: 2.881 at time: 0.210\n",
+ "J_n integrated over the domain: 1.729 at time: 0.210\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.210\n",
+ "d (def. map) integrated over the domain: 12.302 at time: 0.210\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.210\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.210\n",
+ "\n",
+ "J integrated over the domain: 4.607 at time: 0.220\n",
+ "J_n integrated over the domain: 2.881 at time: 0.220\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.220\n",
+ "d (def. map) integrated over the domain: 25.223 at time: 0.220\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.220\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.220\n",
+ "\n",
+ "J integrated over the domain: 6.797 at time: 0.230\n",
+ "J_n integrated over the domain: 4.607 at time: 0.230\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.230\n",
+ "d (def. map) integrated over the domain: 50.200 at time: 0.230\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.230\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.230\n",
+ "\n",
+ "J integrated over the domain: 9.314 at time: 0.240\n",
+ "J_n integrated over the domain: 6.797 at time: 0.240\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.240\n",
+ "d (def. map) integrated over the domain: 90.753 at time: 0.240\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.240\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.240\n",
+ "\n"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "J integrated over the domain: 12.000 at time: 0.250\n",
+ "J_n integrated over the domain: 9.314 at time: 0.250\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.250\n",
+ "d (def. map) integrated over the domain: 148.000 at time: 0.250\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.250\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.250\n",
+ "\n",
+ "J integrated over the domain: 14.686 at time: 0.260\n",
+ "J_n integrated over the domain: 12.000 at time: 0.260\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.260\n",
+ "d (def. map) integrated over the domain: 219.674 at time: 0.260\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.260\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.260\n",
+ "\n",
+ "J integrated over the domain: 17.203 at time: 0.270\n",
+ "J_n integrated over the domain: 14.686 at time: 0.270\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.270\n",
+ "d (def. map) integrated over the domain: 299.941 at time: 0.270\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.270\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.270\n",
+ "\n",
+ "J integrated over the domain: 19.393 at time: 0.280\n",
+ "J_n integrated over the domain: 17.203 at time: 0.280\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.280\n",
+ "d (def. map) integrated over the domain: 380.093 at time: 0.280\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.280\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.280\n",
+ "\n",
+ "J integrated over the domain: 21.119 at time: 0.290\n",
+ "J_n integrated over the domain: 19.393 at time: 0.290\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.290\n",
+ "d (def. map) integrated over the domain: 450.001 at time: 0.290\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.290\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.290\n",
+ "\n",
+ "J integrated over the domain: 22.271 at time: 0.300\n",
+ "J_n integrated over the domain: 21.119 at time: 0.300\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.300\n",
+ "d (def. map) integrated over the domain: 500.016 at time: 0.300\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.300\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.300\n",
+ "\n",
+ "J integrated over the domain: 22.779 at time: 0.310\n",
+ "J_n integrated over the domain: 22.271 at time: 0.310\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.310\n",
+ "d (def. map) integrated over the domain: 522.869 at time: 0.310\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.310\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.310\n",
+ "\n",
+ "J integrated over the domain: 22.609 at time: 0.320\n",
+ "J_n integrated over the domain: 22.779 at time: 0.320\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.320\n",
+ "d (def. map) integrated over the domain: 515.153 at time: 0.320\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.320\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.320\n",
+ "\n",
+ "J integrated over the domain: 21.772 at time: 0.330\n",
+ "J_n integrated over the domain: 22.609 at time: 0.330\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.330\n",
+ "d (def. map) integrated over the domain: 478.026 at time: 0.330\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.330\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.330\n",
+ "\n",
+ "J integrated over the domain: 20.322 at time: 0.340\n",
+ "J_n integrated over the domain: 21.772 at time: 0.340\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.340\n",
+ "d (def. map) integrated over the domain: 416.965 at time: 0.340\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.340\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.340\n",
+ "\n",
+ "J integrated over the domain: 18.348 at time: 0.350\n",
+ "J_n integrated over the domain: 20.322 at time: 0.350\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.350\n",
+ "d (def. map) integrated over the domain: 340.652 at time: 0.350\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.350\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.350\n",
+ "\n",
+ "J integrated over the domain: 15.976 at time: 0.360\n",
+ "J_n integrated over the domain: 18.348 at time: 0.360\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.360\n",
+ "d (def. map) integrated over the domain: 259.224 at time: 0.360\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.360\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.360\n",
+ "\n",
+ "J integrated over the domain: 13.354 at time: 0.370\n",
+ "J_n integrated over the domain: 15.976 at time: 0.370\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.370\n",
+ "d (def. map) integrated over the domain: 182.319 at time: 0.370\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.370\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.370\n",
+ "\n",
+ "J integrated over the domain: 10.646 at time: 0.380\n",
+ "J_n integrated over the domain: 13.354 at time: 0.380\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.380\n",
+ "d (def. map) integrated over the domain: 117.346 at time: 0.380\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.380\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.380\n",
+ "\n",
+ "J integrated over the domain: 8.024 at time: 0.390\n",
+ "J_n integrated over the domain: 10.646 at time: 0.390\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.390\n",
+ "d (def. map) integrated over the domain: 68.389 at time: 0.390\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.390\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.390\n",
+ "\n",
+ "J integrated over the domain: 5.652 at time: 0.400\n",
+ "J_n integrated over the domain: 8.024 at time: 0.400\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.400\n",
+ "d (def. map) integrated over the domain: 35.944 at time: 0.400\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.400\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.400\n",
+ "\n",
+ "J integrated over the domain: 3.678 at time: 0.410\n",
+ "J_n integrated over the domain: 5.652 at time: 0.410\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.410\n",
+ "d (def. map) integrated over the domain: 17.531 at time: 0.410\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.410\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.410\n",
+ "\n",
+ "J integrated over the domain: 2.228 at time: 0.420\n",
+ "J_n integrated over the domain: 3.678 at time: 0.420\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.420\n",
+ "d (def. map) integrated over the domain: 8.963 at time: 0.420\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.420\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.420\n",
+ "\n",
+ "J integrated over the domain: 1.391 at time: 0.430\n",
+ "J_n integrated over the domain: 2.228 at time: 0.430\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.430\n",
+ "d (def. map) integrated over the domain: 5.936 at time: 0.430\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.430\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.430\n",
+ "\n",
+ "J integrated over the domain: 1.221 at time: 0.440\n",
+ "J_n integrated over the domain: 1.391 at time: 0.440\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.440\n",
+ "d (def. map) integrated over the domain: 5.492 at time: 0.440\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.440\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.440\n",
+ "\n",
+ "J integrated over the domain: 1.729 at time: 0.450\n",
+ "J_n integrated over the domain: 1.221 at time: 0.450\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.450\n",
+ "d (def. map) integrated over the domain: 6.988 at time: 0.450\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.450\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.450\n",
+ "\n",
+ "J integrated over the domain: 2.881 at time: 0.460\n",
+ "J_n integrated over the domain: 1.729 at time: 0.460\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.460\n",
+ "d (def. map) integrated over the domain: 12.302 at time: 0.460\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.460\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.460\n",
+ "\n",
+ "J integrated over the domain: 4.607 at time: 0.470\n",
+ "J_n integrated over the domain: 2.881 at time: 0.470\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.470\n",
+ "d (def. map) integrated over the domain: 25.223 at time: 0.470\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.470\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.470\n",
+ "\n",
+ "J integrated over the domain: 6.797 at time: 0.480\n",
+ "J_n integrated over the domain: 4.607 at time: 0.480\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.480\n",
+ "d (def. map) integrated over the domain: 50.200 at time: 0.480\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.480\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.480\n",
+ "\n",
+ "J integrated over the domain: 9.314 at time: 0.490\n",
+ "J_n integrated over the domain: 6.797 at time: 0.490\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.490\n",
+ "d (def. map) integrated over the domain: 90.753 at time: 0.490\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.490\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.490\n",
+ "\n"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "J integrated over the domain: 12.000 at time: 0.500\n",
+ "J_n integrated over the domain: 9.314 at time: 0.500\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.500\n",
+ "d (def. map) integrated over the domain: 148.000 at time: 0.500\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.500\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.500\n",
+ "\n",
+ "J integrated over the domain: 14.686 at time: 0.510\n",
+ "J_n integrated over the domain: 12.000 at time: 0.510\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.510\n",
+ "d (def. map) integrated over the domain: 219.674 at time: 0.510\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.510\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.510\n",
+ "\n",
+ "J integrated over the domain: 17.203 at time: 0.520\n",
+ "J_n integrated over the domain: 14.686 at time: 0.520\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.520\n",
+ "d (def. map) integrated over the domain: 299.941 at time: 0.520\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.520\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.520\n",
+ "\n",
+ "J integrated over the domain: 19.393 at time: 0.530\n",
+ "J_n integrated over the domain: 17.203 at time: 0.530\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.530\n",
+ "d (def. map) integrated over the domain: 380.093 at time: 0.530\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.530\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.530\n",
+ "\n",
+ "J integrated over the domain: 21.119 at time: 0.540\n",
+ "J_n integrated over the domain: 19.393 at time: 0.540\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.540\n",
+ "d (def. map) integrated over the domain: 450.001 at time: 0.540\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.540\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.540\n",
+ "\n",
+ "J integrated over the domain: 22.271 at time: 0.550\n",
+ "J_n integrated over the domain: 21.119 at time: 0.550\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.550\n",
+ "d (def. map) integrated over the domain: 500.016 at time: 0.550\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.550\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.550\n",
+ "\n",
+ "J integrated over the domain: 22.779 at time: 0.560\n",
+ "J_n integrated over the domain: 22.271 at time: 0.560\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.560\n",
+ "d (def. map) integrated over the domain: 522.869 at time: 0.560\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.560\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.560\n",
+ "\n",
+ "J integrated over the domain: 22.609 at time: 0.570\n",
+ "J_n integrated over the domain: 22.779 at time: 0.570\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.570\n",
+ "d (def. map) integrated over the domain: 515.153 at time: 0.570\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.570\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.570\n",
+ "\n",
+ "J integrated over the domain: 21.772 at time: 0.580\n",
+ "J_n integrated over the domain: 22.609 at time: 0.580\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.580\n",
+ "d (def. map) integrated over the domain: 478.026 at time: 0.580\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.580\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.580\n",
+ "\n",
+ "J integrated over the domain: 20.322 at time: 0.590\n",
+ "J_n integrated over the domain: 21.772 at time: 0.590\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.590\n",
+ "d (def. map) integrated over the domain: 416.965 at time: 0.590\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.590\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.590\n",
+ "\n",
+ "J integrated over the domain: 18.348 at time: 0.600\n",
+ "J_n integrated over the domain: 20.322 at time: 0.600\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.600\n",
+ "d (def. map) integrated over the domain: 340.652 at time: 0.600\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.600\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.600\n",
+ "\n",
+ "J integrated over the domain: 15.976 at time: 0.610\n",
+ "J_n integrated over the domain: 18.348 at time: 0.610\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.610\n",
+ "d (def. map) integrated over the domain: 259.224 at time: 0.610\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.610\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.610\n",
+ "\n",
+ "J integrated over the domain: 13.354 at time: 0.620\n",
+ "J_n integrated over the domain: 15.976 at time: 0.620\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.620\n",
+ "d (def. map) integrated over the domain: 182.319 at time: 0.620\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.620\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.620\n",
+ "\n",
+ "J integrated over the domain: 10.646 at time: 0.630\n",
+ "J_n integrated over the domain: 13.354 at time: 0.630\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.630\n",
+ "d (def. map) integrated over the domain: 117.346 at time: 0.630\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.630\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.630\n",
+ "\n",
+ "J integrated over the domain: 8.024 at time: 0.640\n",
+ "J_n integrated over the domain: 10.646 at time: 0.640\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.640\n",
+ "d (def. map) integrated over the domain: 68.389 at time: 0.640\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.640\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.640\n",
+ "\n",
+ "J integrated over the domain: 5.652 at time: 0.650\n",
+ "J_n integrated over the domain: 8.024 at time: 0.650\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.650\n",
+ "d (def. map) integrated over the domain: 35.944 at time: 0.650\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.650\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.650\n",
+ "\n",
+ "J integrated over the domain: 3.678 at time: 0.660\n",
+ "J_n integrated over the domain: 5.652 at time: 0.660\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.660\n",
+ "d (def. map) integrated over the domain: 17.531 at time: 0.660\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.660\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.660\n",
+ "\n",
+ "J integrated over the domain: 2.228 at time: 0.670\n",
+ "J_n integrated over the domain: 3.678 at time: 0.670\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.670\n",
+ "d (def. map) integrated over the domain: 8.963 at time: 0.670\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.670\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.670\n",
+ "\n",
+ "J integrated over the domain: 1.391 at time: 0.680\n",
+ "J_n integrated over the domain: 2.228 at time: 0.680\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.680\n",
+ "d (def. map) integrated over the domain: 5.936 at time: 0.680\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.680\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.680\n",
+ "\n",
+ "J integrated over the domain: 1.221 at time: 0.690\n",
+ "J_n integrated over the domain: 1.391 at time: 0.690\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.690\n",
+ "d (def. map) integrated over the domain: 5.492 at time: 0.690\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.690\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.690\n",
+ "\n",
+ "J integrated over the domain: 1.729 at time: 0.700\n",
+ "J_n integrated over the domain: 1.221 at time: 0.700\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.700\n",
+ "d (def. map) integrated over the domain: 6.988 at time: 0.700\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.700\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.700\n",
+ "\n",
+ "J integrated over the domain: 2.881 at time: 0.710\n",
+ "J_n integrated over the domain: 1.729 at time: 0.710\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.710\n",
+ "d (def. map) integrated over the domain: 12.302 at time: 0.710\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.710\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.710\n",
+ "\n",
+ "J integrated over the domain: 4.607 at time: 0.720\n",
+ "J_n integrated over the domain: 2.881 at time: 0.720\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.720\n",
+ "d (def. map) integrated over the domain: 25.223 at time: 0.720\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.720\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.720\n",
+ "\n",
+ "J integrated over the domain: 6.797 at time: 0.730\n",
+ "J_n integrated over the domain: 4.607 at time: 0.730\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.730\n",
+ "d (def. map) integrated over the domain: 50.200 at time: 0.730\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.730\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.730\n",
+ "\n",
+ "J integrated over the domain: 9.314 at time: 0.740\n",
+ "J_n integrated over the domain: 6.797 at time: 0.740\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.740\n",
+ "d (def. map) integrated over the domain: 90.753 at time: 0.740\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.740\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.740\n",
+ "\n"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "J integrated over the domain: 12.000 at time: 0.750\n",
+ "J_n integrated over the domain: 9.314 at time: 0.750\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.750\n",
+ "d (def. map) integrated over the domain: 148.000 at time: 0.750\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.750\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.750\n",
+ "\n",
+ "J integrated over the domain: 14.686 at time: 0.760\n",
+ "J_n integrated over the domain: 12.000 at time: 0.760\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.760\n",
+ "d (def. map) integrated over the domain: 219.674 at time: 0.760\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.760\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.760\n",
+ "\n",
+ "J integrated over the domain: 17.203 at time: 0.770\n",
+ "J_n integrated over the domain: 14.686 at time: 0.770\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.770\n",
+ "d (def. map) integrated over the domain: 299.941 at time: 0.770\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.770\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.770\n",
+ "\n",
+ "J integrated over the domain: 19.393 at time: 0.780\n",
+ "J_n integrated over the domain: 17.203 at time: 0.780\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.780\n",
+ "d (def. map) integrated over the domain: 380.093 at time: 0.780\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.780\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.780\n",
+ "\n",
+ "J integrated over the domain: 21.119 at time: 0.790\n",
+ "J_n integrated over the domain: 19.393 at time: 0.790\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.790\n",
+ "d (def. map) integrated over the domain: 450.001 at time: 0.790\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.790\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.790\n",
+ "\n",
+ "J integrated over the domain: 22.271 at time: 0.800\n",
+ "J_n integrated over the domain: 21.119 at time: 0.800\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.800\n",
+ "d (def. map) integrated over the domain: 500.016 at time: 0.800\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.800\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.800\n",
+ "\n",
+ "J integrated over the domain: 22.779 at time: 0.810\n",
+ "J_n integrated over the domain: 22.271 at time: 0.810\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.810\n",
+ "d (def. map) integrated over the domain: 522.869 at time: 0.810\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.810\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.810\n",
+ "\n",
+ "J integrated over the domain: 22.609 at time: 0.820\n",
+ "J_n integrated over the domain: 22.779 at time: 0.820\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.820\n",
+ "d (def. map) integrated over the domain: 515.153 at time: 0.820\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.820\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.820\n",
+ "\n",
+ "J integrated over the domain: 21.772 at time: 0.830\n",
+ "J_n integrated over the domain: 22.609 at time: 0.830\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.830\n",
+ "d (def. map) integrated over the domain: 478.026 at time: 0.830\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.830\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.830\n",
+ "\n",
+ "J integrated over the domain: 20.322 at time: 0.840\n",
+ "J_n integrated over the domain: 21.772 at time: 0.840\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.840\n",
+ "d (def. map) integrated over the domain: 416.965 at time: 0.840\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.840\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.840\n",
+ "\n",
+ "J integrated over the domain: 18.348 at time: 0.850\n",
+ "J_n integrated over the domain: 20.322 at time: 0.850\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.850\n",
+ "d (def. map) integrated over the domain: 340.652 at time: 0.850\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.850\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.850\n",
+ "\n",
+ "J integrated over the domain: 15.976 at time: 0.860\n",
+ "J_n integrated over the domain: 18.348 at time: 0.860\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.860\n",
+ "d (def. map) integrated over the domain: 259.224 at time: 0.860\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.860\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.860\n",
+ "\n",
+ "J integrated over the domain: 13.354 at time: 0.870\n",
+ "J_n integrated over the domain: 15.976 at time: 0.870\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.870\n",
+ "d (def. map) integrated over the domain: 182.319 at time: 0.870\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.870\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.870\n",
+ "\n",
+ "J integrated over the domain: 10.646 at time: 0.880\n",
+ "J_n integrated over the domain: 13.354 at time: 0.880\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.880\n",
+ "d (def. map) integrated over the domain: 117.346 at time: 0.880\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.880\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.880\n",
+ "\n",
+ "J integrated over the domain: 8.024 at time: 0.890\n",
+ "J_n integrated over the domain: 10.646 at time: 0.890\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.890\n",
+ "d (def. map) integrated over the domain: 68.389 at time: 0.890\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.890\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.890\n",
+ "\n",
+ "J integrated over the domain: 5.652 at time: 0.900\n",
+ "J_n integrated over the domain: 8.024 at time: 0.900\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.900\n",
+ "d (def. map) integrated over the domain: 35.944 at time: 0.900\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.900\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.900\n",
+ "\n",
+ "J integrated over the domain: 3.678 at time: 0.910\n",
+ "J_n integrated over the domain: 5.652 at time: 0.910\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.910\n",
+ "d (def. map) integrated over the domain: 17.531 at time: 0.910\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.910\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.910\n",
+ "\n",
+ "J integrated over the domain: 2.228 at time: 0.920\n",
+ "J_n integrated over the domain: 3.678 at time: 0.920\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.920\n",
+ "d (def. map) integrated over the domain: 8.963 at time: 0.920\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.920\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.920\n",
+ "\n",
+ "J integrated over the domain: 1.391 at time: 0.930\n",
+ "J_n integrated over the domain: 2.228 at time: 0.930\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.930\n",
+ "d (def. map) integrated over the domain: 5.936 at time: 0.930\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.930\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.930\n",
+ "\n",
+ "J integrated over the domain: 1.221 at time: 0.940\n",
+ "J_n integrated over the domain: 1.391 at time: 0.940\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.940\n",
+ "d (def. map) integrated over the domain: 5.492 at time: 0.940\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.940\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.940\n",
+ "\n",
+ "J integrated over the domain: 1.729 at time: 0.950\n",
+ "J_n integrated over the domain: 1.221 at time: 0.950\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.950\n",
+ "d (def. map) integrated over the domain: 6.988 at time: 0.950\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.950\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.950\n",
+ "\n",
+ "J integrated over the domain: 2.881 at time: 0.960\n",
+ "J_n integrated over the domain: 1.729 at time: 0.960\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.960\n",
+ "d (def. map) integrated over the domain: 12.302 at time: 0.960\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.960\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.960\n",
+ "\n",
+ "J integrated over the domain: 4.607 at time: 0.970\n",
+ "J_n integrated over the domain: 2.881 at time: 0.970\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.970\n",
+ "d (def. map) integrated over the domain: 25.223 at time: 0.970\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.970\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.970\n",
+ "\n",
+ "J integrated over the domain: 6.797 at time: 0.980\n",
+ "J_n integrated over the domain: 4.607 at time: 0.980\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.980\n",
+ "d (def. map) integrated over the domain: 50.200 at time: 0.980\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.980\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.980\n",
+ "\n",
+ "J integrated over the domain: 9.314 at time: 0.990\n",
+ "J_n integrated over the domain: 6.797 at time: 0.990\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.990\n",
+ "d (def. map) integrated over the domain: 90.753 at time: 0.990\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.990\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.990\n",
+ "\n"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "J integrated over the domain: 12.000 at time: 1.000\n",
+ "J_n integrated over the domain: 9.314 at time: 1.000\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.000\n",
+ "d (def. map) integrated over the domain: 148.000 at time: 1.000\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.000\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.000\n",
+ "\n",
+ "J integrated over the domain: 14.686 at time: 1.010\n",
+ "J_n integrated over the domain: 12.000 at time: 1.010\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.010\n",
+ "d (def. map) integrated over the domain: 219.674 at time: 1.010\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.010\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.010\n",
+ "\n",
+ "J integrated over the domain: 17.203 at time: 1.020\n",
+ "J_n integrated over the domain: 14.686 at time: 1.020\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.020\n",
+ "d (def. map) integrated over the domain: 299.941 at time: 1.020\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.020\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.020\n",
+ "\n",
+ "J integrated over the domain: 19.393 at time: 1.030\n",
+ "J_n integrated over the domain: 17.203 at time: 1.030\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.030\n",
+ "d (def. map) integrated over the domain: 380.093 at time: 1.030\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.030\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.030\n",
+ "\n",
+ "J integrated over the domain: 21.119 at time: 1.040\n",
+ "J_n integrated over the domain: 19.393 at time: 1.040\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.040\n",
+ "d (def. map) integrated over the domain: 450.001 at time: 1.040\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.040\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.040\n",
+ "\n",
+ "J integrated over the domain: 22.271 at time: 1.050\n",
+ "J_n integrated over the domain: 21.119 at time: 1.050\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.050\n",
+ "d (def. map) integrated over the domain: 500.016 at time: 1.050\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.050\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.050\n",
+ "\n",
+ "J integrated over the domain: 22.779 at time: 1.060\n",
+ "J_n integrated over the domain: 22.271 at time: 1.060\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.060\n",
+ "d (def. map) integrated over the domain: 522.869 at time: 1.060\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.060\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.060\n",
+ "\n",
+ "J integrated over the domain: 22.609 at time: 1.070\n",
+ "J_n integrated over the domain: 22.779 at time: 1.070\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.070\n",
+ "d (def. map) integrated over the domain: 515.153 at time: 1.070\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.070\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.070\n",
+ "\n",
+ "J integrated over the domain: 21.772 at time: 1.080\n",
+ "J_n integrated over the domain: 22.609 at time: 1.080\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.080\n",
+ "d (def. map) integrated over the domain: 478.026 at time: 1.080\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.080\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.080\n",
+ "\n",
+ "J integrated over the domain: 20.322 at time: 1.090\n",
+ "J_n integrated over the domain: 21.772 at time: 1.090\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.090\n",
+ "d (def. map) integrated over the domain: 416.965 at time: 1.090\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.090\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.090\n",
+ "\n",
+ "J integrated over the domain: 18.348 at time: 1.100\n",
+ "J_n integrated over the domain: 20.322 at time: 1.100\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.100\n",
+ "d (def. map) integrated over the domain: 340.652 at time: 1.100\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.100\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.100\n",
+ "\n",
+ "J integrated over the domain: 15.976 at time: 1.110\n",
+ "J_n integrated over the domain: 18.348 at time: 1.110\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.110\n",
+ "d (def. map) integrated over the domain: 259.224 at time: 1.110\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.110\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.110\n",
+ "\n",
+ "J integrated over the domain: 13.354 at time: 1.120\n",
+ "J_n integrated over the domain: 15.976 at time: 1.120\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.120\n",
+ "d (def. map) integrated over the domain: 182.319 at time: 1.120\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.120\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.120\n",
+ "\n",
+ "J integrated over the domain: 10.646 at time: 1.130\n",
+ "J_n integrated over the domain: 13.354 at time: 1.130\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.130\n",
+ "d (def. map) integrated over the domain: 117.346 at time: 1.130\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.130\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.130\n",
+ "\n",
+ "J integrated over the domain: 8.024 at time: 1.140\n",
+ "J_n integrated over the domain: 10.646 at time: 1.140\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.140\n",
+ "d (def. map) integrated over the domain: 68.389 at time: 1.140\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.140\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.140\n",
+ "\n",
+ "J integrated over the domain: 5.652 at time: 1.150\n",
+ "J_n integrated over the domain: 8.024 at time: 1.150\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.150\n",
+ "d (def. map) integrated over the domain: 35.944 at time: 1.150\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.150\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.150\n",
+ "\n",
+ "J integrated over the domain: 3.678 at time: 1.160\n",
+ "J_n integrated over the domain: 5.652 at time: 1.160\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.160\n",
+ "d (def. map) integrated over the domain: 17.531 at time: 1.160\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.160\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.160\n",
+ "\n",
+ "J integrated over the domain: 2.228 at time: 1.170\n",
+ "J_n integrated over the domain: 3.678 at time: 1.170\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.170\n",
+ "d (def. map) integrated over the domain: 8.963 at time: 1.170\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.170\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.170\n",
+ "\n",
+ "J integrated over the domain: 1.391 at time: 1.180\n",
+ "J_n integrated over the domain: 2.228 at time: 1.180\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.180\n",
+ "d (def. map) integrated over the domain: 5.936 at time: 1.180\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.180\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.180\n",
+ "\n",
+ "J integrated over the domain: 1.221 at time: 1.190\n",
+ "J_n integrated over the domain: 1.391 at time: 1.190\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.190\n",
+ "d (def. map) integrated over the domain: 5.492 at time: 1.190\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.190\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.190\n",
+ "\n",
+ "J integrated over the domain: 1.729 at time: 1.200\n",
+ "J_n integrated over the domain: 1.221 at time: 1.200\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.200\n",
+ "d (def. map) integrated over the domain: 6.988 at time: 1.200\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.200\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.200\n",
+ "\n",
+ "J integrated over the domain: 2.881 at time: 1.210\n",
+ "J_n integrated over the domain: 1.729 at time: 1.210\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.210\n",
+ "d (def. map) integrated over the domain: 12.302 at time: 1.210\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.210\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.210\n",
+ "\n",
+ "J integrated over the domain: 4.607 at time: 1.220\n",
+ "J_n integrated over the domain: 2.881 at time: 1.220\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.220\n",
+ "d (def. map) integrated over the domain: 25.223 at time: 1.220\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.220\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.220\n",
+ "\n",
+ "J integrated over the domain: 6.797 at time: 1.230\n",
+ "J_n integrated over the domain: 4.607 at time: 1.230\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.230\n",
+ "d (def. map) integrated over the domain: 50.200 at time: 1.230\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.230\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.230\n",
+ "\n",
+ "J integrated over the domain: 9.314 at time: 1.240\n",
+ "J_n integrated over the domain: 6.797 at time: 1.240\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.240\n",
+ "d (def. map) integrated over the domain: 90.753 at time: 1.240\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.240\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.240\n",
+ "\n"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "J integrated over the domain: 12.000 at time: 1.250\n",
+ "J_n integrated over the domain: 9.314 at time: 1.250\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.250\n",
+ "d (def. map) integrated over the domain: 148.000 at time: 1.250\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.250\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.250\n",
+ "\n",
+ "J integrated over the domain: 14.686 at time: 1.260\n",
+ "J_n integrated over the domain: 12.000 at time: 1.260\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.260\n",
+ "d (def. map) integrated over the domain: 219.674 at time: 1.260\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.260\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.260\n",
+ "\n",
+ "J integrated over the domain: 17.203 at time: 1.270\n",
+ "J_n integrated over the domain: 14.686 at time: 1.270\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.270\n",
+ "d (def. map) integrated over the domain: 299.941 at time: 1.270\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.270\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.270\n",
+ "\n",
+ "J integrated over the domain: 19.393 at time: 1.280\n",
+ "J_n integrated over the domain: 17.203 at time: 1.280\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.280\n",
+ "d (def. map) integrated over the domain: 380.093 at time: 1.280\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.280\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.280\n",
+ "\n",
+ "J integrated over the domain: 21.119 at time: 1.290\n",
+ "J_n integrated over the domain: 19.393 at time: 1.290\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.290\n",
+ "d (def. map) integrated over the domain: 450.001 at time: 1.290\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.290\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.290\n",
+ "\n",
+ "J integrated over the domain: 22.271 at time: 1.300\n",
+ "J_n integrated over the domain: 21.119 at time: 1.300\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.300\n",
+ "d (def. map) integrated over the domain: 500.016 at time: 1.300\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.300\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.300\n",
+ "\n",
+ "J integrated over the domain: 22.779 at time: 1.310\n",
+ "J_n integrated over the domain: 22.271 at time: 1.310\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.310\n",
+ "d (def. map) integrated over the domain: 522.869 at time: 1.310\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.310\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.310\n",
+ "\n",
+ "J integrated over the domain: 22.609 at time: 1.320\n",
+ "J_n integrated over the domain: 22.779 at time: 1.320\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.320\n",
+ "d (def. map) integrated over the domain: 515.153 at time: 1.320\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.320\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.320\n",
+ "\n",
+ "J integrated over the domain: 21.772 at time: 1.330\n",
+ "J_n integrated over the domain: 22.609 at time: 1.330\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.330\n",
+ "d (def. map) integrated over the domain: 478.026 at time: 1.330\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.330\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.330\n",
+ "\n",
+ "J integrated over the domain: 20.322 at time: 1.340\n",
+ "J_n integrated over the domain: 21.772 at time: 1.340\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.340\n",
+ "d (def. map) integrated over the domain: 416.965 at time: 1.340\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.340\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.340\n",
+ "\n",
+ "J integrated over the domain: 18.348 at time: 1.350\n",
+ "J_n integrated over the domain: 20.322 at time: 1.350\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.350\n",
+ "d (def. map) integrated over the domain: 340.652 at time: 1.350\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.350\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.350\n",
+ "\n",
+ "J integrated over the domain: 15.976 at time: 1.360\n",
+ "J_n integrated over the domain: 18.348 at time: 1.360\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.360\n",
+ "d (def. map) integrated over the domain: 259.224 at time: 1.360\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.360\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.360\n",
+ "\n",
+ "J integrated over the domain: 13.354 at time: 1.370\n",
+ "J_n integrated over the domain: 15.976 at time: 1.370\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.370\n",
+ "d (def. map) integrated over the domain: 182.319 at time: 1.370\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.370\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.370\n",
+ "\n",
+ "J integrated over the domain: 10.646 at time: 1.380\n",
+ "J_n integrated over the domain: 13.354 at time: 1.380\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.380\n",
+ "d (def. map) integrated over the domain: 117.346 at time: 1.380\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.380\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.380\n",
+ "\n",
+ "J integrated over the domain: 8.024 at time: 1.390\n",
+ "J_n integrated over the domain: 10.646 at time: 1.390\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.390\n",
+ "d (def. map) integrated over the domain: 68.389 at time: 1.390\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.390\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.390\n",
+ "\n",
+ "J integrated over the domain: 5.652 at time: 1.400\n",
+ "J_n integrated over the domain: 8.024 at time: 1.400\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.400\n",
+ "d (def. map) integrated over the domain: 35.944 at time: 1.400\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.400\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.400\n",
+ "\n",
+ "J integrated over the domain: 3.678 at time: 1.410\n",
+ "J_n integrated over the domain: 5.652 at time: 1.410\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.410\n",
+ "d (def. map) integrated over the domain: 17.531 at time: 1.410\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.410\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.410\n",
+ "\n",
+ "J integrated over the domain: 2.228 at time: 1.420\n",
+ "J_n integrated over the domain: 3.678 at time: 1.420\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.420\n",
+ "d (def. map) integrated over the domain: 8.963 at time: 1.420\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.420\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.420\n",
+ "\n",
+ "J integrated over the domain: 1.391 at time: 1.430\n",
+ "J_n integrated over the domain: 2.228 at time: 1.430\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.430\n",
+ "d (def. map) integrated over the domain: 5.936 at time: 1.430\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.430\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.430\n",
+ "\n",
+ "J integrated over the domain: 1.221 at time: 1.440\n",
+ "J_n integrated over the domain: 1.391 at time: 1.440\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.440\n",
+ "d (def. map) integrated over the domain: 5.492 at time: 1.440\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.440\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.440\n",
+ "\n",
+ "J integrated over the domain: 1.729 at time: 1.450\n",
+ "J_n integrated over the domain: 1.221 at time: 1.450\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.450\n",
+ "d (def. map) integrated over the domain: 6.988 at time: 1.450\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.450\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.450\n",
+ "\n",
+ "J integrated over the domain: 2.881 at time: 1.460\n",
+ "J_n integrated over the domain: 1.729 at time: 1.460\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.460\n",
+ "d (def. map) integrated over the domain: 12.302 at time: 1.460\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.460\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.460\n",
+ "\n",
+ "J integrated over the domain: 4.607 at time: 1.470\n",
+ "J_n integrated over the domain: 2.881 at time: 1.470\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.470\n",
+ "d (def. map) integrated over the domain: 25.223 at time: 1.470\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.470\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.470\n",
+ "\n",
+ "J integrated over the domain: 6.797 at time: 1.480\n",
+ "J_n integrated over the domain: 4.607 at time: 1.480\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.480\n",
+ "d (def. map) integrated over the domain: 50.200 at time: 1.480\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.480\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.480\n",
+ "\n",
+ "J integrated over the domain: 9.314 at time: 1.490\n",
+ "J_n integrated over the domain: 6.797 at time: 1.490\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.490\n",
+ "d (def. map) integrated over the domain: 90.753 at time: 1.490\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.490\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.490\n",
+ "\n"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "J integrated over the domain: 12.000 at time: 1.500\n",
+ "J_n integrated over the domain: 9.314 at time: 1.500\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.500\n",
+ "d (def. map) integrated over the domain: 148.000 at time: 1.500\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.500\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.500\n",
+ "\n",
+ "J integrated over the domain: 14.686 at time: 1.510\n",
+ "J_n integrated over the domain: 12.000 at time: 1.510\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.510\n",
+ "d (def. map) integrated over the domain: 219.674 at time: 1.510\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.510\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.510\n",
+ "\n",
+ "J integrated over the domain: 17.203 at time: 1.520\n",
+ "J_n integrated over the domain: 14.686 at time: 1.520\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.520\n",
+ "d (def. map) integrated over the domain: 299.941 at time: 1.520\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.520\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.520\n",
+ "\n",
+ "J integrated over the domain: 19.393 at time: 1.530\n",
+ "J_n integrated over the domain: 17.203 at time: 1.530\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.530\n",
+ "d (def. map) integrated over the domain: 380.093 at time: 1.530\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.530\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.530\n",
+ "\n",
+ "J integrated over the domain: 21.119 at time: 1.540\n",
+ "J_n integrated over the domain: 19.393 at time: 1.540\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.540\n",
+ "d (def. map) integrated over the domain: 450.001 at time: 1.540\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.540\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.540\n",
+ "\n",
+ "J integrated over the domain: 22.271 at time: 1.550\n",
+ "J_n integrated over the domain: 21.119 at time: 1.550\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.550\n",
+ "d (def. map) integrated over the domain: 500.016 at time: 1.550\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.550\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.550\n",
+ "\n",
+ "J integrated over the domain: 22.779 at time: 1.560\n",
+ "J_n integrated over the domain: 22.271 at time: 1.560\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.560\n",
+ "d (def. map) integrated over the domain: 522.869 at time: 1.560\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.560\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.560\n",
+ "\n",
+ "J integrated over the domain: 22.609 at time: 1.570\n",
+ "J_n integrated over the domain: 22.779 at time: 1.570\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.570\n",
+ "d (def. map) integrated over the domain: 515.153 at time: 1.570\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.570\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.570\n",
+ "\n",
+ "J integrated over the domain: 21.772 at time: 1.580\n",
+ "J_n integrated over the domain: 22.609 at time: 1.580\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.580\n",
+ "d (def. map) integrated over the domain: 478.026 at time: 1.580\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.580\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.580\n",
+ "\n",
+ "J integrated over the domain: 20.322 at time: 1.590\n",
+ "J_n integrated over the domain: 21.772 at time: 1.590\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.590\n",
+ "d (def. map) integrated over the domain: 416.965 at time: 1.590\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.590\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.590\n",
+ "\n",
+ "J integrated over the domain: 18.348 at time: 1.600\n",
+ "J_n integrated over the domain: 20.322 at time: 1.600\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.600\n",
+ "d (def. map) integrated over the domain: 340.652 at time: 1.600\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.600\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.600\n",
+ "\n",
+ "J integrated over the domain: 15.976 at time: 1.610\n",
+ "J_n integrated over the domain: 18.348 at time: 1.610\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.610\n",
+ "d (def. map) integrated over the domain: 259.224 at time: 1.610\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.610\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.610\n",
+ "\n",
+ "J integrated over the domain: 13.354 at time: 1.620\n",
+ "J_n integrated over the domain: 15.976 at time: 1.620\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.620\n",
+ "d (def. map) integrated over the domain: 182.319 at time: 1.620\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.620\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.620\n",
+ "\n",
+ "J integrated over the domain: 10.646 at time: 1.630\n",
+ "J_n integrated over the domain: 13.354 at time: 1.630\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.630\n",
+ "d (def. map) integrated over the domain: 117.346 at time: 1.630\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.630\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.630\n",
+ "\n",
+ "J integrated over the domain: 8.024 at time: 1.640\n",
+ "J_n integrated over the domain: 10.646 at time: 1.640\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.640\n",
+ "d (def. map) integrated over the domain: 68.389 at time: 1.640\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.640\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.640\n",
+ "\n",
+ "J integrated over the domain: 5.652 at time: 1.650\n",
+ "J_n integrated over the domain: 8.024 at time: 1.650\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.650\n",
+ "d (def. map) integrated over the domain: 35.944 at time: 1.650\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.650\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.650\n",
+ "\n",
+ "J integrated over the domain: 3.678 at time: 1.660\n",
+ "J_n integrated over the domain: 5.652 at time: 1.660\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.660\n",
+ "d (def. map) integrated over the domain: 17.531 at time: 1.660\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.660\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.660\n",
+ "\n",
+ "J integrated over the domain: 2.228 at time: 1.670\n",
+ "J_n integrated over the domain: 3.678 at time: 1.670\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.670\n",
+ "d (def. map) integrated over the domain: 8.963 at time: 1.670\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.670\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.670\n",
+ "\n",
+ "J integrated over the domain: 1.391 at time: 1.680\n",
+ "J_n integrated over the domain: 2.228 at time: 1.680\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.680\n",
+ "d (def. map) integrated over the domain: 5.936 at time: 1.680\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.680\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.680\n",
+ "\n",
+ "J integrated over the domain: 1.221 at time: 1.690\n",
+ "J_n integrated over the domain: 1.391 at time: 1.690\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.690\n",
+ "d (def. map) integrated over the domain: 5.492 at time: 1.690\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.690\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.690\n",
+ "\n",
+ "J integrated over the domain: 1.729 at time: 1.700\n",
+ "J_n integrated over the domain: 1.221 at time: 1.700\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.700\n",
+ "d (def. map) integrated over the domain: 6.988 at time: 1.700\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.700\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.700\n",
+ "\n",
+ "J integrated over the domain: 2.881 at time: 1.710\n",
+ "J_n integrated over the domain: 1.729 at time: 1.710\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.710\n",
+ "d (def. map) integrated over the domain: 12.302 at time: 1.710\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.710\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.710\n",
+ "\n",
+ "J integrated over the domain: 4.607 at time: 1.720\n",
+ "J_n integrated over the domain: 2.881 at time: 1.720\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.720\n",
+ "d (def. map) integrated over the domain: 25.223 at time: 1.720\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.720\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.720\n",
+ "\n",
+ "J integrated over the domain: 6.797 at time: 1.730\n",
+ "J_n integrated over the domain: 4.607 at time: 1.730\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.730\n",
+ "d (def. map) integrated over the domain: 50.200 at time: 1.730\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.730\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.730\n",
+ "\n",
+ "J integrated over the domain: 9.314 at time: 1.740\n",
+ "J_n integrated over the domain: 6.797 at time: 1.740\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.740\n",
+ "d (def. map) integrated over the domain: 90.753 at time: 1.740\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.740\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.740\n",
+ "\n"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "J integrated over the domain: 12.000 at time: 1.750\n",
+ "J_n integrated over the domain: 9.314 at time: 1.750\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.750\n",
+ "d (def. map) integrated over the domain: 148.000 at time: 1.750\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.750\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.750\n",
+ "\n",
+ "J integrated over the domain: 14.686 at time: 1.760\n",
+ "J_n integrated over the domain: 12.000 at time: 1.760\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.760\n",
+ "d (def. map) integrated over the domain: 219.674 at time: 1.760\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.760\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.760\n",
+ "\n",
+ "J integrated over the domain: 17.203 at time: 1.770\n",
+ "J_n integrated over the domain: 14.686 at time: 1.770\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.770\n",
+ "d (def. map) integrated over the domain: 299.941 at time: 1.770\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.770\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.770\n",
+ "\n",
+ "J integrated over the domain: 19.393 at time: 1.780\n",
+ "J_n integrated over the domain: 17.203 at time: 1.780\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.780\n",
+ "d (def. map) integrated over the domain: 380.093 at time: 1.780\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.780\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.780\n",
+ "\n",
+ "J integrated over the domain: 21.119 at time: 1.790\n",
+ "J_n integrated over the domain: 19.393 at time: 1.790\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.790\n",
+ "d (def. map) integrated over the domain: 450.001 at time: 1.790\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.790\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.790\n",
+ "\n",
+ "J integrated over the domain: 22.271 at time: 1.800\n",
+ "J_n integrated over the domain: 21.119 at time: 1.800\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.800\n",
+ "d (def. map) integrated over the domain: 500.016 at time: 1.800\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.800\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.800\n",
+ "\n",
+ "J integrated over the domain: 22.779 at time: 1.810\n",
+ "J_n integrated over the domain: 22.271 at time: 1.810\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.810\n",
+ "d (def. map) integrated over the domain: 522.869 at time: 1.810\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.810\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.810\n",
+ "\n",
+ "J integrated over the domain: 22.609 at time: 1.820\n",
+ "J_n integrated over the domain: 22.779 at time: 1.820\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.820\n",
+ "d (def. map) integrated over the domain: 515.153 at time: 1.820\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.820\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.820\n",
+ "\n",
+ "J integrated over the domain: 21.772 at time: 1.830\n",
+ "J_n integrated over the domain: 22.609 at time: 1.830\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.830\n",
+ "d (def. map) integrated over the domain: 478.026 at time: 1.830\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.830\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.830\n",
+ "\n",
+ "J integrated over the domain: 20.322 at time: 1.840\n",
+ "J_n integrated over the domain: 21.772 at time: 1.840\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.840\n",
+ "d (def. map) integrated over the domain: 416.965 at time: 1.840\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.840\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.840\n",
+ "\n",
+ "J integrated over the domain: 18.348 at time: 1.850\n",
+ "J_n integrated over the domain: 20.322 at time: 1.850\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.850\n",
+ "d (def. map) integrated over the domain: 340.652 at time: 1.850\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.850\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.850\n",
+ "\n",
+ "J integrated over the domain: 15.976 at time: 1.860\n",
+ "J_n integrated over the domain: 18.348 at time: 1.860\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.860\n",
+ "d (def. map) integrated over the domain: 259.224 at time: 1.860\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.860\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.860\n",
+ "\n",
+ "J integrated over the domain: 13.354 at time: 1.870\n",
+ "J_n integrated over the domain: 15.976 at time: 1.870\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.870\n",
+ "d (def. map) integrated over the domain: 182.319 at time: 1.870\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.870\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.870\n",
+ "\n",
+ "J integrated over the domain: 10.646 at time: 1.880\n",
+ "J_n integrated over the domain: 13.354 at time: 1.880\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.880\n",
+ "d (def. map) integrated over the domain: 117.346 at time: 1.880\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.880\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.880\n",
+ "\n",
+ "J integrated over the domain: 8.024 at time: 1.890\n",
+ "J_n integrated over the domain: 10.646 at time: 1.890\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.890\n",
+ "d (def. map) integrated over the domain: 68.389 at time: 1.890\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.890\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.890\n",
+ "\n",
+ "J integrated over the domain: 5.652 at time: 1.900\n",
+ "J_n integrated over the domain: 8.024 at time: 1.900\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.900\n",
+ "d (def. map) integrated over the domain: 35.944 at time: 1.900\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.900\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.900\n",
+ "\n",
+ "J integrated over the domain: 3.678 at time: 1.910\n",
+ "J_n integrated over the domain: 5.652 at time: 1.910\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.910\n",
+ "d (def. map) integrated over the domain: 17.531 at time: 1.910\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.910\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.910\n",
+ "\n",
+ "J integrated over the domain: 2.228 at time: 1.920\n",
+ "J_n integrated over the domain: 3.678 at time: 1.920\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.920\n",
+ "d (def. map) integrated over the domain: 8.963 at time: 1.920\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.920\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.920\n",
+ "\n",
+ "J integrated over the domain: 1.391 at time: 1.930\n",
+ "J_n integrated over the domain: 2.228 at time: 1.930\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.930\n",
+ "d (def. map) integrated over the domain: 5.936 at time: 1.930\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.930\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.930\n",
+ "\n",
+ "J integrated over the domain: 1.221 at time: 1.940\n",
+ "J_n integrated over the domain: 1.391 at time: 1.940\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.940\n",
+ "d (def. map) integrated over the domain: 5.492 at time: 1.940\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.940\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.940\n",
+ "\n",
+ "J integrated over the domain: 1.729 at time: 1.950\n",
+ "J_n integrated over the domain: 1.221 at time: 1.950\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.950\n",
+ "d (def. map) integrated over the domain: 6.988 at time: 1.950\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.950\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.950\n",
+ "\n",
+ "J integrated over the domain: 2.881 at time: 1.960\n",
+ "J_n integrated over the domain: 1.729 at time: 1.960\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.960\n",
+ "d (def. map) integrated over the domain: 12.302 at time: 1.960\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.960\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.960\n",
+ "\n",
+ "J integrated over the domain: 4.607 at time: 1.970\n",
+ "J_n integrated over the domain: 2.881 at time: 1.970\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.970\n",
+ "d (def. map) integrated over the domain: 25.223 at time: 1.970\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.970\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.970\n",
+ "\n",
+ "J integrated over the domain: 6.797 at time: 1.980\n",
+ "J_n integrated over the domain: 4.607 at time: 1.980\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.980\n",
+ "d (def. map) integrated over the domain: 50.200 at time: 1.980\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.980\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.980\n",
+ "\n",
+ "J integrated over the domain: 9.314 at time: 1.990\n",
+ "J_n integrated over the domain: 6.797 at time: 1.990\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.990\n",
+ "d (def. map) integrated over the domain: 90.753 at time: 1.990\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.990\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.990\n",
+ "\n"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "J integrated over the domain: 12.000 at time: 2.000\n",
+ "J_n integrated over the domain: 9.314 at time: 2.000\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 2.000\n",
+ "d (def. map) integrated over the domain: 148.000 at time: 2.000\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 2.000\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 2.000\n",
+ "\n",
+ "DoF for Velocity Space (U): 3298\n",
+ "DoF for Pressure Space (P): 1649\n",
+ "Solution Computed in 35.108 seconds\n",
+ "\n",
+ "----------------Computation Completed!----------------\n",
+ "\n",
+ "\n",
+ "Initializing iNSE problem with Deformation type: High_Osc_con\n",
+ "\n",
+ "\n",
+ "Setup with initial condition: True\n",
+ "Using a non-zero initial condition (2D-Gaussian) for the velocity field!\n",
+ "Defining forms associated to Chorin-Temam scheme...\n",
+ "Using LU Solver...\n",
+ "Starting iteration over time...\n",
+ "E (Energy) of initial t. velocity: 0.01648 at time 0.000\n",
+ "\n",
+ "J integrated over the domain: 9.314 at time: 0.010\n",
+ "J_n integrated over the domain: 12.000 at time: 0.010\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.010\n",
+ "d (def. map) integrated over the domain: 90.753 at time: 0.010\n",
+ "Strain energy E( eps(|u|^2) ): 0.00023 at time 0.010\n",
+ "Residual of scheme -> 'delta' value: -0.00065 at time 0.010\n",
+ "\n",
+ "J integrated over the domain: 6.797 at time: 0.020\n",
+ "J_n integrated over the domain: 9.314 at time: 0.020\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.020\n",
+ "d (def. map) integrated over the domain: 50.200 at time: 0.020\n",
+ "Strain energy E( eps(|u|^2) ): 0.00043 at time 0.020\n",
+ "Residual of scheme -> 'delta' value: -0.00012 at time 0.020\n",
+ "\n",
+ "J integrated over the domain: 4.607 at time: 0.030\n",
+ "J_n integrated over the domain: 6.797 at time: 0.030\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.030\n",
+ "d (def. map) integrated over the domain: 25.223 at time: 0.030\n",
+ "Strain energy E( eps(|u|^2) ): 0.00038 at time 0.030\n",
+ "Residual of scheme -> 'delta' value: -0.00011 at time 0.030\n",
+ "\n",
+ "J integrated over the domain: 2.881 at time: 0.040\n",
+ "J_n integrated over the domain: 4.607 at time: 0.040\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.040\n",
+ "d (def. map) integrated over the domain: 12.302 at time: 0.040\n",
+ "Strain energy E( eps(|u|^2) ): 0.00020 at time 0.040\n",
+ "Residual of scheme -> 'delta' value: -0.00009 at time 0.040\n",
+ "\n",
+ "J integrated over the domain: 1.729 at time: 0.050\n",
+ "J_n integrated over the domain: 2.881 at time: 0.050\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.050\n",
+ "d (def. map) integrated over the domain: 6.988 at time: 0.050\n",
+ "Strain energy E( eps(|u|^2) ): 0.00006 at time 0.050\n",
+ "Residual of scheme -> 'delta' value: -0.00004 at time 0.050\n",
+ "\n",
+ "J integrated over the domain: 1.221 at time: 0.060\n",
+ "J_n integrated over the domain: 1.729 at time: 0.060\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.060\n",
+ "d (def. map) integrated over the domain: 5.492 at time: 0.060\n",
+ "Strain energy E( eps(|u|^2) ): 0.00001 at time 0.060\n",
+ "Residual of scheme -> 'delta' value: -0.00001 at time 0.060\n",
+ "\n",
+ "J integrated over the domain: 1.391 at time: 0.070\n",
+ "J_n integrated over the domain: 1.221 at time: 0.070\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.070\n",
+ "d (def. map) integrated over the domain: 5.936 at time: 0.070\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.070\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.070\n",
+ "\n",
+ "J integrated over the domain: 2.228 at time: 0.080\n",
+ "J_n integrated over the domain: 1.391 at time: 0.080\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.080\n",
+ "d (def. map) integrated over the domain: 8.963 at time: 0.080\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.080\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.080\n",
+ "\n",
+ "J integrated over the domain: 3.678 at time: 0.090\n",
+ "J_n integrated over the domain: 2.228 at time: 0.090\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.090\n",
+ "d (def. map) integrated over the domain: 17.531 at time: 0.090\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.090\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.090\n",
+ "\n",
+ "J integrated over the domain: 5.652 at time: 0.100\n",
+ "J_n integrated over the domain: 3.678 at time: 0.100\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.100\n",
+ "d (def. map) integrated over the domain: 35.944 at time: 0.100\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.100\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.100\n",
+ "\n",
+ "J integrated over the domain: 8.024 at time: 0.110\n",
+ "J_n integrated over the domain: 5.652 at time: 0.110\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.110\n",
+ "d (def. map) integrated over the domain: 68.389 at time: 0.110\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.110\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.110\n",
+ "\n",
+ "J integrated over the domain: 10.646 at time: 0.120\n",
+ "J_n integrated over the domain: 8.024 at time: 0.120\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.120\n",
+ "d (def. map) integrated over the domain: 117.346 at time: 0.120\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.120\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.120\n",
+ "\n",
+ "J integrated over the domain: 13.354 at time: 0.130\n",
+ "J_n integrated over the domain: 10.646 at time: 0.130\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.130\n",
+ "d (def. map) integrated over the domain: 182.319 at time: 0.130\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.130\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.130\n",
+ "\n",
+ "J integrated over the domain: 15.976 at time: 0.140\n",
+ "J_n integrated over the domain: 13.354 at time: 0.140\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.140\n",
+ "d (def. map) integrated over the domain: 259.224 at time: 0.140\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.140\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.140\n",
+ "\n",
+ "J integrated over the domain: 18.348 at time: 0.150\n",
+ "J_n integrated over the domain: 15.976 at time: 0.150\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.150\n",
+ "d (def. map) integrated over the domain: 340.652 at time: 0.150\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.150\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.150\n",
+ "\n",
+ "J integrated over the domain: 20.322 at time: 0.160\n",
+ "J_n integrated over the domain: 18.348 at time: 0.160\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.160\n",
+ "d (def. map) integrated over the domain: 416.965 at time: 0.160\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.160\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.160\n",
+ "\n",
+ "J integrated over the domain: 21.772 at time: 0.170\n",
+ "J_n integrated over the domain: 20.322 at time: 0.170\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.170\n",
+ "d (def. map) integrated over the domain: 478.026 at time: 0.170\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.170\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.170\n",
+ "\n",
+ "J integrated over the domain: 22.609 at time: 0.180\n",
+ "J_n integrated over the domain: 21.772 at time: 0.180\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.180\n",
+ "d (def. map) integrated over the domain: 515.153 at time: 0.180\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.180\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.180\n",
+ "\n",
+ "J integrated over the domain: 22.779 at time: 0.190\n",
+ "J_n integrated over the domain: 22.609 at time: 0.190\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.190\n",
+ "d (def. map) integrated over the domain: 522.869 at time: 0.190\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.190\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.190\n",
+ "\n",
+ "J integrated over the domain: 22.271 at time: 0.200\n",
+ "J_n integrated over the domain: 22.779 at time: 0.200\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.200\n",
+ "d (def. map) integrated over the domain: 500.016 at time: 0.200\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.200\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.200\n",
+ "\n",
+ "J integrated over the domain: 21.119 at time: 0.210\n",
+ "J_n integrated over the domain: 22.271 at time: 0.210\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.210\n",
+ "d (def. map) integrated over the domain: 450.001 at time: 0.210\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.210\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.210\n",
+ "\n",
+ "J integrated over the domain: 19.393 at time: 0.220\n",
+ "J_n integrated over the domain: 21.119 at time: 0.220\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.220\n",
+ "d (def. map) integrated over the domain: 380.093 at time: 0.220\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.220\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.220\n",
+ "\n"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "J integrated over the domain: 17.203 at time: 0.230\n",
+ "J_n integrated over the domain: 19.393 at time: 0.230\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.230\n",
+ "d (def. map) integrated over the domain: 299.941 at time: 0.230\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.230\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.230\n",
+ "\n",
+ "J integrated over the domain: 14.686 at time: 0.240\n",
+ "J_n integrated over the domain: 17.203 at time: 0.240\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.240\n",
+ "d (def. map) integrated over the domain: 219.674 at time: 0.240\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.240\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.240\n",
+ "\n",
+ "J integrated over the domain: 12.000 at time: 0.250\n",
+ "J_n integrated over the domain: 14.686 at time: 0.250\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.250\n",
+ "d (def. map) integrated over the domain: 148.000 at time: 0.250\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.250\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.250\n",
+ "\n",
+ "J integrated over the domain: 9.314 at time: 0.260\n",
+ "J_n integrated over the domain: 12.000 at time: 0.260\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.260\n",
+ "d (def. map) integrated over the domain: 90.753 at time: 0.260\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.260\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.260\n",
+ "\n",
+ "J integrated over the domain: 6.797 at time: 0.270\n",
+ "J_n integrated over the domain: 9.314 at time: 0.270\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.270\n",
+ "d (def. map) integrated over the domain: 50.200 at time: 0.270\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.270\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.270\n",
+ "\n",
+ "J integrated over the domain: 4.607 at time: 0.280\n",
+ "J_n integrated over the domain: 6.797 at time: 0.280\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.280\n",
+ "d (def. map) integrated over the domain: 25.223 at time: 0.280\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.280\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.280\n",
+ "\n",
+ "J integrated over the domain: 2.881 at time: 0.290\n",
+ "J_n integrated over the domain: 4.607 at time: 0.290\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.290\n",
+ "d (def. map) integrated over the domain: 12.302 at time: 0.290\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.290\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.290\n",
+ "\n",
+ "J integrated over the domain: 1.729 at time: 0.300\n",
+ "J_n integrated over the domain: 2.881 at time: 0.300\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.300\n",
+ "d (def. map) integrated over the domain: 6.988 at time: 0.300\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.300\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.300\n",
+ "\n",
+ "J integrated over the domain: 1.221 at time: 0.310\n",
+ "J_n integrated over the domain: 1.729 at time: 0.310\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.310\n",
+ "d (def. map) integrated over the domain: 5.492 at time: 0.310\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.310\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.310\n",
+ "\n",
+ "J integrated over the domain: 1.391 at time: 0.320\n",
+ "J_n integrated over the domain: 1.221 at time: 0.320\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.320\n",
+ "d (def. map) integrated over the domain: 5.936 at time: 0.320\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.320\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.320\n",
+ "\n",
+ "J integrated over the domain: 2.228 at time: 0.330\n",
+ "J_n integrated over the domain: 1.391 at time: 0.330\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.330\n",
+ "d (def. map) integrated over the domain: 8.963 at time: 0.330\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.330\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.330\n",
+ "\n",
+ "J integrated over the domain: 3.678 at time: 0.340\n",
+ "J_n integrated over the domain: 2.228 at time: 0.340\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.340\n",
+ "d (def. map) integrated over the domain: 17.531 at time: 0.340\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.340\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.340\n",
+ "\n",
+ "J integrated over the domain: 5.652 at time: 0.350\n",
+ "J_n integrated over the domain: 3.678 at time: 0.350\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.350\n",
+ "d (def. map) integrated over the domain: 35.944 at time: 0.350\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.350\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.350\n",
+ "\n",
+ "J integrated over the domain: 8.024 at time: 0.360\n",
+ "J_n integrated over the domain: 5.652 at time: 0.360\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.360\n",
+ "d (def. map) integrated over the domain: 68.389 at time: 0.360\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.360\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.360\n",
+ "\n",
+ "J integrated over the domain: 10.646 at time: 0.370\n",
+ "J_n integrated over the domain: 8.024 at time: 0.370\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.370\n",
+ "d (def. map) integrated over the domain: 117.346 at time: 0.370\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.370\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.370\n",
+ "\n",
+ "J integrated over the domain: 13.354 at time: 0.380\n",
+ "J_n integrated over the domain: 10.646 at time: 0.380\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.380\n",
+ "d (def. map) integrated over the domain: 182.319 at time: 0.380\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.380\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.380\n",
+ "\n",
+ "J integrated over the domain: 15.976 at time: 0.390\n",
+ "J_n integrated over the domain: 13.354 at time: 0.390\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.390\n",
+ "d (def. map) integrated over the domain: 259.224 at time: 0.390\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.390\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.390\n",
+ "\n",
+ "J integrated over the domain: 18.348 at time: 0.400\n",
+ "J_n integrated over the domain: 15.976 at time: 0.400\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.400\n",
+ "d (def. map) integrated over the domain: 340.652 at time: 0.400\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.400\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.400\n",
+ "\n",
+ "J integrated over the domain: 20.322 at time: 0.410\n",
+ "J_n integrated over the domain: 18.348 at time: 0.410\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.410\n",
+ "d (def. map) integrated over the domain: 416.965 at time: 0.410\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.410\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.410\n",
+ "\n",
+ "J integrated over the domain: 21.772 at time: 0.420\n",
+ "J_n integrated over the domain: 20.322 at time: 0.420\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.420\n",
+ "d (def. map) integrated over the domain: 478.026 at time: 0.420\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.420\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.420\n",
+ "\n",
+ "J integrated over the domain: 22.609 at time: 0.430\n",
+ "J_n integrated over the domain: 21.772 at time: 0.430\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.430\n",
+ "d (def. map) integrated over the domain: 515.153 at time: 0.430\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.430\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.430\n",
+ "\n",
+ "J integrated over the domain: 22.779 at time: 0.440\n",
+ "J_n integrated over the domain: 22.609 at time: 0.440\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.440\n",
+ "d (def. map) integrated over the domain: 522.869 at time: 0.440\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.440\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.440\n",
+ "\n",
+ "J integrated over the domain: 22.271 at time: 0.450\n",
+ "J_n integrated over the domain: 22.779 at time: 0.450\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.450\n",
+ "d (def. map) integrated over the domain: 500.016 at time: 0.450\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.450\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.450\n",
+ "\n",
+ "J integrated over the domain: 21.119 at time: 0.460\n",
+ "J_n integrated over the domain: 22.271 at time: 0.460\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.460\n",
+ "d (def. map) integrated over the domain: 450.001 at time: 0.460\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.460\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.460\n",
+ "\n"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "J integrated over the domain: 19.393 at time: 0.470\n",
+ "J_n integrated over the domain: 21.119 at time: 0.470\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.470\n",
+ "d (def. map) integrated over the domain: 380.093 at time: 0.470\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.470\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.470\n",
+ "\n",
+ "J integrated over the domain: 17.203 at time: 0.480\n",
+ "J_n integrated over the domain: 19.393 at time: 0.480\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.480\n",
+ "d (def. map) integrated over the domain: 299.941 at time: 0.480\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.480\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.480\n",
+ "\n",
+ "J integrated over the domain: 14.686 at time: 0.490\n",
+ "J_n integrated over the domain: 17.203 at time: 0.490\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.490\n",
+ "d (def. map) integrated over the domain: 219.674 at time: 0.490\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.490\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.490\n",
+ "\n",
+ "J integrated over the domain: 12.000 at time: 0.500\n",
+ "J_n integrated over the domain: 14.686 at time: 0.500\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.500\n",
+ "d (def. map) integrated over the domain: 148.000 at time: 0.500\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.500\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.500\n",
+ "\n",
+ "J integrated over the domain: 9.314 at time: 0.510\n",
+ "J_n integrated over the domain: 12.000 at time: 0.510\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.510\n",
+ "d (def. map) integrated over the domain: 90.753 at time: 0.510\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.510\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.510\n",
+ "\n",
+ "J integrated over the domain: 6.797 at time: 0.520\n",
+ "J_n integrated over the domain: 9.314 at time: 0.520\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.520\n",
+ "d (def. map) integrated over the domain: 50.200 at time: 0.520\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.520\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.520\n",
+ "\n",
+ "J integrated over the domain: 4.607 at time: 0.530\n",
+ "J_n integrated over the domain: 6.797 at time: 0.530\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.530\n",
+ "d (def. map) integrated over the domain: 25.223 at time: 0.530\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.530\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.530\n",
+ "\n",
+ "J integrated over the domain: 2.881 at time: 0.540\n",
+ "J_n integrated over the domain: 4.607 at time: 0.540\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.540\n",
+ "d (def. map) integrated over the domain: 12.302 at time: 0.540\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.540\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.540\n",
+ "\n",
+ "J integrated over the domain: 1.729 at time: 0.550\n",
+ "J_n integrated over the domain: 2.881 at time: 0.550\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.550\n",
+ "d (def. map) integrated over the domain: 6.988 at time: 0.550\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.550\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.550\n",
+ "\n",
+ "J integrated over the domain: 1.221 at time: 0.560\n",
+ "J_n integrated over the domain: 1.729 at time: 0.560\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.560\n",
+ "d (def. map) integrated over the domain: 5.492 at time: 0.560\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.560\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.560\n",
+ "\n",
+ "J integrated over the domain: 1.391 at time: 0.570\n",
+ "J_n integrated over the domain: 1.221 at time: 0.570\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.570\n",
+ "d (def. map) integrated over the domain: 5.936 at time: 0.570\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.570\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.570\n",
+ "\n",
+ "J integrated over the domain: 2.228 at time: 0.580\n",
+ "J_n integrated over the domain: 1.391 at time: 0.580\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.580\n",
+ "d (def. map) integrated over the domain: 8.963 at time: 0.580\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.580\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.580\n",
+ "\n",
+ "J integrated over the domain: 3.678 at time: 0.590\n",
+ "J_n integrated over the domain: 2.228 at time: 0.590\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.590\n",
+ "d (def. map) integrated over the domain: 17.531 at time: 0.590\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.590\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.590\n",
+ "\n",
+ "J integrated over the domain: 5.652 at time: 0.600\n",
+ "J_n integrated over the domain: 3.678 at time: 0.600\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.600\n",
+ "d (def. map) integrated over the domain: 35.944 at time: 0.600\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.600\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.600\n",
+ "\n",
+ "J integrated over the domain: 8.024 at time: 0.610\n",
+ "J_n integrated over the domain: 5.652 at time: 0.610\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.610\n",
+ "d (def. map) integrated over the domain: 68.389 at time: 0.610\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.610\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.610\n",
+ "\n",
+ "J integrated over the domain: 10.646 at time: 0.620\n",
+ "J_n integrated over the domain: 8.024 at time: 0.620\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.620\n",
+ "d (def. map) integrated over the domain: 117.346 at time: 0.620\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.620\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.620\n",
+ "\n",
+ "J integrated over the domain: 13.354 at time: 0.630\n",
+ "J_n integrated over the domain: 10.646 at time: 0.630\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.630\n",
+ "d (def. map) integrated over the domain: 182.319 at time: 0.630\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.630\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.630\n",
+ "\n",
+ "J integrated over the domain: 15.976 at time: 0.640\n",
+ "J_n integrated over the domain: 13.354 at time: 0.640\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.640\n",
+ "d (def. map) integrated over the domain: 259.224 at time: 0.640\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.640\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.640\n",
+ "\n",
+ "J integrated over the domain: 18.348 at time: 0.650\n",
+ "J_n integrated over the domain: 15.976 at time: 0.650\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.650\n",
+ "d (def. map) integrated over the domain: 340.652 at time: 0.650\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.650\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.650\n",
+ "\n",
+ "J integrated over the domain: 20.322 at time: 0.660\n",
+ "J_n integrated over the domain: 18.348 at time: 0.660\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.660\n",
+ "d (def. map) integrated over the domain: 416.965 at time: 0.660\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.660\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.660\n",
+ "\n",
+ "J integrated over the domain: 21.772 at time: 0.670\n",
+ "J_n integrated over the domain: 20.322 at time: 0.670\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.670\n",
+ "d (def. map) integrated over the domain: 478.026 at time: 0.670\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.670\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.670\n",
+ "\n",
+ "J integrated over the domain: 22.609 at time: 0.680\n",
+ "J_n integrated over the domain: 21.772 at time: 0.680\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.680\n",
+ "d (def. map) integrated over the domain: 515.153 at time: 0.680\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.680\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.680\n",
+ "\n",
+ "J integrated over the domain: 22.779 at time: 0.690\n",
+ "J_n integrated over the domain: 22.609 at time: 0.690\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.690\n",
+ "d (def. map) integrated over the domain: 522.869 at time: 0.690\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.690\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.690\n",
+ "\n",
+ "J integrated over the domain: 22.271 at time: 0.700\n",
+ "J_n integrated over the domain: 22.779 at time: 0.700\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.700\n",
+ "d (def. map) integrated over the domain: 500.016 at time: 0.700\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.700\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.700\n",
+ "\n"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "J integrated over the domain: 21.119 at time: 0.710\n",
+ "J_n integrated over the domain: 22.271 at time: 0.710\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.710\n",
+ "d (def. map) integrated over the domain: 450.001 at time: 0.710\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.710\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.710\n",
+ "\n",
+ "J integrated over the domain: 19.393 at time: 0.720\n",
+ "J_n integrated over the domain: 21.119 at time: 0.720\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.720\n",
+ "d (def. map) integrated over the domain: 380.093 at time: 0.720\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.720\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.720\n",
+ "\n",
+ "J integrated over the domain: 17.203 at time: 0.730\n",
+ "J_n integrated over the domain: 19.393 at time: 0.730\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.730\n",
+ "d (def. map) integrated over the domain: 299.941 at time: 0.730\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.730\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.730\n",
+ "\n",
+ "J integrated over the domain: 14.686 at time: 0.740\n",
+ "J_n integrated over the domain: 17.203 at time: 0.740\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.740\n",
+ "d (def. map) integrated over the domain: 219.674 at time: 0.740\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.740\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.740\n",
+ "\n",
+ "J integrated over the domain: 12.000 at time: 0.750\n",
+ "J_n integrated over the domain: 14.686 at time: 0.750\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.750\n",
+ "d (def. map) integrated over the domain: 148.000 at time: 0.750\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.750\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.750\n",
+ "\n",
+ "J integrated over the domain: 9.314 at time: 0.760\n",
+ "J_n integrated over the domain: 12.000 at time: 0.760\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.760\n",
+ "d (def. map) integrated over the domain: 90.753 at time: 0.760\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.760\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.760\n",
+ "\n",
+ "J integrated over the domain: 6.797 at time: 0.770\n",
+ "J_n integrated over the domain: 9.314 at time: 0.770\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.770\n",
+ "d (def. map) integrated over the domain: 50.200 at time: 0.770\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.770\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.770\n",
+ "\n",
+ "J integrated over the domain: 4.607 at time: 0.780\n",
+ "J_n integrated over the domain: 6.797 at time: 0.780\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.780\n",
+ "d (def. map) integrated over the domain: 25.223 at time: 0.780\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.780\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.780\n",
+ "\n",
+ "J integrated over the domain: 2.881 at time: 0.790\n",
+ "J_n integrated over the domain: 4.607 at time: 0.790\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.790\n",
+ "d (def. map) integrated over the domain: 12.302 at time: 0.790\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.790\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.790\n",
+ "\n",
+ "J integrated over the domain: 1.729 at time: 0.800\n",
+ "J_n integrated over the domain: 2.881 at time: 0.800\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.800\n",
+ "d (def. map) integrated over the domain: 6.988 at time: 0.800\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.800\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.800\n",
+ "\n",
+ "J integrated over the domain: 1.221 at time: 0.810\n",
+ "J_n integrated over the domain: 1.729 at time: 0.810\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.810\n",
+ "d (def. map) integrated over the domain: 5.492 at time: 0.810\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.810\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.810\n",
+ "\n",
+ "J integrated over the domain: 1.391 at time: 0.820\n",
+ "J_n integrated over the domain: 1.221 at time: 0.820\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.820\n",
+ "d (def. map) integrated over the domain: 5.936 at time: 0.820\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.820\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.820\n",
+ "\n",
+ "J integrated over the domain: 2.228 at time: 0.830\n",
+ "J_n integrated over the domain: 1.391 at time: 0.830\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.830\n",
+ "d (def. map) integrated over the domain: 8.963 at time: 0.830\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.830\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.830\n",
+ "\n",
+ "J integrated over the domain: 3.678 at time: 0.840\n",
+ "J_n integrated over the domain: 2.228 at time: 0.840\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.840\n",
+ "d (def. map) integrated over the domain: 17.531 at time: 0.840\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.840\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.840\n",
+ "\n",
+ "J integrated over the domain: 5.652 at time: 0.850\n",
+ "J_n integrated over the domain: 3.678 at time: 0.850\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.850\n",
+ "d (def. map) integrated over the domain: 35.944 at time: 0.850\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.850\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.850\n",
+ "\n",
+ "J integrated over the domain: 8.024 at time: 0.860\n",
+ "J_n integrated over the domain: 5.652 at time: 0.860\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.860\n",
+ "d (def. map) integrated over the domain: 68.389 at time: 0.860\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.860\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.860\n",
+ "\n",
+ "J integrated over the domain: 10.646 at time: 0.870\n",
+ "J_n integrated over the domain: 8.024 at time: 0.870\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.870\n",
+ "d (def. map) integrated over the domain: 117.346 at time: 0.870\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.870\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.870\n",
+ "\n",
+ "J integrated over the domain: 13.354 at time: 0.880\n",
+ "J_n integrated over the domain: 10.646 at time: 0.880\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.880\n",
+ "d (def. map) integrated over the domain: 182.319 at time: 0.880\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.880\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.880\n",
+ "\n",
+ "J integrated over the domain: 15.976 at time: 0.890\n",
+ "J_n integrated over the domain: 13.354 at time: 0.890\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.890\n",
+ "d (def. map) integrated over the domain: 259.224 at time: 0.890\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.890\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.890\n",
+ "\n",
+ "J integrated over the domain: 18.348 at time: 0.900\n",
+ "J_n integrated over the domain: 15.976 at time: 0.900\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.900\n",
+ "d (def. map) integrated over the domain: 340.652 at time: 0.900\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.900\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.900\n",
+ "\n",
+ "J integrated over the domain: 20.322 at time: 0.910\n",
+ "J_n integrated over the domain: 18.348 at time: 0.910\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.910\n",
+ "d (def. map) integrated over the domain: 416.965 at time: 0.910\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.910\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.910\n",
+ "\n",
+ "J integrated over the domain: 21.772 at time: 0.920\n",
+ "J_n integrated over the domain: 20.322 at time: 0.920\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.920\n",
+ "d (def. map) integrated over the domain: 478.026 at time: 0.920\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.920\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.920\n",
+ "\n",
+ "J integrated over the domain: 22.609 at time: 0.930\n",
+ "J_n integrated over the domain: 21.772 at time: 0.930\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.930\n",
+ "d (def. map) integrated over the domain: 515.153 at time: 0.930\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.930\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.930\n",
+ "\n",
+ "J integrated over the domain: 22.779 at time: 0.940\n",
+ "J_n integrated over the domain: 22.609 at time: 0.940\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.940\n",
+ "d (def. map) integrated over the domain: 522.869 at time: 0.940\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.940\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.940\n",
+ "\n"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "J integrated over the domain: 22.271 at time: 0.950\n",
+ "J_n integrated over the domain: 22.779 at time: 0.950\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.950\n",
+ "d (def. map) integrated over the domain: 500.016 at time: 0.950\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.950\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.950\n",
+ "\n",
+ "J integrated over the domain: 21.119 at time: 0.960\n",
+ "J_n integrated over the domain: 22.271 at time: 0.960\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.960\n",
+ "d (def. map) integrated over the domain: 450.001 at time: 0.960\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.960\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.960\n",
+ "\n",
+ "J integrated over the domain: 19.393 at time: 0.970\n",
+ "J_n integrated over the domain: 21.119 at time: 0.970\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.970\n",
+ "d (def. map) integrated over the domain: 380.093 at time: 0.970\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.970\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.970\n",
+ "\n",
+ "J integrated over the domain: 17.203 at time: 0.980\n",
+ "J_n integrated over the domain: 19.393 at time: 0.980\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.980\n",
+ "d (def. map) integrated over the domain: 299.941 at time: 0.980\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.980\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.980\n",
+ "\n",
+ "J integrated over the domain: 14.686 at time: 0.990\n",
+ "J_n integrated over the domain: 17.203 at time: 0.990\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 0.990\n",
+ "d (def. map) integrated over the domain: 219.674 at time: 0.990\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 0.990\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 0.990\n",
+ "\n",
+ "J integrated over the domain: 12.000 at time: 1.000\n",
+ "J_n integrated over the domain: 14.686 at time: 1.000\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.000\n",
+ "d (def. map) integrated over the domain: 148.000 at time: 1.000\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.000\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.000\n",
+ "\n",
+ "J integrated over the domain: 9.314 at time: 1.010\n",
+ "J_n integrated over the domain: 12.000 at time: 1.010\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.010\n",
+ "d (def. map) integrated over the domain: 90.753 at time: 1.010\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.010\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.010\n",
+ "\n",
+ "J integrated over the domain: 6.797 at time: 1.020\n",
+ "J_n integrated over the domain: 9.314 at time: 1.020\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.020\n",
+ "d (def. map) integrated over the domain: 50.200 at time: 1.020\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.020\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.020\n",
+ "\n",
+ "J integrated over the domain: 4.607 at time: 1.030\n",
+ "J_n integrated over the domain: 6.797 at time: 1.030\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.030\n",
+ "d (def. map) integrated over the domain: 25.223 at time: 1.030\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.030\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.030\n",
+ "\n",
+ "J integrated over the domain: 2.881 at time: 1.040\n",
+ "J_n integrated over the domain: 4.607 at time: 1.040\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.040\n",
+ "d (def. map) integrated over the domain: 12.302 at time: 1.040\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.040\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.040\n",
+ "\n",
+ "J integrated over the domain: 1.729 at time: 1.050\n",
+ "J_n integrated over the domain: 2.881 at time: 1.050\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.050\n",
+ "d (def. map) integrated over the domain: 6.988 at time: 1.050\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.050\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.050\n",
+ "\n",
+ "J integrated over the domain: 1.221 at time: 1.060\n",
+ "J_n integrated over the domain: 1.729 at time: 1.060\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.060\n",
+ "d (def. map) integrated over the domain: 5.492 at time: 1.060\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.060\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.060\n",
+ "\n",
+ "J integrated over the domain: 1.391 at time: 1.070\n",
+ "J_n integrated over the domain: 1.221 at time: 1.070\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.070\n",
+ "d (def. map) integrated over the domain: 5.936 at time: 1.070\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.070\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.070\n",
+ "\n",
+ "J integrated over the domain: 2.228 at time: 1.080\n",
+ "J_n integrated over the domain: 1.391 at time: 1.080\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.080\n",
+ "d (def. map) integrated over the domain: 8.963 at time: 1.080\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.080\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.080\n",
+ "\n",
+ "J integrated over the domain: 3.678 at time: 1.090\n",
+ "J_n integrated over the domain: 2.228 at time: 1.090\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.090\n",
+ "d (def. map) integrated over the domain: 17.531 at time: 1.090\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.090\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.090\n",
+ "\n",
+ "J integrated over the domain: 5.652 at time: 1.100\n",
+ "J_n integrated over the domain: 3.678 at time: 1.100\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.100\n",
+ "d (def. map) integrated over the domain: 35.944 at time: 1.100\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.100\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.100\n",
+ "\n",
+ "J integrated over the domain: 8.024 at time: 1.110\n",
+ "J_n integrated over the domain: 5.652 at time: 1.110\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.110\n",
+ "d (def. map) integrated over the domain: 68.389 at time: 1.110\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.110\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.110\n",
+ "\n",
+ "J integrated over the domain: 10.646 at time: 1.120\n",
+ "J_n integrated over the domain: 8.024 at time: 1.120\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.120\n",
+ "d (def. map) integrated over the domain: 117.346 at time: 1.120\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.120\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.120\n",
+ "\n",
+ "J integrated over the domain: 13.354 at time: 1.130\n",
+ "J_n integrated over the domain: 10.646 at time: 1.130\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.130\n",
+ "d (def. map) integrated over the domain: 182.319 at time: 1.130\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.130\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.130\n",
+ "\n",
+ "J integrated over the domain: 15.976 at time: 1.140\n",
+ "J_n integrated over the domain: 13.354 at time: 1.140\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.140\n",
+ "d (def. map) integrated over the domain: 259.224 at time: 1.140\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.140\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.140\n",
+ "\n",
+ "J integrated over the domain: 18.348 at time: 1.150\n",
+ "J_n integrated over the domain: 15.976 at time: 1.150\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.150\n",
+ "d (def. map) integrated over the domain: 340.652 at time: 1.150\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.150\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.150\n",
+ "\n",
+ "J integrated over the domain: 20.322 at time: 1.160\n",
+ "J_n integrated over the domain: 18.348 at time: 1.160\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.160\n",
+ "d (def. map) integrated over the domain: 416.965 at time: 1.160\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.160\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.160\n",
+ "\n",
+ "J integrated over the domain: 21.772 at time: 1.170\n",
+ "J_n integrated over the domain: 20.322 at time: 1.170\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.170\n",
+ "d (def. map) integrated over the domain: 478.026 at time: 1.170\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.170\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.170\n",
+ "\n",
+ "J integrated over the domain: 22.609 at time: 1.180\n",
+ "J_n integrated over the domain: 21.772 at time: 1.180\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.180\n",
+ "d (def. map) integrated over the domain: 515.153 at time: 1.180\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.180\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.180\n",
+ "\n"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "J integrated over the domain: 22.779 at time: 1.190\n",
+ "J_n integrated over the domain: 22.609 at time: 1.190\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.190\n",
+ "d (def. map) integrated over the domain: 522.869 at time: 1.190\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.190\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.190\n",
+ "\n",
+ "J integrated over the domain: 22.271 at time: 1.200\n",
+ "J_n integrated over the domain: 22.779 at time: 1.200\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.200\n",
+ "d (def. map) integrated over the domain: 500.016 at time: 1.200\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.200\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.200\n",
+ "\n",
+ "J integrated over the domain: 21.119 at time: 1.210\n",
+ "J_n integrated over the domain: 22.271 at time: 1.210\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.210\n",
+ "d (def. map) integrated over the domain: 450.001 at time: 1.210\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.210\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.210\n",
+ "\n",
+ "J integrated over the domain: 19.393 at time: 1.220\n",
+ "J_n integrated over the domain: 21.119 at time: 1.220\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.220\n",
+ "d (def. map) integrated over the domain: 380.093 at time: 1.220\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.220\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.220\n",
+ "\n",
+ "J integrated over the domain: 17.203 at time: 1.230\n",
+ "J_n integrated over the domain: 19.393 at time: 1.230\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.230\n",
+ "d (def. map) integrated over the domain: 299.941 at time: 1.230\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.230\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.230\n",
+ "\n",
+ "J integrated over the domain: 14.686 at time: 1.240\n",
+ "J_n integrated over the domain: 17.203 at time: 1.240\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.240\n",
+ "d (def. map) integrated over the domain: 219.674 at time: 1.240\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.240\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.240\n",
+ "\n",
+ "J integrated over the domain: 12.000 at time: 1.250\n",
+ "J_n integrated over the domain: 14.686 at time: 1.250\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.250\n",
+ "d (def. map) integrated over the domain: 148.000 at time: 1.250\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.250\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.250\n",
+ "\n",
+ "J integrated over the domain: 9.314 at time: 1.260\n",
+ "J_n integrated over the domain: 12.000 at time: 1.260\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.260\n",
+ "d (def. map) integrated over the domain: 90.753 at time: 1.260\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.260\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.260\n",
+ "\n",
+ "J integrated over the domain: 6.797 at time: 1.270\n",
+ "J_n integrated over the domain: 9.314 at time: 1.270\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.270\n",
+ "d (def. map) integrated over the domain: 50.200 at time: 1.270\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.270\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.270\n",
+ "\n",
+ "J integrated over the domain: 4.607 at time: 1.280\n",
+ "J_n integrated over the domain: 6.797 at time: 1.280\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.280\n",
+ "d (def. map) integrated over the domain: 25.223 at time: 1.280\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.280\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.280\n",
+ "\n",
+ "J integrated over the domain: 2.881 at time: 1.290\n",
+ "J_n integrated over the domain: 4.607 at time: 1.290\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.290\n",
+ "d (def. map) integrated over the domain: 12.302 at time: 1.290\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.290\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.290\n",
+ "\n",
+ "J integrated over the domain: 1.729 at time: 1.300\n",
+ "J_n integrated over the domain: 2.881 at time: 1.300\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.300\n",
+ "d (def. map) integrated over the domain: 6.988 at time: 1.300\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.300\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.300\n",
+ "\n",
+ "J integrated over the domain: 1.221 at time: 1.310\n",
+ "J_n integrated over the domain: 1.729 at time: 1.310\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.310\n",
+ "d (def. map) integrated over the domain: 5.492 at time: 1.310\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.310\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.310\n",
+ "\n",
+ "J integrated over the domain: 1.391 at time: 1.320\n",
+ "J_n integrated over the domain: 1.221 at time: 1.320\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.320\n",
+ "d (def. map) integrated over the domain: 5.936 at time: 1.320\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.320\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.320\n",
+ "\n",
+ "J integrated over the domain: 2.228 at time: 1.330\n",
+ "J_n integrated over the domain: 1.391 at time: 1.330\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.330\n",
+ "d (def. map) integrated over the domain: 8.963 at time: 1.330\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.330\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.330\n",
+ "\n",
+ "J integrated over the domain: 3.678 at time: 1.340\n",
+ "J_n integrated over the domain: 2.228 at time: 1.340\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.340\n",
+ "d (def. map) integrated over the domain: 17.531 at time: 1.340\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.340\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.340\n",
+ "\n",
+ "J integrated over the domain: 5.652 at time: 1.350\n",
+ "J_n integrated over the domain: 3.678 at time: 1.350\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.350\n",
+ "d (def. map) integrated over the domain: 35.944 at time: 1.350\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.350\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.350\n",
+ "\n",
+ "J integrated over the domain: 8.024 at time: 1.360\n",
+ "J_n integrated over the domain: 5.652 at time: 1.360\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.360\n",
+ "d (def. map) integrated over the domain: 68.389 at time: 1.360\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.360\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.360\n",
+ "\n",
+ "J integrated over the domain: 10.646 at time: 1.370\n",
+ "J_n integrated over the domain: 8.024 at time: 1.370\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.370\n",
+ "d (def. map) integrated over the domain: 117.346 at time: 1.370\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.370\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.370\n",
+ "\n",
+ "J integrated over the domain: 13.354 at time: 1.380\n",
+ "J_n integrated over the domain: 10.646 at time: 1.380\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.380\n",
+ "d (def. map) integrated over the domain: 182.319 at time: 1.380\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.380\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.380\n",
+ "\n",
+ "J integrated over the domain: 15.976 at time: 1.390\n",
+ "J_n integrated over the domain: 13.354 at time: 1.390\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.390\n",
+ "d (def. map) integrated over the domain: 259.224 at time: 1.390\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.390\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.390\n",
+ "\n",
+ "J integrated over the domain: 18.348 at time: 1.400\n",
+ "J_n integrated over the domain: 15.976 at time: 1.400\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.400\n",
+ "d (def. map) integrated over the domain: 340.652 at time: 1.400\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.400\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.400\n",
+ "\n",
+ "J integrated over the domain: 20.322 at time: 1.410\n",
+ "J_n integrated over the domain: 18.348 at time: 1.410\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.410\n",
+ "d (def. map) integrated over the domain: 416.965 at time: 1.410\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.410\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.410\n",
+ "\n",
+ "J integrated over the domain: 21.772 at time: 1.420\n",
+ "J_n integrated over the domain: 20.322 at time: 1.420\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.420\n",
+ "d (def. map) integrated over the domain: 478.026 at time: 1.420\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.420\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.420\n",
+ "\n",
+ "J integrated over the domain: 22.609 at time: 1.430\n",
+ "J_n integrated over the domain: 21.772 at time: 1.430\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.430\n",
+ "d (def. map) integrated over the domain: 515.153 at time: 1.430\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.430\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.430\n",
+ "\n"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "J integrated over the domain: 22.779 at time: 1.440\n",
+ "J_n integrated over the domain: 22.609 at time: 1.440\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.440\n",
+ "d (def. map) integrated over the domain: 522.869 at time: 1.440\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.440\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.440\n",
+ "\n",
+ "J integrated over the domain: 22.271 at time: 1.450\n",
+ "J_n integrated over the domain: 22.779 at time: 1.450\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.450\n",
+ "d (def. map) integrated over the domain: 500.016 at time: 1.450\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.450\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.450\n",
+ "\n",
+ "J integrated over the domain: 21.119 at time: 1.460\n",
+ "J_n integrated over the domain: 22.271 at time: 1.460\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.460\n",
+ "d (def. map) integrated over the domain: 450.001 at time: 1.460\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.460\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.460\n",
+ "\n",
+ "J integrated over the domain: 19.393 at time: 1.470\n",
+ "J_n integrated over the domain: 21.119 at time: 1.470\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.470\n",
+ "d (def. map) integrated over the domain: 380.093 at time: 1.470\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.470\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.470\n",
+ "\n",
+ "J integrated over the domain: 17.203 at time: 1.480\n",
+ "J_n integrated over the domain: 19.393 at time: 1.480\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.480\n",
+ "d (def. map) integrated over the domain: 299.941 at time: 1.480\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.480\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.480\n",
+ "\n",
+ "J integrated over the domain: 14.686 at time: 1.490\n",
+ "J_n integrated over the domain: 17.203 at time: 1.490\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.490\n",
+ "d (def. map) integrated over the domain: 219.674 at time: 1.490\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.490\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.490\n",
+ "\n",
+ "J integrated over the domain: 12.000 at time: 1.500\n",
+ "J_n integrated over the domain: 14.686 at time: 1.500\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.500\n",
+ "d (def. map) integrated over the domain: 148.000 at time: 1.500\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.500\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.500\n",
+ "\n",
+ "J integrated over the domain: 9.314 at time: 1.510\n",
+ "J_n integrated over the domain: 12.000 at time: 1.510\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.510\n",
+ "d (def. map) integrated over the domain: 90.753 at time: 1.510\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.510\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.510\n",
+ "\n",
+ "J integrated over the domain: 6.797 at time: 1.520\n",
+ "J_n integrated over the domain: 9.314 at time: 1.520\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.520\n",
+ "d (def. map) integrated over the domain: 50.200 at time: 1.520\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.520\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.520\n",
+ "\n",
+ "J integrated over the domain: 4.607 at time: 1.530\n",
+ "J_n integrated over the domain: 6.797 at time: 1.530\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.530\n",
+ "d (def. map) integrated over the domain: 25.223 at time: 1.530\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.530\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.530\n",
+ "\n",
+ "J integrated over the domain: 2.881 at time: 1.540\n",
+ "J_n integrated over the domain: 4.607 at time: 1.540\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.540\n",
+ "d (def. map) integrated over the domain: 12.302 at time: 1.540\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.540\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.540\n",
+ "\n",
+ "J integrated over the domain: 1.729 at time: 1.550\n",
+ "J_n integrated over the domain: 2.881 at time: 1.550\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.550\n",
+ "d (def. map) integrated over the domain: 6.988 at time: 1.550\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.550\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.550\n",
+ "\n",
+ "J integrated over the domain: 1.221 at time: 1.560\n",
+ "J_n integrated over the domain: 1.729 at time: 1.560\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.560\n",
+ "d (def. map) integrated over the domain: 5.492 at time: 1.560\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.560\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.560\n",
+ "\n",
+ "J integrated over the domain: 1.391 at time: 1.570\n",
+ "J_n integrated over the domain: 1.221 at time: 1.570\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.570\n",
+ "d (def. map) integrated over the domain: 5.936 at time: 1.570\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.570\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.570\n",
+ "\n",
+ "J integrated over the domain: 2.228 at time: 1.580\n",
+ "J_n integrated over the domain: 1.391 at time: 1.580\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.580\n",
+ "d (def. map) integrated over the domain: 8.963 at time: 1.580\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.580\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.580\n",
+ "\n",
+ "J integrated over the domain: 3.678 at time: 1.590\n",
+ "J_n integrated over the domain: 2.228 at time: 1.590\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.590\n",
+ "d (def. map) integrated over the domain: 17.531 at time: 1.590\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.590\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.590\n",
+ "\n",
+ "J integrated over the domain: 5.652 at time: 1.600\n",
+ "J_n integrated over the domain: 3.678 at time: 1.600\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.600\n",
+ "d (def. map) integrated over the domain: 35.944 at time: 1.600\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.600\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.600\n",
+ "\n",
+ "J integrated over the domain: 8.024 at time: 1.610\n",
+ "J_n integrated over the domain: 5.652 at time: 1.610\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.610\n",
+ "d (def. map) integrated over the domain: 68.389 at time: 1.610\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.610\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.610\n",
+ "\n",
+ "J integrated over the domain: 10.646 at time: 1.620\n",
+ "J_n integrated over the domain: 8.024 at time: 1.620\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.620\n",
+ "d (def. map) integrated over the domain: 117.346 at time: 1.620\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.620\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.620\n",
+ "\n",
+ "J integrated over the domain: 13.354 at time: 1.630\n",
+ "J_n integrated over the domain: 10.646 at time: 1.630\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.630\n",
+ "d (def. map) integrated over the domain: 182.319 at time: 1.630\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.630\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.630\n",
+ "\n",
+ "J integrated over the domain: 15.976 at time: 1.640\n",
+ "J_n integrated over the domain: 13.354 at time: 1.640\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.640\n",
+ "d (def. map) integrated over the domain: 259.224 at time: 1.640\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.640\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.640\n",
+ "\n",
+ "J integrated over the domain: 18.348 at time: 1.650\n",
+ "J_n integrated over the domain: 15.976 at time: 1.650\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.650\n",
+ "d (def. map) integrated over the domain: 340.652 at time: 1.650\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.650\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.650\n",
+ "\n",
+ "J integrated over the domain: 20.322 at time: 1.660\n",
+ "J_n integrated over the domain: 18.348 at time: 1.660\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.660\n",
+ "d (def. map) integrated over the domain: 416.965 at time: 1.660\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.660\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.660\n",
+ "\n",
+ "J integrated over the domain: 21.772 at time: 1.670\n",
+ "J_n integrated over the domain: 20.322 at time: 1.670\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.670\n",
+ "d (def. map) integrated over the domain: 478.026 at time: 1.670\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.670\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.670\n",
+ "\n"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "J integrated over the domain: 22.609 at time: 1.680\n",
+ "J_n integrated over the domain: 21.772 at time: 1.680\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.680\n",
+ "d (def. map) integrated over the domain: 515.153 at time: 1.680\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.680\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.680\n",
+ "\n",
+ "J integrated over the domain: 22.779 at time: 1.690\n",
+ "J_n integrated over the domain: 22.609 at time: 1.690\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.690\n",
+ "d (def. map) integrated over the domain: 522.869 at time: 1.690\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.690\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.690\n",
+ "\n",
+ "J integrated over the domain: 22.271 at time: 1.700\n",
+ "J_n integrated over the domain: 22.779 at time: 1.700\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.700\n",
+ "d (def. map) integrated over the domain: 500.016 at time: 1.700\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.700\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.700\n",
+ "\n",
+ "J integrated over the domain: 21.119 at time: 1.710\n",
+ "J_n integrated over the domain: 22.271 at time: 1.710\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.710\n",
+ "d (def. map) integrated over the domain: 450.001 at time: 1.710\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.710\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.710\n",
+ "\n",
+ "J integrated over the domain: 19.393 at time: 1.720\n",
+ "J_n integrated over the domain: 21.119 at time: 1.720\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.720\n",
+ "d (def. map) integrated over the domain: 380.093 at time: 1.720\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.720\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.720\n",
+ "\n",
+ "J integrated over the domain: 17.203 at time: 1.730\n",
+ "J_n integrated over the domain: 19.393 at time: 1.730\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.730\n",
+ "d (def. map) integrated over the domain: 299.941 at time: 1.730\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.730\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.730\n",
+ "\n",
+ "J integrated over the domain: 14.686 at time: 1.740\n",
+ "J_n integrated over the domain: 17.203 at time: 1.740\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.740\n",
+ "d (def. map) integrated over the domain: 219.674 at time: 1.740\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.740\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.740\n",
+ "\n",
+ "J integrated over the domain: 12.000 at time: 1.750\n",
+ "J_n integrated over the domain: 14.686 at time: 1.750\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.750\n",
+ "d (def. map) integrated over the domain: 148.000 at time: 1.750\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.750\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.750\n",
+ "\n",
+ "J integrated over the domain: 9.314 at time: 1.760\n",
+ "J_n integrated over the domain: 12.000 at time: 1.760\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.760\n",
+ "d (def. map) integrated over the domain: 90.753 at time: 1.760\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.760\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.760\n",
+ "\n",
+ "J integrated over the domain: 6.797 at time: 1.770\n",
+ "J_n integrated over the domain: 9.314 at time: 1.770\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.770\n",
+ "d (def. map) integrated over the domain: 50.200 at time: 1.770\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.770\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.770\n",
+ "\n",
+ "J integrated over the domain: 4.607 at time: 1.780\n",
+ "J_n integrated over the domain: 6.797 at time: 1.780\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.780\n",
+ "d (def. map) integrated over the domain: 25.223 at time: 1.780\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.780\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.780\n",
+ "\n",
+ "J integrated over the domain: 2.881 at time: 1.790\n",
+ "J_n integrated over the domain: 4.607 at time: 1.790\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.790\n",
+ "d (def. map) integrated over the domain: 12.302 at time: 1.790\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.790\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.790\n",
+ "\n",
+ "J integrated over the domain: 1.729 at time: 1.800\n",
+ "J_n integrated over the domain: 2.881 at time: 1.800\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.800\n",
+ "d (def. map) integrated over the domain: 6.988 at time: 1.800\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.800\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.800\n",
+ "\n",
+ "J integrated over the domain: 1.221 at time: 1.810\n",
+ "J_n integrated over the domain: 1.729 at time: 1.810\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.810\n",
+ "d (def. map) integrated over the domain: 5.492 at time: 1.810\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.810\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.810\n",
+ "\n",
+ "J integrated over the domain: 1.391 at time: 1.820\n",
+ "J_n integrated over the domain: 1.221 at time: 1.820\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.820\n",
+ "d (def. map) integrated over the domain: 5.936 at time: 1.820\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.820\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.820\n",
+ "\n",
+ "J integrated over the domain: 2.228 at time: 1.830\n",
+ "J_n integrated over the domain: 1.391 at time: 1.830\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.830\n",
+ "d (def. map) integrated over the domain: 8.963 at time: 1.830\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.830\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.830\n",
+ "\n",
+ "J integrated over the domain: 3.678 at time: 1.840\n",
+ "J_n integrated over the domain: 2.228 at time: 1.840\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.840\n",
+ "d (def. map) integrated over the domain: 17.531 at time: 1.840\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.840\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.840\n",
+ "\n",
+ "J integrated over the domain: 5.652 at time: 1.850\n",
+ "J_n integrated over the domain: 3.678 at time: 1.850\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.850\n",
+ "d (def. map) integrated over the domain: 35.944 at time: 1.850\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.850\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.850\n",
+ "\n",
+ "J integrated over the domain: 8.024 at time: 1.860\n",
+ "J_n integrated over the domain: 5.652 at time: 1.860\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.860\n",
+ "d (def. map) integrated over the domain: 68.389 at time: 1.860\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.860\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.860\n",
+ "\n",
+ "J integrated over the domain: 10.646 at time: 1.870\n",
+ "J_n integrated over the domain: 8.024 at time: 1.870\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.870\n",
+ "d (def. map) integrated over the domain: 117.346 at time: 1.870\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.870\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.870\n",
+ "\n",
+ "J integrated over the domain: 13.354 at time: 1.880\n",
+ "J_n integrated over the domain: 10.646 at time: 1.880\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.880\n",
+ "d (def. map) integrated over the domain: 182.319 at time: 1.880\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.880\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.880\n",
+ "\n",
+ "J integrated over the domain: 15.976 at time: 1.890\n",
+ "J_n integrated over the domain: 13.354 at time: 1.890\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.890\n",
+ "d (def. map) integrated over the domain: 259.224 at time: 1.890\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.890\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.890\n",
+ "\n",
+ "J integrated over the domain: 18.348 at time: 1.900\n",
+ "J_n integrated over the domain: 15.976 at time: 1.900\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.900\n",
+ "d (def. map) integrated over the domain: 340.652 at time: 1.900\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.900\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.900\n",
+ "\n",
+ "J integrated over the domain: 20.322 at time: 1.910\n",
+ "J_n integrated over the domain: 18.348 at time: 1.910\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.910\n",
+ "d (def. map) integrated over the domain: 416.965 at time: 1.910\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.910\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.910\n",
+ "\n"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "J integrated over the domain: 21.772 at time: 1.920\n",
+ "J_n integrated over the domain: 20.322 at time: 1.920\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.920\n",
+ "d (def. map) integrated over the domain: 478.026 at time: 1.920\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.920\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.920\n",
+ "\n",
+ "J integrated over the domain: 22.609 at time: 1.930\n",
+ "J_n integrated over the domain: 21.772 at time: 1.930\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.930\n",
+ "d (def. map) integrated over the domain: 515.153 at time: 1.930\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.930\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.930\n",
+ "\n",
+ "J integrated over the domain: 22.779 at time: 1.940\n",
+ "J_n integrated over the domain: 22.609 at time: 1.940\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.940\n",
+ "d (def. map) integrated over the domain: 522.869 at time: 1.940\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.940\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.940\n",
+ "\n",
+ "J integrated over the domain: 22.271 at time: 1.950\n",
+ "J_n integrated over the domain: 22.779 at time: 1.950\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.950\n",
+ "d (def. map) integrated over the domain: 500.016 at time: 1.950\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.950\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.950\n",
+ "\n",
+ "J integrated over the domain: 21.119 at time: 1.960\n",
+ "J_n integrated over the domain: 22.271 at time: 1.960\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.960\n",
+ "d (def. map) integrated over the domain: 450.001 at time: 1.960\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.960\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.960\n",
+ "\n",
+ "J integrated over the domain: 19.393 at time: 1.970\n",
+ "J_n integrated over the domain: 21.119 at time: 1.970\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.970\n",
+ "d (def. map) integrated over the domain: 380.093 at time: 1.970\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.970\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.970\n",
+ "\n",
+ "J integrated over the domain: 17.203 at time: 1.980\n",
+ "J_n integrated over the domain: 19.393 at time: 1.980\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.980\n",
+ "d (def. map) integrated over the domain: 299.941 at time: 1.980\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.980\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.980\n",
+ "\n",
+ "J integrated over the domain: 14.686 at time: 1.990\n",
+ "J_n integrated over the domain: 17.203 at time: 1.990\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 1.990\n",
+ "d (def. map) integrated over the domain: 219.674 at time: 1.990\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 1.990\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 1.990\n",
+ "\n",
+ "J integrated over the domain: 12.000 at time: 2.000\n",
+ "J_n integrated over the domain: 14.686 at time: 2.000\n",
+ "Well-posedness condition 3J - J_n > 0: True at time 2.000\n",
+ "d (def. map) integrated over the domain: 148.000 at time: 2.000\n",
+ "Strain energy E( eps(|u|^2) ): 0.00000 at time 2.000\n",
+ "Residual of scheme -> 'delta' value: -0.00000 at time 2.000\n",
+ "\n",
+ "DoF for Velocity Space (U): 3298\n",
+ "DoF for Pressure Space (P): 1649\n",
+ "Solution Computed in 34.295 seconds\n",
+ "\n",
+ "----------------Computation Completed!----------------\n",
+ "\n",
+ "\n",
+ "----------------Simulations Done!----------------.\n",
+ "\n",
+ "\n",
+ "Computing error figures for both schemes...\n",
+ "\n",
+ "\n",
+ "All computations done and figures saved...\n",
+ "\n",
+ "\n",
+ "------------------------------------------\n",
+ "\n"
+ ]
+ }
+ ],
+ "source": [
+ "from main import testing_ALE, testing_defs_ALE, testing_defs_ALE_CT\n",
+ "#testing_defs_ALE(solver_to_use='LU')\n",
+ "#testing_defs_ALE_CT(solver_to_use='LU')\n",
+ "dict_mt, dict_ct = testing_ALE(solver_to_use='LU') # 'LU', 'Krylov'"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "\n",
+ "Computing error figures for both schemes...\n",
+ "\n",
+ "\n",
+ "All computations done and figures saved...\n",
+ "\n",
+ "\n",
+ "------------------------------------------\n",
+ "\n"
+ ]
+ }
+ ],
+ "source": [
+ "import matplotlib.pyplot as plt\n",
+ "def testing_comparative_plots(dict_fields_mt: dict, dict_fields_ct: dict, *args) -> None:\n",
+ " \"\"\"\n",
+ " Computes error figures between the schemes with Jacobian evaluation at times {n, n+1}, i.e.\n",
+ " with explicit and implicit treatment of the time-derivative term.\n",
+ " ...\n",
+ " \n",
+ " Input Parameters\n",
+ " ----------------\n",
+ " dict_fields_mt : tuple -> (dict, dict, dict)\n",
+ " tuple containing dictionaries of fields (def, vel, pre) from the iNSE ALE Monolithic solver.\n",
+ " \n",
+ " dict_fields_ct : tupel -> (dict, dict, dict)\n",
+ " tuple containing dictionaries of fields (def, vel, pre) from the iNSE ALE CT solver. \n",
+ " \"\"\"\n",
+ " print(\"\\nComputing error figures for both schemes...\\n\")\n",
+ " # Creates dictionaries for \"expanding\" and \"contracting\" functions\n",
+ " # Time dictionary\n",
+ " time_list = {\n",
+ " 'MT': {jac_name: [] for jac_name in dict_fields_mt.keys()},\n",
+ " 'CT': {jac_name: [] for jac_name in dict_fields_ct.keys()}\n",
+ " }\n",
+ " # Numerical dissipation dictionary --> int (| J^{n+1} u^{n+1} - J^{n} u^{n} |)\n",
+ " dis_value_exp = {\n",
+ " 'MT': {jac_name: [] for jac_name in dict_fields_mt.keys()},\n",
+ " 'CT': {jac_name: [] for jac_name in dict_fields_ct.keys()}\n",
+ " }\n",
+ " dis_value_con = {\n",
+ " 'MT': {jac_name: [] for jac_name in dict_fields_mt.keys()},\n",
+ " 'CT': {jac_name: [] for jac_name in dict_fields_ct.keys()}\n",
+ " }\n",
+ " # Physical dissipation dictionary --> int ( 2*mu* | eps(u) |^2 )\n",
+ " eps_value_exp = {\n",
+ " 'MT': {jac_name: [] for jac_name in dict_fields_mt.keys()},\n",
+ " 'CT': {jac_name: [] for jac_name in dict_fields_ct.keys()}\n",
+ " }\n",
+ " eps_value_con = {\n",
+ " 'MT': {jac_name: [] for jac_name in dict_fields_mt.keys()},\n",
+ " 'CT': {jac_name: [] for jac_name in dict_fields_ct.keys()}\n",
+ " }\n",
+ " # 'delta' values dictionary\n",
+ " delta_value_exp = {\n",
+ " 'MT': {jac_name: [] for jac_name in dict_fields_mt.keys()},\n",
+ " 'CT': {jac_name: [] for jac_name in dict_fields_ct.keys()}\n",
+ " }\n",
+ " delta_value_con = {\n",
+ " 'MT': {jac_name: [] for jac_name in dict_fields_mt.keys()},\n",
+ " 'CT': {jac_name: [] for jac_name in dict_fields_ct.keys()}\n",
+ " }\n",
+ " # Normalized 'delta' values dictionary (w.r.t physical dissipation)\n",
+ " delta_hat_value_exp = {\n",
+ " 'MT': {jac_name: [] for jac_name in dict_fields_mt.keys()},\n",
+ " 'CT': {jac_name: [] for jac_name in dict_fields_ct.keys()}\n",
+ " }\n",
+ " delta_hat_value_con = {\n",
+ " 'MT': {jac_name: [] for jac_name in dict_fields_mt.keys()},\n",
+ " 'CT': {jac_name: [] for jac_name in dict_fields_ct.keys()}\n",
+ " }\n",
+ " # Normalized 'delta' values dictionary (w.r.t numerical dissipation)\n",
+ " delta_hat_dis_exp = {\n",
+ " 'MT': {jac_name: [] for jac_name in dict_fields_mt.keys()},\n",
+ " 'CT': {jac_name: [] for jac_name in dict_fields_ct.keys()}\n",
+ " }\n",
+ " delta_hat_dis_con = {\n",
+ " 'MT': {jac_name: [] for jac_name in dict_fields_mt.keys()},\n",
+ " 'CT': {jac_name: [] for jac_name in dict_fields_ct.keys()}\n",
+ " }\n",
+ " # Iterate over the different cases in MT (Monolithic) and CT (Chorin-Temam) schemes\n",
+ " for scheme in ['MT', 'CT']: # 'MT', 'CT'\n",
+ " if scheme == 'MT':\n",
+ " dict_fields = dict_fields_mt\n",
+ " else:\n",
+ " dict_fields = dict_fields_ct\n",
+ " # Iterate over different cases 'j_implicit', 'j_explicit'\n",
+ " for jac_name in dict_fields.keys():\n",
+ " dict_vel = dict_fields[jac_name][1]\n",
+ " for i in range(len(dict_vel['High_Osc_exp'])):\n",
+ " # Saving time steps\n",
+ " time_list[scheme][jac_name].append(dict_vel['High_Osc_exp'][i][1])\n",
+ " # Add 'delta' values\n",
+ " delta_value_exp[scheme][jac_name].append(dict_vel['High_Osc_exp'][i][2])\n",
+ " #delta_value_con[scheme][jac_name].append(dict_vel['High_Osc_con'][i][2])\n",
+ " # Add physical dissipation\n",
+ " eps_value_exp[scheme][jac_name].append(dict_vel['High_Osc_exp'][i][3])\n",
+ " #eps_value_con[scheme][jac_name].append(dict_vel['High_Osc_con'][i][3])\n",
+ " # Add numerical dissipation\n",
+ " dis_value_exp[scheme][jac_name].append(dict_vel['High_Osc_exp'][i][4])\n",
+ " #dis_value_con[scheme][jac_name].append(dict_vel['High_Osc_con'][i][4])\n",
+ " # Compute normalized 'delta' values w.r.t the physical dissipation\n",
+ " delta_hat_value_exp[scheme][jac_name].append(dict_vel['High_Osc_exp'][i][2]/dict_vel['High_Osc_exp'][i][3])\n",
+ " #delta_hat_value_con[scheme][jac_name].append(dict_vel['High_Osc_con'][i][2]/dict_vel['High_Osc_con'][i][3])\n",
+ " # Compute normalized 'delta' values w.r.t the numerical dissipation\n",
+ " delta_hat_dis_exp[scheme][jac_name].append(dict_vel['High_Osc_exp'][i][2]/dict_vel['High_Osc_exp'][i][4])\n",
+ " #delta_hat_dis_con[scheme][jac_name].append(dict_vel['High_Osc_con'][i][2]/dict_vel['High_Osc_con'][i][4])\n",
+ "\n",
+ " # Auxiliary indexes for plotting\n",
+ " # TODO: Test this line and automatize the \"100\"!\n",
+ " init = 0\n",
+ " out = 101 #len(time_list['CT']['j_implicit']) # at tau = 0.01, T = 2 --> 200 time steps\n",
+ "\n",
+ " # ---------------------- #\n",
+ " # DELTA VALUE CASE\n",
+ " # ---------------------- #\n",
+ " # CASE CT\n",
+ " plt.subplots(figsize=(10, 4))\n",
+ " # Top \n",
+ " lf_ax = plt.subplot(1, 2, 2)\n",
+ " lf_j_exp, = lf_ax.plot(time_list['CT']['j_explicit'][init:out], delta_value_exp['CT']['j_explicit'][init:out], color='blue', ls='--')\n",
+ " lf_j_imp, = lf_ax.plot(time_list['CT']['j_implicit'][init:out], delta_value_exp['CT']['j_implicit'][init:out], color='blue')\n",
+ " lf_ax.set_xlabel(r\"Simulation time [t]\")\n",
+ " lf_ax.set_ylabel(r\"$\\delta_{CT}$\", color='blue')\n",
+ " lf_ax.set_title(r\"Residual Energy $\\delta_{CT}$\")\n",
+ " lf_ax.tick_params(axis='y', labelcolor='blue')\n",
+ " lf_ax.ticklabel_format(style='sci', axis='y', scilimits=(0,0))\n",
+ " #rh_ax = lf_ax.twinx()\n",
+ " #rh_j_exp, = rh_ax.plot(time_list['CT']['j_explicit'][init:out], delta_value_con['CT']['j_explicit'][init:out], color='red', ls='--')\n",
+ " #rh_j_imp, = rh_ax.plot(time_list['CT']['j_implicit'][init:out], delta_value_con['CT']['j_implicit'][init:out], color='red')\n",
+ " #rh_ax.set_ylabel(r\"$\\delta_{CT}$ def. II\", color='red')\n",
+ " #rh_ax.tick_params(axis='y', labelcolor='red')\n",
+ " #rh_ax.ticklabel_format(style='sci', axis='y', scilimits=(0,0))\n",
+ " plt.legend((lf_j_exp, lf_j_imp), (r'CT $\\bigstar\\bigstar = n$', r'CT $\\bigstar\\bigstar = n+1$'), loc='center right')\n",
+ " plt.grid(True)\n",
+ " # CASE M\n",
+ " # Bottom\n",
+ " lf_ax = plt.subplot(1, 2, 1)\n",
+ " lf_j_exp, = lf_ax.plot(time_list['MT']['j_explicit'][init:out], delta_value_exp['MT']['j_explicit'][init:out], color='blue', ls='--')\n",
+ " lf_j_imp, = lf_ax.plot(time_list['MT']['j_implicit'][init:out], delta_value_exp['MT']['j_implicit'][init:out], color='blue')\n",
+ " lf_ax.set_xlabel(r\"Simulation time [t]\")\n",
+ " lf_ax.set_ylabel(r\"$\\delta_{M}$\", color='blue')\n",
+ " lf_ax.set_title(r\"Residual Energy $\\delta_{M}$\")\n",
+ " lf_ax.tick_params(axis='y', labelcolor='blue')\n",
+ " lf_ax.ticklabel_format(style='sci', axis='y', scilimits=(0,0))\n",
+ " #rh_ax = lf_ax.twinx()\n",
+ " #rh_j_exp, = rh_ax.plot(time_list['MT']['j_explicit'][init:out], delta_value_con['MT']['j_explicit'][init:out], color='red', ls='--')\n",
+ " #rh_j_imp, = rh_ax.plot(time_list['MT']['j_implicit'][init:out], delta_value_con['MT']['j_implicit'][init:out], color='red')\n",
+ " #rh_ax.set_ylabel(r\"$\\delta_{M}$ def. II\", color='red')\n",
+ " #rh_ax.tick_params(axis='y', labelcolor='red')\n",
+ " #rh_ax.ticklabel_format(style='sci', axis='y', scilimits=(0,0))\n",
+ " plt.legend((lf_j_exp, lf_j_imp), (r'M $\\bigstar\\bigstar = n$', r'M $\\bigstar\\bigstar = n+1$'), loc='center right')\n",
+ " plt.grid(True)\n",
+ " plt.subplots_adjust(hspace=0.8)\n",
+ " plt.tight_layout()\n",
+ " plt.savefig('Comparison_Delta_Value_GCL_{}_Solver_{}.png'.format(args[0], args[1]), dpi=300)\n",
+ " plt.close()\n",
+ "\n",
+ " # ---------------------- #\n",
+ " # NORMALIZED DELTA CASE (w.r.t physical dissipation)\n",
+ " # ---------------------- #\n",
+ " plt.subplots(figsize=(10, 4))\n",
+ " # CASE CT\n",
+ " # Top\n",
+ " lf_ax = plt.subplot(1, 2, 2)\n",
+ " lf_j_exp, = lf_ax.plot(time_list['CT']['j_explicit'][init:out], delta_hat_value_exp['CT']['j_explicit'][init:out], color='blue', ls='--')\n",
+ " lf_j_imp, = lf_ax.plot(time_list['CT']['j_implicit'][init:out], delta_hat_value_exp['CT']['j_implicit'][init:out], color='blue')\n",
+ " lf_ax.set_xlabel(r\"Simulation time [t]\")\n",
+ " lf_ax.set_ylabel(r\"$\\hat{\\delta}_{CT}$\", color='blue')\n",
+ " lf_ax.set_title(r\"Normalized value $\\hat{\\delta}_{CT}$\")\n",
+ " lf_ax.tick_params(axis='y', labelcolor='blue')\n",
+ " lf_ax.ticklabel_format(style='sci', axis='y', scilimits=(0,0))\n",
+ " #rh_ax = lf_ax.twinx()\n",
+ " #rh_j_exp, = rh_ax.plot(time_list['CT']['j_explicit'][init:out], delta_hat_value_con['CT']['j_explicit'][init:out], color='red', ls='--')\n",
+ " #rh_j_imp, = rh_ax.plot(time_list['CT']['j_implicit'][init:out], delta_hat_value_con['CT']['j_implicit'][init:out], color='red')\n",
+ " #rh_ax.set_ylabel(r\"$\\hat{\\delta}_{CT}$ def. II\", color='red')\n",
+ " #rh_ax.tick_params(axis='y', labelcolor='red')\n",
+ " #rh_ax.ticklabel_format(style='sci', axis='y', scilimits=(0,0))\n",
+ " plt.legend((lf_j_exp, lf_j_imp), (r'CT $\\bigstar\\bigstar = n$', r'CT $\\bigstar\\bigstar = n+1$'), loc='lower right')\n",
+ " plt.grid(True)\n",
+ " # CASE M\n",
+ " # Bottom\n",
+ " lf_ax = plt.subplot(1, 2, 1)\n",
+ " lf_j_exp, = lf_ax.plot(time_list['MT']['j_explicit'][init:out], delta_hat_value_exp['MT']['j_explicit'][init:out], color='blue', ls='--')\n",
+ " lf_j_imp, = lf_ax.plot(time_list['MT']['j_implicit'][init:out], delta_hat_value_exp['MT']['j_implicit'][init:out], color='blue')\n",
+ " lf_ax.set_xlabel(r\"Simulation time [t]\")\n",
+ " lf_ax.set_ylabel(r\"$\\hat{\\delta}_{M}$\", color='blue')\n",
+ " lf_ax.set_title(r\"Normalized value $\\hat{\\delta}_{M}$\")\n",
+ " lf_ax.tick_params(axis='y', labelcolor='blue')\n",
+ " lf_ax.ticklabel_format(style='sci', axis='y', scilimits=(0,0))\n",
+ " #rh_ax = lf_ax.twinx()\n",
+ " #rh_j_exp, = rh_ax.plot(time_list['MT']['j_explicit'][init:out], delta_hat_value_con['MT']['j_explicit'][init:out], color='red', ls='--')\n",
+ " #rh_j_imp, = rh_ax.plot(time_list['MT']['j_implicit'][init:out], delta_hat_value_con['MT']['j_implicit'][init:out], color='red')\n",
+ " #rh_ax.set_ylabel(r\"$\\hat{\\delta}_{M}$ def. II\", color='red')\n",
+ " #rh_ax.tick_params(axis='y', labelcolor='red')\n",
+ " #rh_ax.ticklabel_format(style='sci', axis='y', scilimits=(0,0))\n",
+ " plt.legend((lf_j_exp, lf_j_imp), (r'M $\\bigstar\\bigstar = n$', r'M $\\bigstar\\bigstar = n+1$'), loc='upper right')\n",
+ " plt.grid(True)\n",
+ " plt.subplots_adjust(hspace=0.8)\n",
+ " plt.tight_layout()\n",
+ " plt.savefig('Comparison_Delta_Hat_Value_GCL_{}_solver_{}.png'.format(args[0], args[1]), dpi=300)\n",
+ " plt.close()\n",
+ "\n",
+ " # ---------------------- #\n",
+ " # NORMALIZED DELTA CASE (w.r.t numerical dissipation)\n",
+ " # ---------------------- #\n",
+ " plt.subplots(figsize=(10, 4))\n",
+ " # CASE CT\n",
+ " # Top\n",
+ " lf_ax = plt.subplot(1, 2, 2)\n",
+ " lf_j_exp, = lf_ax.plot(time_list['CT']['j_explicit'][init:out], delta_hat_dis_exp['CT']['j_explicit'][init:out], color='blue', ls='--')\n",
+ " lf_j_imp, = lf_ax.plot(time_list['CT']['j_implicit'][init:out], delta_hat_dis_exp['CT']['j_implicit'][init:out], color='blue')\n",
+ " lf_ax.set_xlabel(r\"Simulation time [t]\")\n",
+ " lf_ax.set_ylabel(r\"$\\hat{\\delta}_{CT}$ dis. \", color='blue')\n",
+ " lf_ax.set_title(r\"Normalized value $\\hat{\\delta}_{CT}$ (dis)\")\n",
+ " lf_ax.tick_params(axis='y', labelcolor='blue')\n",
+ " lf_ax.ticklabel_format(style='sci', axis='y', scilimits=(0,0))\n",
+ " #rh_ax = lf_ax.twinx()\n",
+ " #rh_j_exp, = rh_ax.plot(time_list['CT']['j_explicit'][init:out], delta_hat_dis_con['CT']['j_explicit'][init:out], color='red', ls='--')\n",
+ " #rh_j_imp, = rh_ax.plot(time_list['CT']['j_implicit'][init:out], delta_hat_dis_con['CT']['j_implicit'][init:out], color='red')\n",
+ " #rh_ax.set_ylabel(r\"$\\hat{\\delta}_{CT}$ def. II\", color='red')\n",
+ " #rh_ax.tick_params(axis='y', labelcolor='red')\n",
+ " #rh_ax.ticklabel_format(style='sci', axis='y', scilimits=(0,0))\n",
+ " plt.legend((lf_j_exp, lf_j_imp), (r'CT $\\bigstar\\bigstar = n$', r'CT $\\bigstar\\bigstar = n+1$'), loc='lower right')\n",
+ " plt.grid(True)\n",
+ " # CASE M\n",
+ " # Bottom\n",
+ " lf_ax = plt.subplot(1, 2, 1)\n",
+ " lf_j_exp, = lf_ax.plot(time_list['MT']['j_explicit'][init:out], delta_hat_dis_exp['MT']['j_explicit'][init:out], color='blue', ls='--')\n",
+ " lf_j_imp, = lf_ax.plot(time_list['MT']['j_implicit'][init:out], delta_hat_dis_exp['MT']['j_implicit'][init:out], color='blue')\n",
+ " lf_ax.set_xlabel(r\"Simulation time [t]\")\n",
+ " lf_ax.set_ylabel(r\"$\\hat{\\delta}_{M}$ dis.\", color='blue')\n",
+ " lf_ax.set_title(r\"Normalized value $\\hat{\\delta}_{M}$ (dis)\")\n",
+ " lf_ax.tick_params(axis='y', labelcolor='blue')\n",
+ " lf_ax.ticklabel_format(style='sci', axis='y', scilimits=(0,0))\n",
+ " #rh_ax = lf_ax.twinx()\n",
+ " #rh_j_exp, = rh_ax.plot(time_list['MT']['j_explicit'][init:out], delta_hat_dis_con['MT']['j_explicit'][init:out], color='red', ls='--')\n",
+ " #rh_j_imp, = rh_ax.plot(time_list['MT']['j_implicit'][init:out], delta_hat_dis_con['MT']['j_implicit'][init:out], color='red')\n",
+ " #rh_ax.set_ylabel(r\"$\\hat{\\delta}_{M}$ def. II\", color='red')\n",
+ " #rh_ax.tick_params(axis='y', labelcolor='red')\n",
+ " #rh_ax.ticklabel_format(style='sci', axis='y', scilimits=(0,0))\n",
+ " plt.legend((lf_j_exp, lf_j_imp), (r'M $\\bigstar\\bigstar = n$', r'M $\\bigstar\\bigstar = n+1$'), loc='lower right')\n",
+ " plt.grid(True)\n",
+ " plt.subplots_adjust(hspace=0.8)\n",
+ " plt.tight_layout()\n",
+ " plt.savefig('Comparison_Delta_Hat_Dis_Value_GCL_{}_solver_{}.png'.format(args[0], args[1]), dpi=300)\n",
+ " plt.close()\n",
+ "\n",
+ " # ---------------------- #\n",
+ " # PHYSICAL DISSIPATION PLOT\n",
+ " # ---------------------- #\n",
+ " plt.subplots(figsize=(10, 4))\n",
+ " # CASE CT\n",
+ " # Top\n",
+ " lf_ax = plt.subplot(1, 2, 2)\n",
+ " lf_j_exp, = lf_ax.plot(time_list['CT']['j_explicit'][init:out], eps_value_exp['CT']['j_explicit'][init:out], color='blue', ls='--')\n",
+ " lf_j_imp, = lf_ax.plot(time_list['CT']['j_implicit'][init:out], eps_value_exp['CT']['j_implicit'][init:out], color='blue')\n",
+ " lf_ax.set_xlabel(r\"Simulation time [t]\")\n",
+ " lf_ax.set_ylabel(r\"CT\", color='blue')\n",
+ " lf_ax.set_title(r\"Physical Dissipation (CT)\")\n",
+ " lf_ax.tick_params(axis='y', labelcolor='blue')\n",
+ " lf_ax.ticklabel_format(style='sci', axis='y', scilimits=(0,0))\n",
+ " #rh_ax = lf_ax.twinx()\n",
+ " #rh_j_exp, = rh_ax.plot(time_list['CT']['j_explicit'][init:out], eps_value_con['CT']['j_explicit'][init:out], color='red', ls='--')\n",
+ " #rh_j_imp, = rh_ax.plot(time_list['CT']['j_implicit'][init:out], eps_value_con['CT']['j_implicit'][init:out], color='red')\n",
+ " #rh_ax.set_ylabel(r\"On def. II\", color='red')\n",
+ " #rh_ax.tick_params(axis='y', labelcolor='red')\n",
+ " #rh_ax.ticklabel_format(style='sci', axis='y', scilimits=(0,0))\n",
+ " plt.legend((lf_j_exp, lf_j_imp), \\\n",
+ " (r'CT $\\star\\star = n$', r'CT $\\bigstar\\bigstar = n+1$'), loc='lower right')\n",
+ " plt.grid(True)\n",
+ " # CASE M\n",
+ " # Bottom\n",
+ " lf_ax = plt.subplot(1, 2, 1)\n",
+ " lf_j_exp, = lf_ax.plot(time_list['MT']['j_explicit'][init:out], eps_value_exp['MT']['j_explicit'][init:out], color='blue', ls='--')\n",
+ " lf_j_imp, = lf_ax.plot(time_list['MT']['j_implicit'][init:out], eps_value_exp['MT']['j_implicit'][init:out], color='blue')\n",
+ " lf_ax.set_xlabel(r\"Simulation time [t]\")\n",
+ " lf_ax.set_ylabel(r\"M\", color='blue')\n",
+ " lf_ax.set_title(r\"Physical Dissipation (M)\")\n",
+ " lf_ax.tick_params(axis='y', labelcolor='blue')\n",
+ " lf_ax.ticklabel_format(style='sci', axis='y', scilimits=(0,0))\n",
+ " #rh_ax = lf_ax.twinx()\n",
+ " #rh_j_exp, = rh_ax.plot(time_list['MT']['j_explicit'][init:out], eps_value_con['MT']['j_explicit'][init:out], color='red', ls='--')\n",
+ " #rh_j_imp, = rh_ax.plot(time_list['MT']['j_implicit'][init:out], eps_value_con['MT']['j_implicit'][init:out], color='red')\n",
+ " #rh_ax.set_ylabel(r\"On def. II\", color='red')\n",
+ " #rh_ax.tick_params(axis='y', labelcolor='red')\n",
+ " #rh_ax.ticklabel_format(style='sci', axis='y', scilimits=(0,0))\n",
+ " plt.legend((lf_j_exp, lf_j_imp), (r'M $\\bigstar\\bigstar = n$', r'M $\\bigstar\\bigstar = n+1$'), loc='lower right')\n",
+ " plt.grid(True)\n",
+ " plt.subplots_adjust(hspace=0.8)\n",
+ " plt.tight_layout()\n",
+ " plt.savefig('Comparison_Eps_Value_GCL_{}_solver_{}.png'.format(args[0], args[1]), dpi=300)\n",
+ " plt.close()\n",
+ "\n",
+ " # ---------------------- #\n",
+ " # NUMERICAL DISSIPATION PLOT\n",
+ " # ---------------------- #\n",
+ " plt.subplots(figsize=(10, 4))\n",
+ " # CASE CT\n",
+ " # Top\n",
+ " lf_ax = plt.subplot(1, 2, 2)\n",
+ " lf_j_exp, = lf_ax.plot(time_list['CT']['j_explicit'][init:out], dis_value_exp['CT']['j_explicit'][init:out], color='blue', ls='--')\n",
+ " lf_j_imp, = lf_ax.plot(time_list['CT']['j_implicit'][init:out], dis_value_exp['CT']['j_implicit'][init:out], color='blue')\n",
+ " lf_ax.set_xlabel(r\"Simulation time [t]\")\n",
+ " lf_ax.set_ylabel(r\"CT\", color='blue')\n",
+ " lf_ax.set_title(r\"Numerical Dissipation (CT)\")\n",
+ " lf_ax.tick_params(axis='y', labelcolor='blue')\n",
+ " lf_ax.ticklabel_format(style='sci', axis='y', scilimits=(0,0))\n",
+ " #rh_ax = lf_ax.twinx()\n",
+ " #rh_j_exp, = rh_ax.plot(time_list['CT']['j_explicit'][init:out], dis_value_con['CT']['j_explicit'][init:out], color='red', ls='--')\n",
+ " #rh_j_imp, = rh_ax.plot(time_list['CT']['j_implicit'][init:out], dis_value_con['CT']['j_implicit'][init:out], color='red')\n",
+ " #rh_ax.set_ylabel(r\"On def. II\", color='red')\n",
+ " #rh_ax.tick_params(axis='y', labelcolor='red')\n",
+ " #rh_ax.ticklabel_format(style='sci', axis='y', scilimits=(0,0))\n",
+ " plt.legend((lf_j_exp, lf_j_imp), (r'CT $\\bigstar\\bigstar = n$', r'CT $\\bigstar\\bigstar = n+1$'), loc='lower right')\n",
+ " plt.grid(True)\n",
+ " # CASE M\n",
+ " # Bottom\n",
+ " lf_ax = plt.subplot(1, 2, 1)\n",
+ " lf_j_exp, = lf_ax.plot(time_list['MT']['j_explicit'][init:out], dis_value_exp['MT']['j_explicit'][init:out], color='blue', ls='--')\n",
+ " lf_j_imp, = lf_ax.plot(time_list['MT']['j_implicit'][init:out], dis_value_exp['MT']['j_implicit'][init:out], color='blue')\n",
+ " lf_ax.set_xlabel(r\"Simulation time [t]\")\n",
+ " lf_ax.set_ylabel(r\"M\", color='blue')\n",
+ " lf_ax.set_title(r\"Numerical Dissipation (M)\")\n",
+ " lf_ax.tick_params(axis='y', labelcolor='blue')\n",
+ " lf_ax.ticklabel_format(style='sci', axis='y', scilimits=(0,0))\n",
+ " #rh_ax = lf_ax.twinx()\n",
+ " #rh_j_exp, = rh_ax.plot(time_list['MT']['j_explicit'][init:out], dis_value_con['MT']['j_explicit'][init:out], color='red', ls='--')\n",
+ " #rh_j_imp, = rh_ax.plot(time_list['MT']['j_implicit'][init:out], dis_value_con['MT']['j_implicit'][init:out], color='red')\n",
+ " #rh_ax.set_ylabel(r\"On def. II\", color='red')\n",
+ " #rh_ax.tick_params(axis='y', labelcolor='red')\n",
+ " #rh_ax.ticklabel_format(style='sci', axis='y', scilimits=(0,0))\n",
+ " plt.legend((lf_j_exp, lf_j_imp), (r'M $\\bigstar\\bigstar = n$', r'M $\\bigstar\\bigstar = n+1$'), loc='lower right')\n",
+ " plt.grid(True)\n",
+ " plt.subplots_adjust(hspace=0.8)\n",
+ " plt.tight_layout()\n",
+ " plt.savefig('Comparison_Num_Dis_Value_GCL_{}_solver_{}.png'.format(args[0], args[1]), dpi=300)\n",
+ " plt.close()\n",
+ " print(\"\\nAll computations done and figures saved...\\n\")\n",
+ " print(\"\\n------------------------------------------\\n\")\n",
+ " return None\n",
+ "\n",
+ "testing_comparative_plots(dict_mt, dict_ct, True, 'LU')"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.6.9"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/README.rst b/README.rst
new file mode 100644
index 0000000..8bed904
--- /dev/null
+++ b/README.rst
@@ -0,0 +1,63 @@
+NavierStokes
+============
+
+This repository implements via finite element solvers for incompressible
+Navier-Stokes (iNSE) equations in Arbitrary Lagrangian-Eulerian (ALE) formalism the schemes
+proposed on [RA20]_.
+
+In particular, it aims to replicate the energy results shown in the article [RA20]_
+for both Monolithic and Chorin-Temam solvers.
+
+Solvers
+-------
+
+Both monolithic solver and a fractional step solver are implemented.
+
+* Monolithic solver for the iNSE-ALE problem with linearized convective term
+and Taylor-Hood (P2/P1) stable finite element space.
+
+
+* Fractional step solver for the iNSE-ALE problem with linealized convective term
+and P1/P1 finite element space. The Chorin-Temam schemes proposed is described in [RA20]_.
+
+Flow model
+----------
+
+A rectangle domain is taken with fully Dirichlet homogeneous boundary conditions
+and non-zero initial velocity profile. Further description of the problem also can be found
+in the reference.
+
+Usage
+----------
+
+Since the repository aims to directly reproduce the results of the reference,
+no configuration files where implemented to further customize the problem.
+Nevertheless, the solvers are easily modified since its implementation is done via
+FEniCS [LO12]_.
+
+An ipynb file is included to reproduce the results and recommended to use.
+
+If desired to run the simulations only, execute::
+
+ python main.py
+
+
+Dependencies
+------------
+
+- Python >= 3.5
+- FEniCS_ >= 2019.1.0
+
+
+
+Reference
+^^^^^^^^^^
+
+.. [RA20] ArĂ³stica R., Bertoglio C. (2020) On monolithic and Chorin-Temam
+ schemes for incompressible flows in moving domains.
+ Applied Mathematics Letters, doi: https://doi.org/10.1016/j.aml.2020.106830
+ ISBN: 978-3-642-23099-8
+
+.. [LO12] Logg A., Mardal K.-A., Wells G. N. (2012) Automated Solution of Differential
+ Equations by the Finite Element Method.
+ Springer, Berlin, Heidelberg, doi: https://doi.org/10.1007/978-3-642-23099-8
diff --git a/common.py b/common.py
new file mode 100644
index 0000000..4ed5b7d
--- /dev/null
+++ b/common.py
@@ -0,0 +1,54 @@
+"""
+This module contains all common functions used in variational form.
+All operators are defined with respect to the reference coordiantes.
+"""
+import fenics as fn
+
+__version__ = "0.1"
+__author__ = "Reidmen Arostica"
+__date__ = "25/06/2020"
+
+def F_(coordinates: fn.Function) -> fn.grad:
+ """
+ Computes the deformation gradient operator (dx/dX).
+ """
+ return fn.grad(coordinates)
+
+def inv_F_(coordinates: fn.Function) -> fn.inv:
+ """
+ Computes the inverse of the deformation gradient.
+ """
+ return fn.inv(F_(coordinates))
+
+def J_(coordinates: fn.Function) -> fn.det:
+ """
+ Computes the determinant of the deformation gradient.
+ """
+ return fn.det(F_(coordinates))
+
+def grad_(u: fn.Function, coordinates: fn.Function) -> fn.Function:
+ """
+ Computes the grad operator on the reference configuration.
+ """
+ inv_F = fn.inv(F_(coordinates))
+ return fn.dot(fn.grad(u), inv_F)
+
+def nabla_grad_(u: fn.Function, coordinates: fn.Function) -> fn.Function:
+ """
+ Computes the nabla_grad on the reference configuration.
+ """
+ return grad_(u, coordinates).T
+
+def sym_grad_(u: fn.Function, coordinates: fn.Function) -> fn.Function:
+ """
+ Computes the symmetric gradient operator w.r.t. the reference configuration.
+ """
+ return 0.5*(grad_(u, coordinates) + grad_(u, coordinates).T)
+
+def div_(u: fn.Function, coordinates: fn.Function) -> fn.tr:
+ """
+ Computes the Piola div operator w.r.t. the reference configuration.
+ """
+ J = J_(coordinates)
+ inv_F = inv_F_(coordinates)
+ return fn.div(J*fn.dot(inv_F, u))
diff --git a/main.py b/main.py
new file mode 100644
index 0000000..1d2c3ed
--- /dev/null
+++ b/main.py
@@ -0,0 +1,144 @@
+__version__ = "0.2"
+__author__ = "Reidmen Arostica"
+__date__ = "18/07/2020"
+
+# Libraries
+from solvers import iNSE_Monolithic_Solver, iNSE_CT_Solver
+from solvers import testing_comparative_plots
+
+# Basic info to user
+# print("SOLVER VERSION: {}".format(__version__))
+# print("__author__: {}".format(__author__))
+
+
+def testing_defs_ALE(solver_to_use='LU', gcl_stab=True, jac_at_n=False):
+ """
+ Computes the iNSE problem under several deformations (including the Identity).
+ - Identity -> ('x[0]', 'x[1]')
+ - High Oscillation (init with expansion ) -> ('x[0]*(1+0.9*sin(16*pi*t/2))', 'x[1]')
+ - High Oscillation (init with contraction) -> ('x[0]*(1+0.9*sin(16*pi*t/2))', 'x[1]')
+ """
+ print("""Initializing testing of two deformation cases with input parameters:
+ Solver to use -solver_to_use- : {}
+ GCL-stabilization term -gcl_stab- : {}
+ Evaluation of jacobian at n in time-derivate term -jac_at_n- : {}
+ """.format(solver_to_use, gcl_stab, jac_at_n))
+ # Define dict of deformation used and output names
+ dict_def = {
+ # 'Identity': ('x[0] + 0*t', 'x[1]'),
+ 'High_Osc_exp': ('x[0]*(1+0.9*sin(16*pi*t/2))', 'x[1]'),
+ 'High_Osc_con': ('x[0]*(1-0.9*sin(16*pi*t/2))', 'x[1]')
+ }
+ dict_def_names = {
+ # 'Identity': ('Idx', 'Idy'),
+ 'High_Osc_exp': ('High_Osc_exp', 'Idy'),
+ 'High_Osc_con': ('High_Osc_con', 'Idy')
+ }
+ dict_defs = {def_type: None for def_type in dict_def.keys()}
+ dict_vels = {def_type: None for def_type in dict_def.keys()}
+ dict_pres = {def_type: None for def_type in dict_def.keys()}
+ for def_type in dict_defs.keys():
+ print("\nInitializing iNSE problem with Deformation type: {}\n".format(def_type))
+ parameters = {
+ 'gcl_stab': gcl_stab, # True, False whenever we want to impose CGL in the scheme
+ 'jac_at_n': jac_at_n, # Choose True, False for taking the Jacobian evaluated at time k+1 or k
+ 'init_cond': True,
+ 'Nx': 6*16,
+ 'Ny': 16,
+ 'T': 2.0, #0.5, 1.0, 2.0
+ 'mu': 0.035,
+ 'rho_f': 1.2,
+ 'tau': 0.01, # 0.01
+ 'deg_U': 2,
+ 'deg_P': 1
+ }
+ deformation = {
+ 'expression': dict_def[def_type],
+ 'output_name': dict_def_names[def_type]
+ }
+ stabilization = {
+ 'type': None
+ }
+ print("\nSetup with initial condition: {}".format(True))
+ dict_defs[def_type], dict_vels[def_type], dict_pres[def_type] = iNSE_Monolithic_Solver(parameters, deformation, stabilization, solver_to_use=solver_to_use)
+ print("\n----------------Computation Completed!----------------\n")
+ print("\n----------------Simulations Done!----------------.\n")
+
+ # Return dictionaries with values for further processing...
+ return dict_defs, dict_vels, dict_pres
+
+
+def testing_defs_ALE_CT(solver_to_use='LU', gcl_stab=True, jac_at_n=False):
+ """
+ Computes the iNSE problem under several deformations (including the Identity).
+ - Identity -> ('x[0]', 'x[1]')
+ - High Oscillation (init with expansion ) -> ('x[0]*(1+0.9*sin(16*pi*t/2))', 'x[1]')
+ - High Oscillation (init with contraction) -> ('x[0]*(1+0.9*sin(16*pi*t/2))', 'x[1]')
+ """
+ print("""Initializing testing of two deformation cases with input parameters:
+ Solver to use -solver_to_use- : {}
+ """.format(solver_to_use))
+ # Define dict of deformation used and output names
+ dict_def = {
+ # 'Identity': ('x[0] + 0*t', 'x[1]'),
+ 'High_Osc_exp': ('x[0]*(1+0.9*sin(16*pi*t/2))', 'x[1]'),
+ 'High_Osc_con': ('x[0]*(1-0.9*sin(16*pi*t/2))', 'x[1]')
+ }
+ dict_def_names = {
+ # 'Identity': ('Idx', 'Idy'),
+ 'High_Osc_exp': ('High_Osc_exp', 'Idy'),
+ 'High_Osc_con': ('High_Osc_con', 'Idy')
+ }
+ dict_defs = {def_type: None for def_type in dict_def.keys()}
+ dict_vels = {def_type: None for def_type in dict_def.keys()}
+ dict_pres = {def_type: None for def_type in dict_def.keys()}
+ for def_type in dict_defs.keys():
+ print("\nInitializing iNSE problem with Deformation type: {}\n".format(def_type))
+ parameters = {
+ 'gcl_stab': gcl_stab,
+ 'jac_at_n': jac_at_n,
+ 'init_cond': True,
+ 'Nx': 6*16,
+ 'Ny': 16,
+ 'T': 2.0, #0.5, 1.0, 2.0
+ 'mu': 0.035,
+ 'rho_f': 1.2,
+ 'tau': 0.01, # 0.01
+ 'deg_U': 1,
+ 'deg_P': 1
+ }
+ deformation = {
+ 'expression': dict_def[def_type],
+ 'output_name': dict_def_names[def_type]
+ }
+ stabilization = {
+ 'type': None
+ }
+ print("\nSetup with initial condition: {}".format(True))
+ dict_defs[def_type], dict_vels[def_type], dict_pres[def_type] = iNSE_CT_Solver(parameters, deformation, stabilization, solver_to_use=solver_to_use)
+ print("\n----------------Computation Completed!----------------\n")
+ print("\n----------------Simulations Done!----------------.\n")
+
+ # Return dictionaries with values for further processing...
+ return dict_defs, dict_vels, dict_pres
+
+
+def testing_ALE(solver_to_use='LU', gcl_stab=True):
+ """
+ Computes testing_defs_ALE (each deformation case) for two different monolithic schemes, i.e.
+ using evaluation of J at {n, n+1}, both with GCL + Temam stabilizations.
+ """
+ print("The solution of the linear system is done with built-in PETS Krylov solver.")
+ dict_fields_mt = {jac_name: None for jac_name in ['j_implicit', 'j_explicit']}
+ dict_fields_ct = {jac_name: None for jac_name in ['j_implicit', 'j_explicit']}
+ for jac_name, jac_at_n in zip(['j_implicit', 'j_explicit'], [False, True]):
+ dict_fields_mt[jac_name] = testing_defs_ALE(solver_to_use=solver_to_use, gcl_stab=gcl_stab, jac_at_n=jac_at_n)
+ dict_fields_ct[jac_name] = testing_defs_ALE_CT(solver_to_use=solver_to_use, gcl_stab=gcl_stab, jac_at_n=jac_at_n)
+ # Generate comparative figures for cases 'j_implicit', 'j_explicit'
+ testing_comparative_plots(dict_fields_mt, dict_fields_ct, gcl_stab, solver_to_use)
+ return dict_fields_mt, dict_fields_ct
+
+if __name__ == "__main__":
+ #testing_defs_ALE_CT(solver_to_use='Krylov')
+ #testing_defs_ALE(solver_to_use='LU')
+ testing_ALE(solver_to_use='LU') # 'LU', 'Krylov'
\ No newline at end of file
diff --git a/solvers.py b/solvers.py
new file mode 100644
index 0000000..cc749cc
--- /dev/null
+++ b/solvers.py
@@ -0,0 +1,1005 @@
+"""
+This module contains the problem definition and solver for iNSE ALE article.
+It enables to replicate all results
+"""
+__version__ = "0.2"
+__author__ = "Reidmen Arostica"
+__date__ = "18/07/2020"
+
+# Libraries
+import fenics as fn
+from dolfin import __version__ as df_version
+import numpy as np
+import matplotlib.pyplot as plt
+import time
+from common import *
+
+# Basic info to user
+print("DOLFIN VERSION: {}".format(df_version))
+print("SOLVER VERSION: {}".format(__version__))
+print("__author__: {}".format(__author__))
+
+
+def iNSE_Monolithic_Solver(parameters, deformation, stabilization, solver_to_use='LU'):
+ """ This solver computes the incompressible Navier-Stokes (iNSE) problem in the ALE formalism.
+ To do so, the FEniCS framework is used and the convective term within iNSE is linealized.
+ To solve the problem, a monolithic scheme is employed with finite diferences for time
+ and FE for space.
+ ...
+
+ Input Parameters
+ ----------------
+ parameter: dict
+ dictionary containing several options for the scheme used.
+ deformation: dict
+ dictionary containing deformation mapping properties and options.
+ stabilization: dict
+ dictionary specifying stabilization used.
+
+
+ Output
+ ----------------
+ None.
+ The solver print the results to console, and returns None, saving solutions and figures.
+ """
+ # Starting time
+ start = time.time()
+ # Default parameters
+ mu, rho_f = parameters['mu'], parameters['rho_f']
+ Nx, Ny = parameters['Nx'], parameters['Ny']
+ tau, T = parameters['tau'], parameters['T']
+
+ def def_mesh_tuple(def_params: dict) -> tuple:
+ """
+ Computes a list (len 2) containing the parametrized mesh velocity.
+ ...
+
+ Input Parameters
+ ----------------
+ def_params: dict
+ dictionary with keys 'expression' and 'output_name'.
+
+ """
+ if 'expression' in def_params.keys():
+ if 'output_name' in def_params.keys():
+ output_name = def_params['output_name']
+ else:
+ output_name = ('X', 'Y')
+ return def_params['expression'], output_name
+ else:
+ raise Exception("Key 'expression' was not found in the dictionary!")
+
+ def exps_at_bdry(bdry_params: dict, def_params):
+ """
+ Computes the boundary FEniCS expressions for this particular Dirichlet Homogeneous case.
+ """
+ u_inlet = fn.Constant((0.0, 0.0))
+ u_outlet = fn.Constant((0.0, 0.0))
+ u_bottom = fn.Constant((0.0, 0.0))
+ u_top = fn.Constant((0.0, 0.0))
+ return u_inlet, u_outlet, u_bottom, u_top
+
+ # Define boundary domain classes
+ class inlet(fn.SubDomain):
+ def inside(self, x, on_boundary):
+ return fn.near(x[0], 0) and on_boundary
+ class outlet(fn.SubDomain):
+ def inside(self, x, on_boundary):
+ return fn.near(x[0], 6) and on_boundary
+ class top(fn.SubDomain):
+ def inside(self, x, on_boundary):
+ return fn.near(x[1], 1) and on_boundary
+ class bottom(fn.SubDomain):
+ def inside(self, x, on_boundary):
+ return fn.near(x[1], -1) and on_boundary
+
+ # Define mesh object
+ mesh_f = fn.RectangleMesh(fn.Point(0, -1), fn.Point(6, 1), Nx, Ny)
+ #h = fn.CellDiameter(mesh_f)
+
+ # Obtain mesh deformation tuple and output name
+ def_tuple, def_name = def_mesh_tuple(deformation)
+
+ # Define displacement expressions at previous and actual time stepss
+ def_n = fn.Expression(def_tuple, t=0.0, domain=mesh_f, degree=2)
+ def_t = fn.Expression(def_tuple, t=tau, domain=mesh_f, degree=2)
+
+ # Functional Spaces (Mixed Element)
+ U = fn.VectorElement("CG", mesh_f.ufl_cell(), parameters['deg_U'])
+ P = fn.FiniteElement("CG", mesh_f.ufl_cell(), parameters['deg_P'])
+ M = fn.FunctionSpace(mesh_f, fn.MixedElement([U, P]))
+
+ # Functional spaces (Separately)
+ U_ = fn.VectorFunctionSpace(mesh_f, "CG", parameters['deg_U'])
+ P_ = fn.FunctionSpace(mesh_f, "CG", parameters['deg_P'])
+
+ # Assigner between spaces
+ assigner_to_M = fn.FunctionAssigner(M, [U_, P_])
+ assigner_to_UP = fn.FunctionAssigner([U_, P_], M)
+
+ # Boundary expressions in the reference domain
+ u_inflow, u_outflow, u_bottom, u_top = exps_at_bdry(parameters, deformation)
+ # Define and mark boundaries
+ bdry_markers = fn.MeshFunction('size_t', mesh_f, mesh_f.topology().dim()-1)
+ inlet().mark(bdry_markers, 1) # Inlet marked with label 1
+ outlet().mark(bdry_markers, 2) # Outlet marked with label 2
+ bottom().mark(bdry_markers, 3) # Bottom marked with label 3
+ top().mark(bdry_markers, 4) # Top marked with label 4
+
+ # Define measures for weak formulation
+ dx_f = fn.Measure('dx', domain=mesh_f, subdomain_data=bdry_markers)
+ #ds_f = fn.Measure('ds', domain=mesh_f, subdomain_data=bdry_markers)
+
+ # Define boundary conditions with pressure condition to obtain uniqueness (case LU solver!)
+ bdries = [fn.DirichletBC(M.sub(0), u_inflow, bdry_markers, 1),
+ fn.DirichletBC(M.sub(0), u_outflow, bdry_markers, 2),
+ fn.DirichletBC(M.sub(0), u_bottom, bdry_markers, 3),
+ fn.DirichletBC(M.sub(0), u_top, bdry_markers, 4),
+ fn.DirichletBC(M.sub(1), fn.Constant(0.), "near(x[0], 0) && near(x[1], 0)", 'pointwise')]
+
+ # Trial/Test function definition
+ (u, p) = fn.TrialFunctions(M)
+ (v, q) = fn.TestFunctions(M)
+ aux_n = fn.Function(M, name='MixedSolution')
+ # Define initial condition (non-zero)
+ if parameters["init_cond"] == True:
+ print("Using a non-zero initial condition (2D-Gaussian) for the velocity field!")
+ cpp_aux = '0.001*(1 - pow(x[1], 2))*x[0]*(6 - x[0])'
+ aux_n.assign(fn.Expression((cpp_aux, '0.', '0.'), domain=mesh_f, degree=2))
+ u_n, _ = fn.split(aux_n)
+ else:
+ u_n, _ = fn.split(aux_n)
+
+ # Define normal for backflow stabilization term
+ #N = fn.FacetNormal(mesh_f)
+ # Compute its jacobians
+ J_n = J_(def_n)
+ J = J_(def_t)
+ # Define operators wrt to the reference domain
+ grad = lambda u: grad_(u, def_t)
+ sym_grad = lambda u: sym_grad_(u, def_t)
+ #inv_F = inv_F_(def_t)
+ div = lambda u: div_(u, def_t)
+ # Define domain velocity as a first order finite difference
+ w = (def_t - def_n)/tau
+
+ # All formulations contain GCL + Temam's stabilization term
+ if parameters['gcl_stab'] == True:
+ if parameters['jac_at_n'] == False:
+ print("Using time-derivative term approximated with Jacobian at n+1...")
+ F = fn.Constant(rho_f/tau)*J*fn.inner(u - u_n, v)*dx_f\
+ + fn.Constant(0.5*rho_f/tau)*(J - J_n)*fn.inner(u, v)*dx_f\
+ + fn.Constant(0.5*rho_f)*div(u_n - w)*fn.inner(u, v)*dx_f
+ else:
+ print("Using time-derivative term approximated with Jacobian at n...")
+ F = fn.Constant(rho_f/tau)*J_n*fn.inner(u - u_n, v)*dx_f\
+ + fn.Constant(0.5*rho_f/tau)*(J - J_n)*fn.inner(u, v)*dx_f\
+ + fn.Constant(0.5*rho_f)*div(u_n - w)*fn.inner(u, v)*dx_f
+ else:
+ raise Exception("Solver implemented only for cases with 'gcl_stab': True")
+
+ # Adding remaining term of the weak formulation
+ # The convective term is linearized!
+ F += fn.Constant(rho_f)*J*fn.dot(fn.dot(grad(u), u_n - w), v)*dx_f\
+ + fn.Constant(2*mu)*J*fn.inner(sym_grad(u), sym_grad(v))*dx_f\
+ - p*div(v)*dx_f + q*div(u)*dx_f
+
+ # Add stabilization when required
+ if stabilization['type'] == None:
+ pass
+ else:
+ raise Exception("Other stabilization not required for this monolithic test model!")
+
+ # Obtain lhs and rhs
+ a, L = fn.lhs(F), fn.rhs(F)
+ # Assemble lhs of the formulation
+ A = fn.PETScMatrix()
+ fn.assemble(a, tensor = A)
+ # Define Krylov solver for the problem
+ if solver_to_use == 'LU':
+ print("Using LU Solver...")
+ solver = fn.LUSolver()
+ solver.set_operator(A)
+ elif solver_to_use == 'Krylov':
+ krylov_method = 'gmres'#'minres', 'gmres', 'bicgstab'
+ precond = 'icc'#'ilu', 'icc', 'hypre_amg', 'amg'
+ print("Using Krylov Solver --> Method: {}, Precond: {}\n".format(krylov_method, precond))
+ solver = fn.PETScKrylovSolver(krylov_method, precond)
+ solver.set_operator(A)
+
+ # TODO: Remove the zero-mean space for pressure fields
+ # Create normalized vector that spans the pressure null space (P)
+ p_ = fn.Function(P_)
+ null_p_vec = fn.Vector(p_.vector())
+ P_.dofmap().set(null_p_vec, 1.0)
+ null_p_vec *= 1.0/null_p_vec.norm("l2")
+ p_.vector()[:] = null_p_vec
+ # Create zero-vector that spans M by Function assigning it
+ null_func = fn.Function(M)
+ u_ = fn.Function(U_)
+ assigner_to_M.assign(null_func, [u_, p_])
+ null_vec = fn.Vector(null_func.vector())
+ # Create null space basis object and attach to PETSc matrix
+ null_space = fn.VectorSpaceBasis([null_vec])
+ fn.as_backend_type(A).set_nullspace(null_space)
+
+ fn.PETScOptions.set("ksp_monitor")
+ #solver.parameters['monitor_convergence'] = True
+ solver.parameters['maximum_iterations'] = 300
+ solver.parameters['relative_tolerance'] = 1E-2
+ solver.parameters['absolute_tolerance'] = 1E-4
+
+ else:
+ raise Exception("Solver type not implemented, available choices: 'LU', 'Krylov'")
+
+ # Define nicely the output file to save!
+ base_name = "iNSE_ALE"
+ base_name += "_{}_{}".format(def_name[0], def_name[1])
+ base_name += "_P{}P{}_GCL_{}".format(parameters['deg_U'], parameters['deg_P'], parameters['gcl_stab'])
+
+ if stabilization['type'] == None:
+ filename = base_name + "_NoStab.xdmf"
+ else:
+ raise Exception("Other stabilizations not implemented!")
+ # Create XDMF file (It saves multiple fields)
+ file_output = fn.XDMFFile('tests/rectangle/'+filename)
+ file_output.parameters['functions_share_mesh'] = True
+
+ # Starts from dt, we take at 0 the initial solution
+ print("Starting iteration over time...")
+ saved_defs = []
+ saved_vels = []
+ saved_pres = []
+ # Depending on time step tau, output some results to user!
+ if tau == 0.1 and T <= 1: nb = 2
+ else: nb = 1
+ # Saving velocity and deformation fields at time t = 0.
+ u_n, _ = aux_n.split(deepcopy=True)
+ file_output.write(u_n, 0.0)
+ energy_assembled = fn.assemble(J_n*fn.inner(u_n, u_n)*dx_f)*0.5*rho_f/tau
+ print("E (Energy) of initial velocity field: {:.5f} at time {:2.3f}\n".format(energy_assembled, 0.0))
+ aux_ = fn.Function(M.sub(0).collapse(), name="Deformation")
+ aux_.assign(fn.project(def_n, M.sub(0).collapse()))
+ file_output.write(aux_, 0.0)
+ # Main iteration
+ for count, t in enumerate(np.arange(tau, T+tau, tau)):
+ # re-Assemble lhs vector
+ fn.assemble(a, tensor=A)
+ [bc.apply(A) for bc in bdries]
+ # Assemble rhs vector (changes over time)
+ b = fn.assemble(L)
+
+ # if Krylov solver is used, then ortogonalize also b
+ if solver_to_use == 'Krylov':
+ null_space.orthogonalize(b)
+
+ [bc.apply(b) for bc in bdries]
+
+ # Solve linear system and save solution
+ aux = fn.Function(M, name="MixedSolution")
+ num_iters = solver.solve(aux.vector(), b)
+ # Split and save velocity field
+ u, p = aux.split(deepcopy=True)
+ file_output.write(u, t)
+ # Saving computed
+ aux_ = fn.Function(M.sub(0).collapse(), name="Deformation")
+ aux_.assign(fn.project(def_t, M.sub(0).collapse()))
+ file_output.write(aux_, t)
+ # Print only a couple of solutions to the user!
+ if count % nb == 0:
+ J_assembled = fn.assemble(J*dx_f)
+ J_n_assembled = fn.assemble(J_n*dx_f)
+ def_assembled = fn.assemble(fn.dot(def_t, def_t)*dx_f)
+ #w_assembled = fn.assemble(fn.dot(w, w)*dx_f)
+ energy_assembled = fn.assemble(J*fn.inner(u, u)*dx_f)*0.5*rho_f/tau
+ energy_n_assembled = fn.assemble(J_n*fn.inner(u_n, u_n)*dx_f)*0.5*rho_f/tau
+ energy_strain_assembled = fn.assemble(J*fn.inner(sym_grad(u), sym_grad(u))*dx_f)*2*mu
+ if parameters['jac_at_n'] == False:
+ energy_var_assembled = fn.assemble(J*fn.inner(u - u_n, u - u_n)*dx_f)*0.5*rho_f/tau
+ else:
+ energy_var_assembled = fn.assemble(J_n*fn.inner(u - u_n, u - u_n)*dx_f)*0.5*rho_f/tau
+ delta_value = energy_assembled - energy_n_assembled + energy_strain_assembled + energy_var_assembled
+ # Give info to user
+ print("J integrated over the domain: {:.3f} at time: {:2.3f}".format(J_assembled, t))
+ print("J_n integrated over the domain: {:.3f} at time: {:2.3f}".format(J_n_assembled, t))
+ print("Well-posedness condition 3J - J_n > 0: {} at time {:2.3f}".format(3*J_assembled - J_n_assembled > 0, t))
+ print("d (def. map) integrated over the domain: {:.3f} at time: {:2.3f}".format(def_assembled, t))
+ #print("w (vel. map)integrated over the domain: {:.3f} at time: {:2.3f}".format(w_assembled, t))
+ print("Strain energy E( eps(|u|^2) ): {:.5f} at time {:2.3f}".format(energy_strain_assembled, t))
+ print("Residual of scheme -> 'delta' value: {:.5f} at time {:2.3f}\n".format(delta_value, t))
+ # Saving results for postprocessing
+ if solver_to_use == 'LU':
+ saved_vels.append((u, t, delta_value , energy_strain_assembled, energy_var_assembled))
+ else:
+ saved_vels.append((u, t, delta_value , energy_strain_assembled, energy_var_assembled, num_iters))
+
+ # Update velocity profile
+ aux_n.assign(aux)
+ u_n, _ = fn.split(aux_n)
+ # Updates deformation mapping
+ def_n.t = t
+ def_t.t = t+tau
+
+ # Number of elements used and total time
+ print("Number of degrees of freedom: {}".format(M.dim()))
+ print("Solution Computed in {:.5} seconds".format(time.time()-start))
+ return saved_defs, saved_vels, saved_pres
+
+
+def iNSE_CT_Solver(parameters, deformation, stabilization, solver_to_use='LU'):
+ """ This solver computes the incompressible Navier-Stokes (iNSE) problem in the ALE formalism.
+ To do so, the FEniCS framework is used and the convective term within iNSE is linealized.
+ To solve the problem, a Chorin-Temam scheme is employed with finite diferences for time
+ and FE for space.
+ The Chorin-Temam Scheme here is taken in the order: PPS_0 --> FVS_0 --> PPS_1 --> FVS_1...
+ ...
+
+ Input Parameters
+ ----------------
+ parameter: dict
+ dictionary containing several options for the scheme used.
+ deformation: dict
+ dictionary containing deformation mapping properties and options.
+ stabilization: dict
+ dictionary specifying stabilization used.
+
+
+ Output
+ ----------------
+ None.
+ The solver print the results to console, and returns None, saving solutions and figures.
+ """
+ # Starting time
+ start = time.time()
+ # Default parameters
+ mu, rho_f = parameters['mu'], parameters['rho_f']
+ Nx, Ny = parameters['Nx'], parameters['Ny']
+ tau, T = parameters['tau'], parameters['T']
+
+ def def_mesh_tuple(def_params: dict) -> tuple:
+ """
+ Computes a list (len 2) containing the parametrized mesh velocity.
+ ...
+
+ Input Parameters
+ ----------------
+ def_params: dict
+ dictionary with keys 'expression' and 'output_name'.
+
+ """
+ if 'expression' in def_params.keys():
+ if 'output_name' in def_params.keys():
+ output_name = def_params['output_name']
+ else:
+ output_name = ('X', 'Y')
+ return def_params['expression'], output_name
+ else:
+ raise Exception("Key 'expression' was not found in the dictionary!")
+
+ def exps_at_bdry(bdry_params: dict, def_params: dict) -> tuple:
+ """
+ Computes the boundary FEniCS expressions for this particular Dirichlet Homogeneous case.
+ """
+ u_inlet = fn.Constant((0.0, 0.0))
+ u_outlet = fn.Constant((0.0, 0.0))
+ u_bottom = fn.Constant((0.0, 0.0))
+ u_top = fn.Constant((0.0, 0.0))
+ return u_inlet, u_outlet, u_bottom, u_top
+
+ def corrected_vel(u, ut, p) -> fn.Function:
+ """
+ Computes the corrected velocity field within CT update scheme.
+ """
+ grad_p = fn.project(grad(p), U)
+ u.vector()[:] = ut.vector()[:] - (tau/rho_f)*grad_p.vector()[:]
+ return u
+
+ # Define boundary domain classes
+ class inlet(fn.SubDomain):
+ def inside(self, x, on_boundary):
+ return fn.near(x[0], 0) and on_boundary
+ class outlet(fn.SubDomain):
+ def inside(self, x, on_boundary):
+ return fn.near(x[0], 6) and on_boundary
+ class top(fn.SubDomain):
+ def inside(self, x, on_boundary):
+ return fn.near(x[1], 1) and on_boundary
+ class bottom(fn.SubDomain):
+ def inside(self, x, on_boundary):
+ return fn.near(x[1], -1) and on_boundary
+
+ # Define mesh object
+ mesh_f = fn.RectangleMesh(fn.Point(0, -1), fn.Point(6, 1), Nx, Ny)
+ #h = fn.CellDiameter(mesh_f)
+
+ # Obtain mesh deformation tuple and output name
+ def_tuple, def_name = def_mesh_tuple(deformation)
+
+ # Define displacement expressions at previous and actual time steps
+ def_n = fn.Expression(def_tuple, t=0.0, domain=mesh_f, degree=2)
+ def_t = fn.Expression(def_tuple, t=tau, domain=mesh_f, degree=2)
+
+ # Functional Spaces
+ U = fn.VectorFunctionSpace(mesh_f, "CG", parameters['deg_U'])
+ P = fn.FunctionSpace(mesh_f, "CG", parameters['deg_P'])
+
+ # Boundary expressions in the reference domain
+ u_inflow, u_outflow, u_bottom, u_top = exps_at_bdry(parameters, deformation)
+ # Define and mark boundaries
+ bdry_markers = fn.MeshFunction('size_t', mesh_f, mesh_f.topology().dim()-1)
+ inlet().mark(bdry_markers, 1) # Inlet marked with label 1
+ outlet().mark(bdry_markers, 2) # Outlet marked with label 2
+ bottom().mark(bdry_markers, 3) # Bottom marked with label 3
+ top().mark(bdry_markers, 4) # Top marked with label 4
+
+ # Define measures
+ dx_f = fn.Measure('dx', domain=mesh_f, subdomain_data=bdry_markers)
+ #ds_f = fn.Measure('ds', domain=mesh_f, subdomain_data=bdry_markers)
+
+ # Define boundary conditions with pressure condition to obtain uniqueness (case LU solver!)
+ bdries_u = [
+ fn.DirichletBC(U, u_inflow, bdry_markers, 1),
+ fn.DirichletBC(U, u_outflow, bdry_markers, 2),
+ fn.DirichletBC(U, u_bottom, bdry_markers, 3),
+ fn.DirichletBC(U, u_top, bdry_markers, 4)
+ ]
+ bdries_p = [
+ fn.DirichletBC(P, fn.Constant(0.), "near(x[0], 0) && near(x[1], 0)", 'pointwise')
+ ]
+
+ # Trial/Test function definition
+ ut, v = fn.TrialFunction(U), fn.TestFunction(U)
+ p, q = fn.TrialFunction(P), fn.TestFunction(P)
+ ut_n, p_n = fn.Function(U, name='T. Velocity'), fn.Function(P, name='Pressure')
+ #u, u_n = fn.Function(U, name='C. Velocity'), fn.Function(U, name='C. Velocity')
+ # Define initial condition (non-zero)
+ if parameters["init_cond"] == True:
+ print("Using a non-zero initial condition (2D-Gaussian) for the velocity field!")
+ cpp_aux = '0.001*(1 - pow(x[1], 2))*x[0]*(6 - x[0])'
+ ut_n.assign(fn.Expression((cpp_aux, '0.'), domain=mesh_f, degree=2))
+ else:
+ pass
+
+ # Define normal for backflow stabilization term
+ #N = fn.FacetNormal(mesh_f)
+ # Compute its jacobians
+ J_n = J_(def_n)
+ J = J_(def_t)
+ # Define operators wrt to the reference domain
+ grad = lambda u: grad_(u, def_t)
+ grad_n = lambda u: grad_(u, def_n)
+ sym_grad = lambda u: sym_grad_(u, def_t)
+ div = lambda u: div_(u, def_t)
+ div_n = lambda u: div_(u, def_n)
+ # Define domain velocity as a first order finite difference
+ w = (def_t - def_n)/tau
+
+ # (FVS) Step. Finding tentative velocity field
+ # The formulation has GCL+Temam Stabilization term
+ print("Defining forms associated to Chorin-Temam scheme...")
+ if parameters['gcl_stab'] == True:
+ if parameters['jac_at_n'] == False:
+ F_fvs = fn.Constant(rho_f/tau)*J*fn.inner(ut - ut_n, v)*dx_f\
+ + fn.Constant(0.5*rho_f/tau)*(J - J_n)*fn.inner(ut, v)*dx_f\
+ + fn.Constant(0.5*rho_f)*div(ut_n - w)*fn.inner(ut, v)*dx_f
+ else:
+ F_fvs = fn.Constant(rho_f/tau)*J_n*fn.inner(ut - ut_n, v)*dx_f\
+ + fn.Constant(0.5*rho_f/tau)*(J - J_n)*fn.inner(ut, v)*dx_f\
+ + fn.Constant(0.5*rho_f)*div(ut_n - w)*fn.inner(ut, v)*dx_f
+ else:
+ raise Exception("Solver implemented only for cases with 'gcl_stab': True")
+
+ # Adding remaining term of the weak formulation
+ # The convective term is linearized!
+ F_fvs += fn.Constant(rho_f)*J*fn.dot(fn.dot(grad(ut), ut_n - w), v)*dx_f\
+ + fn.Constant(2*mu)*J*fn.inner(sym_grad(ut), sym_grad(v))*dx_f\
+ - p_n*div_n(v)*dx_f
+
+ # Add stabilization when required
+ if stabilization['type'] == None:
+ pass
+ else:
+ raise Exception("Other stabilization not required for this CT test scheme!")
+
+ # (PPS) Step. Projecting into the div-free solution space
+ ut_pps = fn.Function(U) # Define tentative vel. object for pps form
+ F_pps = fn.Constant(tau/rho_f)*J_n*fn.inner(grad_n(p), grad_n(q))*dx_f\
+ + div_n(ut_pps)*q*dx_f
+
+ # Obtain lhs and rhs
+ a_fvs, L_fvs = fn.lhs(F_fvs), fn.rhs(F_fvs)
+ a_pps, L_pps = fn.lhs(F_pps), fn.rhs(F_pps)
+ # Assemble lhs of the formulation
+ A_fvs = fn.PETScMatrix()
+ A_pps = fn.PETScMatrix()
+ fn.assemble(a_fvs, tensor = A_fvs)
+ fn.assemble(a_pps, tensor = A_pps)
+
+ # Define Krylov solver for the problem
+ # With 'Krylov' using 'gmres'+'ilu' the solver works smoothly
+ if solver_to_use == 'LU':
+ print("Using LU Solver...")
+ solver_fvs = fn.LUSolver()
+ solver_pps = fn.LUSolver()
+ [solver.set_operator(A) for solver, A in zip([solver_fvs, solver_pps], [A_fvs, A_pps])]
+ elif solver_to_use == 'Krylov':
+ krylov_method = 'gmres'#'minres', 'gmres', 'bicgstab'
+ precond = 'amg'#'ilu', 'icc', 'hypre_amg', 'petsc_amg'
+ print("Using Krylov Solver --> Method: {}, Precond: {}\n".format(krylov_method, precond))
+ solver_fvs = fn.PETScKrylovSolver(krylov_method, precond)
+ solver_pps = fn.PETScKrylovSolver(krylov_method, precond)
+ for solver, A in zip([solver_fvs, solver_pps], [A_fvs, A_pps]):
+ solver.set_operator(A)
+ solver.parameters['report'] = True
+ #solver.parameters['monitor_convergence'] = True
+ solver.parameters['maximum_iterations'] = 2000
+ solver.parameters['relative_tolerance'] = 1E-4
+ solver.parameters['absolute_tolerance'] = 1E-7
+ #solver.parameters.str(True)
+ else:
+ raise Exception("Solver type not implemented, available choices: 'LU', 'Krylov'")
+
+ # Define nicely the output file to save!
+ base_name = "iNSE_ALE_CT"
+ base_name += "_{}_{}".format(def_name[0], def_name[1])
+ base_name += "_P{}P{}_GCL_{}".format(parameters['deg_U'], parameters['deg_P'], parameters['gcl_stab'])
+
+ if stabilization['type'] == None:
+ filename = base_name + "_NoStab.xdmf"
+ else:
+ raise Exception("Other stabilizations not implemented!")
+ # Create XDMF file (It saves multiple fields)
+ file_output = fn.XDMFFile('tests/rectangle/'+filename)
+ file_output.parameters['functions_share_mesh'] = True
+
+ # Starts from dt, we take at 0 the initial solution
+ print("Starting iteration over time...")
+ saved_defs = []
+ saved_vels = []
+ saved_pres = []
+ # Depending on time step tau, save and export some solutions
+ if tau == 0.1 and T <= 1: nb = 2
+ else: nb = 1
+
+ ##-----Saving deformation field at time t = 0-----##
+ aux_ = fn.Function(U, name="Deformation")
+ aux_.assign(fn.project(def_n, U))
+ file_output.write(aux_, 0.0)
+ # Saving velocity (t., div-free) and pressure fields
+ # by solving an initial PPS
+ fn.assemble(a_pps, tensor=A_pps)
+ [bc.apply(A_pps) for bc in bdries_p]
+ # Assemble rhs (changes over time)
+ b_pps = fn.assemble(L_pps)
+ [bc.apply(b_pps) for bc in bdries_p]
+ # Solve linear system
+ p = fn.Function(P, name='Pressure')
+ num_iters_pps = solver_pps.solve(p.vector(), b_pps)
+ file_output.write(p, 0.0)
+ # Compute and save updated (t.) velocity
+ corrected_vel(ut_n, ut_n, p)
+ file_output.write(ut_n, 0.0)
+ #corrected_vel(u_n, ut_n, p_n)
+ #file_output.write(u_n, 0.0)
+ energy_assembled = fn.assemble(J_n*fn.inner(ut_n, ut_n)*dx_f)*0.5*rho_f/tau
+ print("E (Energy) of initial t. velocity: {:.5f} at time {:2.3f}\n".format(energy_assembled, 0.0))
+ ## -------------------------------------------- ##
+ ## ----------------Main iteration---------------##
+ for count, t in enumerate(np.arange(tau, T+tau, tau)):
+ # (PPS) Pressure-Projection Step
+ # Update t. velocity
+ ut_pps.assign(ut_n)
+ # Assemble lhs
+ fn.assemble(a_pps, tensor=A_pps)
+ [bc.apply(A_pps) for bc in bdries_p]
+ # Assemble rhs (changes over time)
+ b_pps = fn.assemble(L_pps)
+ [bc.apply(b_pps) for bc in bdries_p]
+ # Solve linear system
+ p = fn.Function(P, name='Pressure')
+ num_iters_pps = solver_pps.solve(p.vector(), b_pps)
+ # Save pressure
+ file_output.write(p, t)
+
+ # (FVS) Fluid-Viscous Step
+ # Update pressure
+ p_n.assign(p)
+ # re-Assemble lhs vector
+ fn.assemble(a_fvs, tensor=A_fvs)
+ [bc.apply(A_fvs) for bc in bdries_u]
+ # Assemble rhs vector (changes over time)
+ b_fvs = fn.assemble(L_fvs)
+ [bc.apply(b_fvs) for bc in bdries_u]
+ # Solve linear system and save solution
+ ut = fn.Function(U, name='T. Velocity')
+ num_iters_fvs = solver_fvs.solve(ut.vector(), b_fvs)
+
+ # (CVS) Computation Corrected Velocity (Optional)
+ #corrected_vel(u, ut, p)
+
+ # Save deformation (proj. into U)
+ aux_ = fn.Function(U, name="Deformation")
+ aux_.assign(fn.project(def_t, U))
+ file_output.write(aux_, t)
+ # Save t. velocity
+ file_output.write(ut, t)
+ #file_output.write(u, t)
+
+ # Print and save solutions to the user!
+ if count % nb == 0:
+ J_assembled = fn.assemble(J*dx_f)
+ J_n_assembled = fn.assemble(J_n*dx_f)
+ def_assembled = fn.assemble(fn.dot(def_t, def_t)*dx_f)
+ #w_assembled = fn.assemble(fn.dot(w, w)*dx_f)
+ energy_assembled = fn.assemble(J*fn.inner(ut, ut)*dx_f)*0.5*rho_f/tau
+ energy_n_assembled = fn.assemble(J_n*fn.inner(ut_n, ut_n)*dx_f)*0.5*rho_f/tau
+ energy_strain_assembled = fn.assemble(J*fn.inner(sym_grad(ut), sym_grad(ut))*dx_f)*2*mu
+ pres_assembled = fn.assemble(J_n*fn.inner(grad_n(p), grad_n(p))*dx_f)*0.5*tau/rho_f
+ delta_value = energy_assembled - energy_n_assembled + energy_strain_assembled + pres_assembled
+ if parameters['jac_at_n'] == False:
+ energy_var_assembled = fn.assemble(J*fn.inner(ut - ut_n, ut - ut_n)*dx_f)*0.5*rho_f/tau
+ else:
+ energy_var_assembled = fn.assemble(J_n*fn.inner(ut - ut_n, ut - ut_n)*dx_f)*0.5*rho_f/tau
+ # Providing info to user
+ print("J integrated over the domain: {:.3f} at time: {:2.3f}".format(J_assembled, t))
+ print("J_n integrated over the domain: {:.3f} at time: {:2.3f}".format(J_n_assembled, t))
+ print("Well-posedness condition 3J - J_n > 0: {} at time {:2.3f}".format(3*J_assembled - J_n_assembled > 0, t))
+ print("d (def. map) integrated over the domain: {:.3f} at time: {:2.3f}".format(def_assembled, t))
+ #print("w (vel. map)integrated over the domain: {:.3f} at time: {:2.3f}".format(w_assembled, t))
+ print("Strain energy E( eps(|u|^2) ): {:.5f} at time {:2.3f}".format(energy_strain_assembled, t))
+ print("Residual of scheme -> 'delta' value: {:.5f} at time {:2.3f}\n".format(delta_value, t))
+ # Saving results
+ if solver_to_use == 'LU':
+ saved_vels.append((ut, t, delta_value, energy_strain_assembled, energy_var_assembled))
+ else:
+ saved_vels.append((ut, t, delta_value, energy_strain_assembled, energy_var_assembled, num_iters_fvs, num_iters_pps))
+
+ # Update t. velocity
+ ut_n.assign(ut)
+ #u_n.assign(u)
+ # Updates deformation mapping
+ def_n.t = t
+ def_t.t = t+tau
+
+ # Number of elements used and total time
+ print("DoF for Velocity Space (U): {}".format(U.dim()))
+ print("DoF for Pressure Space (P): {}".format(P.dim()))
+ print("Solution Computed in {:.5} seconds".format(time.time()-start))
+ return saved_defs, saved_vels, saved_pres
+
+def testing_comparative_plots(dict_fields_mt: dict, dict_fields_ct: dict, *args) -> None:
+ """
+ Computes error figures between the schemes with Jacobian evaluation at times {n, n+1}, i.e.
+ with explicit and implicit treatment of the time-derivative term.
+ ...
+
+ Input Parameters
+ ----------------
+ dict_fields_mt : tuple -> (dict, dict, dict)
+ tuple containing dictionaries of fields (def, vel, pre) from the iNSE ALE Monolithic solver.
+
+ dict_fields_ct : tupel -> (dict, dict, dict)
+ tuple containing dictionaries of fields (def, vel, pre) from the iNSE ALE CT solver.
+ """
+ print("\nComputing error figures for both schemes...\n")
+ # Creates dictionaries for "expanding" and "contracting" functions
+ # Time dictionary
+ time_list = {
+ 'MT': {jac_name: [] for jac_name in dict_fields_mt.keys()},
+ 'CT': {jac_name: [] for jac_name in dict_fields_ct.keys()}
+ }
+ # Numerical dissipation dictionary --> int (| J^{n+1} u^{n+1} - J^{n} u^{n} |)
+ dis_value_exp = {
+ 'MT': {jac_name: [] for jac_name in dict_fields_mt.keys()},
+ 'CT': {jac_name: [] for jac_name in dict_fields_ct.keys()}
+ }
+ dis_value_con = {
+ 'MT': {jac_name: [] for jac_name in dict_fields_mt.keys()},
+ 'CT': {jac_name: [] for jac_name in dict_fields_ct.keys()}
+ }
+ # Physical dissipation dictionary --> int ( 2*mu* | eps(u) |^2 )
+ eps_value_exp = {
+ 'MT': {jac_name: [] for jac_name in dict_fields_mt.keys()},
+ 'CT': {jac_name: [] for jac_name in dict_fields_ct.keys()}
+ }
+ eps_value_con = {
+ 'MT': {jac_name: [] for jac_name in dict_fields_mt.keys()},
+ 'CT': {jac_name: [] for jac_name in dict_fields_ct.keys()}
+ }
+ # 'delta' values dictionary
+ delta_value_exp = {
+ 'MT': {jac_name: [] for jac_name in dict_fields_mt.keys()},
+ 'CT': {jac_name: [] for jac_name in dict_fields_ct.keys()}
+ }
+ delta_value_con = {
+ 'MT': {jac_name: [] for jac_name in dict_fields_mt.keys()},
+ 'CT': {jac_name: [] for jac_name in dict_fields_ct.keys()}
+ }
+ # Normalized 'delta' values dictionary (w.r.t physical dissipation)
+ delta_hat_value_exp = {
+ 'MT': {jac_name: [] for jac_name in dict_fields_mt.keys()},
+ 'CT': {jac_name: [] for jac_name in dict_fields_ct.keys()}
+ }
+ delta_hat_value_con = {
+ 'MT': {jac_name: [] for jac_name in dict_fields_mt.keys()},
+ 'CT': {jac_name: [] for jac_name in dict_fields_ct.keys()}
+ }
+ # Normalized 'delta' values dictionary (w.r.t numerical dissipation)
+ delta_hat_dis_exp = {
+ 'MT': {jac_name: [] for jac_name in dict_fields_mt.keys()},
+ 'CT': {jac_name: [] for jac_name in dict_fields_ct.keys()}
+ }
+ delta_hat_dis_con = {
+ 'MT': {jac_name: [] for jac_name in dict_fields_mt.keys()},
+ 'CT': {jac_name: [] for jac_name in dict_fields_ct.keys()}
+ }
+ # Iterate over the different cases in MT (Monolithic) and CT (Chorin-Temam) schemes
+ for scheme in ['MT', 'CT']: # 'MT', 'CT'
+ if scheme == 'MT':
+ dict_fields = dict_fields_mt
+ else:
+ dict_fields = dict_fields_ct
+ # Iterate over different cases 'j_implicit', 'j_explicit'
+ for jac_name in dict_fields.keys():
+ dict_vel = dict_fields[jac_name][1]
+ for i in range(len(dict_vel['High_Osc_exp'])):
+ # Saving time steps
+ time_list[scheme][jac_name].append(dict_vel['High_Osc_exp'][i][1])
+ # Add 'delta' values
+ delta_value_exp[scheme][jac_name].append(dict_vel['High_Osc_exp'][i][2])
+ delta_value_con[scheme][jac_name].append(dict_vel['High_Osc_con'][i][2])
+ # Add physical dissipation
+ eps_value_exp[scheme][jac_name].append(dict_vel['High_Osc_exp'][i][3])
+ eps_value_con[scheme][jac_name].append(dict_vel['High_Osc_con'][i][3])
+ # Add numerical dissipation
+ dis_value_exp[scheme][jac_name].append(dict_vel['High_Osc_exp'][i][4])
+ dis_value_con[scheme][jac_name].append(dict_vel['High_Osc_con'][i][4])
+ # Compute normalized 'delta' values w.r.t the physical dissipation
+ delta_hat_value_exp[scheme][jac_name].append(dict_vel['High_Osc_exp'][i][2]/dict_vel['High_Osc_exp'][i][3])
+ delta_hat_value_con[scheme][jac_name].append(dict_vel['High_Osc_con'][i][2]/dict_vel['High_Osc_con'][i][3])
+ # Compute normalized 'delta' values w.r.t the numerical dissipation
+ delta_hat_dis_exp[scheme][jac_name].append(dict_vel['High_Osc_exp'][i][2]/dict_vel['High_Osc_exp'][i][4])
+ delta_hat_dis_con[scheme][jac_name].append(dict_vel['High_Osc_con'][i][2]/dict_vel['High_Osc_con'][i][4])
+
+ # Auxiliary indexes for plotting
+ # TODO: Test this line and automatize the "100"!
+ init = 0
+ out = 101 #len(time_list['CT']['j_implicit']) # at tau = 0.01, T = 2 --> 200 time steps
+
+ # ---------------------- #
+ # DELTA VALUE CASE
+ # ---------------------- #
+ # CASE CT
+ plt.subplots(figsize=(10, 4))
+ # Top
+ lf_ax = plt.subplot(1, 2, 2)
+ lf_j_exp, = lf_ax.plot(time_list['CT']['j_explicit'][init:out], delta_value_exp['CT']['j_explicit'][init:out], color='blue', ls='--')
+ lf_j_imp, = lf_ax.plot(time_list['CT']['j_implicit'][init:out], delta_value_exp['CT']['j_implicit'][init:out], color='blue')
+ lf_ax.set_xlabel(r"Simulation time [t]")
+ lf_ax.set_ylabel(r"$\delta_{CT}$ def. I", color='blue')
+ lf_ax.set_title(r"Residual Energy $\delta_{CT}$")
+ lf_ax.tick_params(axis='y', labelcolor='blue')
+ lf_ax.ticklabel_format(style='sci', axis='y', scilimits=(0,0))
+ rh_ax = lf_ax.twinx()
+ rh_j_exp, = rh_ax.plot(time_list['CT']['j_explicit'][init:out], delta_value_con['CT']['j_explicit'][init:out], color='red', ls='--')
+ rh_j_imp, = rh_ax.plot(time_list['CT']['j_implicit'][init:out], delta_value_con['CT']['j_implicit'][init:out], color='red')
+ rh_ax.set_ylabel(r"$\delta_{CT}$ def. II", color='red')
+ rh_ax.tick_params(axis='y', labelcolor='red')
+ rh_ax.ticklabel_format(style='sci', axis='y', scilimits=(0,0))
+ plt.legend((lf_j_exp, lf_j_imp, rh_j_exp, rh_j_imp), \
+ (r'CT $\star\star = n$', r'CT $\star\star = n+1$', r'CT $\star\star = n$', r'CT $\star\star = n+1$'), loc='center right')
+ plt.grid(True)
+ # CASE M
+ # Bottom
+ lf_ax = plt.subplot(1, 2, 1)
+ lf_j_exp, = lf_ax.plot(time_list['MT']['j_explicit'][init:out], delta_value_exp['MT']['j_explicit'][init:out], color='blue', ls='--')
+ lf_j_imp, = lf_ax.plot(time_list['MT']['j_implicit'][init:out], delta_value_exp['MT']['j_implicit'][init:out], color='blue')
+ lf_ax.set_xlabel(r"Simulation time [t]")
+ lf_ax.set_ylabel(r"$\delta_{M}$ def. I", color='blue')
+ lf_ax.set_title(r"Residual Energy $\delta_{M}$")
+ lf_ax.tick_params(axis='y', labelcolor='blue')
+ lf_ax.ticklabel_format(style='sci', axis='y', scilimits=(0,0))
+ rh_ax = lf_ax.twinx()
+ rh_j_exp, = rh_ax.plot(time_list['MT']['j_explicit'][init:out], delta_value_con['MT']['j_explicit'][init:out], color='red', ls='--')
+ rh_j_imp, = rh_ax.plot(time_list['MT']['j_implicit'][init:out], delta_value_con['MT']['j_implicit'][init:out], color='red')
+ rh_ax.set_ylabel(r"$\delta_{M}$ def. II", color='red')
+ rh_ax.tick_params(axis='y', labelcolor='red')
+ rh_ax.ticklabel_format(style='sci', axis='y', scilimits=(0,0))
+ plt.legend((lf_j_exp, lf_j_imp, rh_j_exp, rh_j_imp), \
+ (r'M $\star\star = n$', r'M $\star\star = n+1$', r'M $\star\star = n$', r'M $\star\star = n+1$'), loc='center right')
+ plt.grid(True)
+ plt.subplots_adjust(hspace=0.8)
+ plt.tight_layout()
+ plt.savefig('Comparison_Delta_Value_GCL_{}_Solver_{}.png'.format(args[0], args[1]), dpi=300)
+ plt.close()
+
+ # ---------------------- #
+ # NORMALIZED DELTA CASE (w.r.t physical dissipation)
+ # ---------------------- #
+ plt.subplots(figsize=(10, 4))
+ # CASE CT
+ # Top
+ lf_ax = plt.subplot(1, 2, 2)
+ lf_j_exp, = lf_ax.plot(time_list['CT']['j_explicit'][init:out], delta_hat_value_exp['CT']['j_explicit'][init:out], color='blue', ls='--')
+ lf_j_imp, = lf_ax.plot(time_list['CT']['j_implicit'][init:out], delta_hat_value_exp['CT']['j_implicit'][init:out], color='blue')
+ lf_ax.set_xlabel(r"Simulation time [t]")
+ lf_ax.set_ylabel(r"$\hat{\delta}_{CT}$ def. I", color='blue')
+ lf_ax.set_title(r"Normalized value $\hat{\delta}_{CT}$")
+ lf_ax.tick_params(axis='y', labelcolor='blue')
+ lf_ax.ticklabel_format(style='sci', axis='y', scilimits=(0,0))
+ rh_ax = lf_ax.twinx()
+ rh_j_exp, = rh_ax.plot(time_list['CT']['j_explicit'][init:out], delta_hat_value_con['CT']['j_explicit'][init:out], color='red', ls='--')
+ rh_j_imp, = rh_ax.plot(time_list['CT']['j_implicit'][init:out], delta_hat_value_con['CT']['j_implicit'][init:out], color='red')
+ rh_ax.set_ylabel(r"$\hat{\delta}_{CT}$ def. II", color='red')
+ rh_ax.tick_params(axis='y', labelcolor='red')
+ rh_ax.ticklabel_format(style='sci', axis='y', scilimits=(0,0))
+ plt.legend((lf_j_exp, lf_j_imp, rh_j_exp, rh_j_imp), \
+ (r'CT $\star\star = n$', r'CT $\star\star = n+1$', r'CT $\star\star = n$', r'CT $\star\star = n+1$'), loc='lower right')
+ plt.grid(True)
+ # CASE M
+ # Bottom
+ lf_ax = plt.subplot(1, 2, 1)
+ lf_j_exp, = lf_ax.plot(time_list['MT']['j_explicit'][init:out], delta_hat_value_exp['MT']['j_explicit'][init:out], color='blue', ls='--')
+ lf_j_imp, = lf_ax.plot(time_list['MT']['j_implicit'][init:out], delta_hat_value_exp['MT']['j_implicit'][init:out], color='blue')
+ lf_ax.set_xlabel(r"Simulation time [t]")
+ lf_ax.set_ylabel(r"$\hat{\delta}_{M}$ def. I", color='blue')
+ lf_ax.set_title(r"Normalized value $\hat{\delta}_{M}$")
+ lf_ax.tick_params(axis='y', labelcolor='blue')
+ lf_ax.ticklabel_format(style='sci', axis='y', scilimits=(0,0))
+ rh_ax = lf_ax.twinx()
+ rh_j_exp, = rh_ax.plot(time_list['MT']['j_explicit'][init:out], delta_hat_value_con['MT']['j_explicit'][init:out], color='red', ls='--')
+ rh_j_imp, = rh_ax.plot(time_list['MT']['j_implicit'][init:out], delta_hat_value_con['MT']['j_implicit'][init:out], color='red')
+ rh_ax.set_ylabel(r"$\hat{\delta}_{M}$ def. II", color='red')
+ rh_ax.tick_params(axis='y', labelcolor='red')
+ rh_ax.ticklabel_format(style='sci', axis='y', scilimits=(0,0))
+ plt.legend((lf_j_exp, lf_j_imp, rh_j_exp, rh_j_imp), \
+ (r'M $\star\star = n$', r'M $\star\star = n+1$', r'M $\star\star = n$', r'M $\star\star = n+1$'), loc='upper right')
+ plt.grid(True)
+ plt.subplots_adjust(hspace=0.8)
+ plt.tight_layout()
+ plt.savefig('Comparison_Delta_Hat_Value_GCL_{}_solver_{}.png'.format(args[0], args[1]), dpi=300)
+ plt.close()
+
+ # ---------------------- #
+ # NORMALIZED DELTA CASE (w.r.t numerical dissipation)
+ # ---------------------- #
+ plt.subplots(figsize=(10, 4))
+ # CASE CT
+ # Top
+ lf_ax = plt.subplot(1, 2, 2)
+ lf_j_exp, = lf_ax.plot(time_list['CT']['j_explicit'][init:out], delta_hat_dis_exp['CT']['j_explicit'][init:out], color='blue', ls='--')
+ lf_j_imp, = lf_ax.plot(time_list['CT']['j_implicit'][init:out], delta_hat_dis_exp['CT']['j_implicit'][init:out], color='blue')
+ lf_ax.set_xlabel(r"Simulation time [t]")
+ lf_ax.set_ylabel(r"$\hat{\delta}_{CT}$ dis. def. I", color='blue')
+ lf_ax.set_title(r"Normalized value $\hat{\delta}_{CT}$ (dis)")
+ lf_ax.tick_params(axis='y', labelcolor='blue')
+ lf_ax.ticklabel_format(style='sci', axis='y', scilimits=(0,0))
+ rh_ax = lf_ax.twinx()
+ rh_j_exp, = rh_ax.plot(time_list['CT']['j_explicit'][init:out], delta_hat_dis_con['CT']['j_explicit'][init:out], color='red', ls='--')
+ rh_j_imp, = rh_ax.plot(time_list['CT']['j_implicit'][init:out], delta_hat_dis_con['CT']['j_implicit'][init:out], color='red')
+ rh_ax.set_ylabel(r"$\hat{\delta}_{CT}$ def. II", color='red')
+ rh_ax.tick_params(axis='y', labelcolor='red')
+ rh_ax.ticklabel_format(style='sci', axis='y', scilimits=(0,0))
+ plt.legend((lf_j_exp, lf_j_imp, rh_j_exp, rh_j_imp), \
+ (r'CT $\star\star = n$', r'CT $\star\star = n+1$', r'CT $\star\star = n$', r'CT $\star\star = n+1$'), loc='lower right')
+ plt.grid(True)
+ # CASE M
+ # Bottom
+ lf_ax = plt.subplot(1, 2, 1)
+ lf_j_exp, = lf_ax.plot(time_list['MT']['j_explicit'][init:out], delta_hat_dis_exp['MT']['j_explicit'][init:out], color='blue', ls='--')
+ lf_j_imp, = lf_ax.plot(time_list['MT']['j_implicit'][init:out], delta_hat_dis_exp['MT']['j_implicit'][init:out], color='blue')
+ lf_ax.set_xlabel(r"Simulation time [t]")
+ lf_ax.set_ylabel(r"$\hat{\delta}_{M}$ dis. def. I", color='blue')
+ lf_ax.set_title(r"Normalized value $\hat{\delta}_{M}$ (dis)")
+ lf_ax.tick_params(axis='y', labelcolor='blue')
+ lf_ax.ticklabel_format(style='sci', axis='y', scilimits=(0,0))
+ rh_ax = lf_ax.twinx()
+ rh_j_exp, = rh_ax.plot(time_list['MT']['j_explicit'][init:out], delta_hat_dis_con['MT']['j_explicit'][init:out], color='red', ls='--')
+ rh_j_imp, = rh_ax.plot(time_list['MT']['j_implicit'][init:out], delta_hat_dis_con['MT']['j_implicit'][init:out], color='red')
+ rh_ax.set_ylabel(r"$\hat{\delta}_{M}$ def. II", color='red')
+ rh_ax.tick_params(axis='y', labelcolor='red')
+ rh_ax.ticklabel_format(style='sci', axis='y', scilimits=(0,0))
+ plt.legend((lf_j_exp, lf_j_imp, rh_j_exp, rh_j_imp), \
+ (r'M $\star\star = n$', r'M $\star\star = n+1$', r'M $\star\star = n$', r'M $\star\star = n+1$'), loc='lower right')
+ plt.grid(True)
+ plt.subplots_adjust(hspace=0.8)
+ plt.tight_layout()
+ plt.savefig('Comparison_Delta_Hat_Dis_Value_GCL_{}_solver_{}.png'.format(args[0], args[1]), dpi=300)
+ plt.close()
+
+ # ---------------------- #
+ # PHYSICAL DISSIPATION PLOT
+ # ---------------------- #
+ plt.subplots(figsize=(10, 4))
+ # CASE CT
+ # Top
+ lf_ax = plt.subplot(1, 2, 2)
+ lf_j_exp, = lf_ax.plot(time_list['CT']['j_explicit'][init:out], eps_value_exp['CT']['j_explicit'][init:out], color='blue', ls='--')
+ lf_j_imp, = lf_ax.plot(time_list['CT']['j_implicit'][init:out], eps_value_exp['CT']['j_implicit'][init:out], color='blue')
+ lf_ax.set_xlabel(r"Simulation time [t]")
+ lf_ax.set_ylabel(r"On def. I", color='blue')
+ lf_ax.set_title(r"Physical Dissipation (CT)")
+ lf_ax.tick_params(axis='y', labelcolor='blue')
+ lf_ax.ticklabel_format(style='sci', axis='y', scilimits=(0,0))
+ rh_ax = lf_ax.twinx()
+ rh_j_exp, = rh_ax.plot(time_list['CT']['j_explicit'][init:out], eps_value_con['CT']['j_explicit'][init:out], color='red', ls='--')
+ rh_j_imp, = rh_ax.plot(time_list['CT']['j_implicit'][init:out], eps_value_con['CT']['j_implicit'][init:out], color='red')
+ rh_ax.set_ylabel(r"On def. II", color='red')
+ rh_ax.tick_params(axis='y', labelcolor='red')
+ rh_ax.ticklabel_format(style='sci', axis='y', scilimits=(0,0))
+ plt.legend((lf_j_exp, lf_j_imp, rh_j_exp, rh_j_imp), \
+ (r'CT $\star\star = n$', r'CT $\star\star = n+1$', r'CT $\star\star = n$', r'CT $\star\star = n+1$'), loc='lower right')
+ plt.grid(True)
+ # CASE M
+ # Bottom
+ lf_ax = plt.subplot(1, 2, 1)
+ lf_j_exp, = lf_ax.plot(time_list['MT']['j_explicit'][init:out], eps_value_exp['MT']['j_explicit'][init:out], color='blue', ls='--')
+ lf_j_imp, = lf_ax.plot(time_list['MT']['j_implicit'][init:out], eps_value_exp['MT']['j_implicit'][init:out], color='blue')
+ lf_ax.set_xlabel(r"Simulation time [t]")
+ lf_ax.set_ylabel(r"On dis. def. I", color='blue')
+ lf_ax.set_title(r"Physical Dissipation (M)")
+ lf_ax.tick_params(axis='y', labelcolor='blue')
+ lf_ax.ticklabel_format(style='sci', axis='y', scilimits=(0,0))
+ rh_ax = lf_ax.twinx()
+ rh_j_exp, = rh_ax.plot(time_list['MT']['j_explicit'][init:out], eps_value_con['MT']['j_explicit'][init:out], color='red', ls='--')
+ rh_j_imp, = rh_ax.plot(time_list['MT']['j_implicit'][init:out], eps_value_con['MT']['j_implicit'][init:out], color='red')
+ rh_ax.set_ylabel(r"On def. II", color='red')
+ rh_ax.tick_params(axis='y', labelcolor='red')
+ rh_ax.ticklabel_format(style='sci', axis='y', scilimits=(0,0))
+ plt.legend((lf_j_exp, lf_j_imp, rh_j_exp, rh_j_imp), \
+ (r'M $\star\star = n$', r'M $\star\star = n+1$', r'M $\star\star = n$', r'M $\star\star = n+1$'), loc='lower right')
+ plt.grid(True)
+ plt.subplots_adjust(hspace=0.8)
+ plt.tight_layout()
+ plt.savefig('Comparison_Eps_Value_GCL_{}_solver_{}.png'.format(args[0], args[1]), dpi=300)
+ plt.close()
+
+ # ---------------------- #
+ # NUMERICAL DISSIPATION PLOT
+ # ---------------------- #
+ plt.subplots(figsize=(10, 4))
+ # CASE CT
+ # Top
+ lf_ax = plt.subplot(1, 2, 2)
+ lf_j_exp, = lf_ax.plot(time_list['CT']['j_explicit'][init:out], dis_value_exp['CT']['j_explicit'][init:out], color='blue', ls='--')
+ lf_j_imp, = lf_ax.plot(time_list['CT']['j_implicit'][init:out], dis_value_exp['CT']['j_implicit'][init:out], color='blue')
+ lf_ax.set_xlabel(r"Simulation time [t]")
+ lf_ax.set_ylabel(r"On def. I", color='blue')
+ lf_ax.set_title(r"Numerical Dissipation (CT)")
+ lf_ax.tick_params(axis='y', labelcolor='blue')
+ lf_ax.ticklabel_format(style='sci', axis='y', scilimits=(0,0))
+ rh_ax = lf_ax.twinx()
+ rh_j_exp, = rh_ax.plot(time_list['CT']['j_explicit'][init:out], dis_value_con['CT']['j_explicit'][init:out], color='red', ls='--')
+ rh_j_imp, = rh_ax.plot(time_list['CT']['j_implicit'][init:out], dis_value_con['CT']['j_implicit'][init:out], color='red')
+ rh_ax.set_ylabel(r"On def. II", color='red')
+ rh_ax.tick_params(axis='y', labelcolor='red')
+ rh_ax.ticklabel_format(style='sci', axis='y', scilimits=(0,0))
+ plt.legend((lf_j_exp, lf_j_imp, rh_j_exp, rh_j_imp), \
+ (r'CT $\star\star = n$', r'CT $\star\star = n+1$', r'CT $\star\star = n$', r'CT $\star\star = n+1$'), loc='lower right')
+ plt.grid(True)
+ # CASE M
+ # Bottom
+ lf_ax = plt.subplot(1, 2, 1)
+ lf_j_exp, = lf_ax.plot(time_list['MT']['j_explicit'][init:out], dis_value_exp['MT']['j_explicit'][init:out], color='blue', ls='--')
+ lf_j_imp, = lf_ax.plot(time_list['MT']['j_implicit'][init:out], dis_value_exp['MT']['j_implicit'][init:out], color='blue')
+ lf_ax.set_xlabel(r"Simulation time [t]")
+ lf_ax.set_ylabel(r"On def. I", color='blue')
+ lf_ax.set_title(r"Numerical Dissipation (M)")
+ lf_ax.tick_params(axis='y', labelcolor='blue')
+ lf_ax.ticklabel_format(style='sci', axis='y', scilimits=(0,0))
+ rh_ax = lf_ax.twinx()
+ rh_j_exp, = rh_ax.plot(time_list['MT']['j_explicit'][init:out], dis_value_con['MT']['j_explicit'][init:out], color='red', ls='--')
+ rh_j_imp, = rh_ax.plot(time_list['MT']['j_implicit'][init:out], dis_value_con['MT']['j_implicit'][init:out], color='red')
+ rh_ax.set_ylabel(r"On def. II", color='red')
+ rh_ax.tick_params(axis='y', labelcolor='red')
+ rh_ax.ticklabel_format(style='sci', axis='y', scilimits=(0,0))
+ plt.legend((lf_j_exp, lf_j_imp, rh_j_exp, rh_j_imp), \
+ (r'M $\star\star = n$', r'M $\star\star = n+1$', r'M $\star\star = n$', r'M $\star\star = n+1$'), loc='lower right')
+ plt.grid(True)
+ plt.subplots_adjust(hspace=0.8)
+ plt.tight_layout()
+ plt.savefig('Comparison_Num_Dis_Value_GCL_{}_solver_{}.png'.format(args[0], args[1]), dpi=300)
+ plt.close()
+ print("\nAll computations done and figures saved...\n")
+ print("\n------------------------------------------\n")
+ return None
\ No newline at end of file