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jeremias
2020-01-17 16:24:10 +01:00
parent 14cffd5876
commit 2da253f278
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14
codes/MATLAB/leo/CREATE_MESH.m Executable file
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% Program to create a structured mesh using the codes of Leo Sok
clear all; close all
nodes = load('LEO_files/nodes.txt');
ux = load('LEO_files/ux.txt') ;
uy = load('LEO_files/uy.txt') ;
uz = load('LEO_files/uz.txt') ;
u = sqrt(ux.^2 + uy.^2 + uz.^2);
resol = load('LEO_files/resol.txt') ;
dx = resol(1); dy = resol(2) ; dz = resol(3);
nodes_masked = maskFEM(nodes,u);
[N,tets,faces] = meshStructTess(nodes_masked,dx,dy,dz,0,0);
writemesh('/home/yeye/Desktop/leomesh',N,tets,faces)

19
codes/MATLAB/leo/maskFEM.m Executable file
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function nodes2 = maskFEM(nodes,vel)
a = [];
b = [];
c = [];
ind = 1;
for i=1:length(nodes)
if vel(i)>0
a(ind) = nodes(i,1);
b(ind) = nodes(i,2);
c(ind) = nodes(i,3);
ind = ind +1;
end
end
nodes2 = [a', b', c'];

169
codes/MATLAB/leo/meshStructTess.m Executable file
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function [nodes, tets, faces, P] = meshStructTess(nodes, dx, dy, dz, check_mesh, plot_mesh)
%% [nodes, tets, faces] = meshStructTess(nodes, dx, dy, dz, check_mesh, plot_mesh)
% Generate a tessalation from a list of structured nodes.
% input: nodes: n times 3 matrix with on the rows the coordinates of
% the n points in the mesh
% dx, dy, dz: the mesh-size in the directions x, y and z
% check_mesh: if true, then it solves a Poisson problem
% plot_mesh: if true, then it plots the mesh
% output: nodes: m times 3 matrix with on the rows the coordinates of
% the m <= n points in the triangulationedi
% tets: l times 4 matrix with on the rows the tetrahedra
% faces: k times 3 matrix with on the rows the triangles of the
% boundary of the mesh
% P: Transformation matrix from input nodes to output nodes.
% Useful also for transforming node-valued functions on
% the input nodes to node-valued functions on the output
% nodes
%
% The triangulation can be plotted using tetramesh(tets,nodes)
% compute the minimum and number of points in each direction
if size(nodes,1) < 4
error('Triangulation needs at least 4 points')
end
mn = min(nodes);
xmin = mn(1);
ymin = mn(2);
zmin = mn(3);
mn = max(nodes);
xmax = mn(1);
ymax = mn(2);
zmax = mn(3);
nx = round((xmax-xmin)/dx +1);
ny = round((ymax-ymin)/dy +1);
nz = round((zmax-zmin)/dz +1);
Nnodes = size(nodes,1);
% Define tensor which consist of nodes indices, used for the creation of
% the tetrahedra
nodes3d = zeros(nx,ny,nz); % preallocate
for i=1:Nnodes
nodes3d(round((nodes(i,1)-xmin)/dx)+1,round((nodes(i,2)-ymin)/dy)+1,round((nodes(i,3)-zmin)/dz)+1)=i;
end
disp('Creating Tetrahedra')
% create tetrahedral mesh in cube, which we will reuse.
ii = 1;
X = zeros(8,3);
for i=0:1
for j=0:1
for k=0:1
X(ii,:) = [i,j,k];
ii = ii+1;
end
end
end
cubetet = delaunay(X);
% Run through the mesh
el = 1;
Tetrahedra = zeros(6*(nnz(nodes3d)),4); % preallocate
for i=1:nx-1
for j=1:ny-1
for k=1:nz-1
% take [i:i+1,j:j+1,k:k+1] as cube
nod = zeros(1,8); % perallocate
for l = 1:8
% nod is vector with node indices of cube
nod(l) = nodes3d(i + X(l,1), j + X(l,2), k + X(l,3));
end
if nnz(nod) == 8 % then the cube is inside the mesh
tet = nod(cubetet);
else % then there is at least one point of the cube outside the mesh
Xs = X(logical(nod),:); % take only nodes inside the mesh
nodx = nod(logical(nod));
if nnz(nod) == 4 % 4 nodes, check if points are coplanar
C = cross(Xs(2,:)-Xs(1,:), Xs(3,:)-Xs(1,:));
cop = logical(dot(C,Xs(4,:)-Xs(1,:)));
% if cop = 0, then points are coplanar end thus no
% tetrahedra exists.
end
if (nnz(nod)>4) || (nnz(nod) == 4 && cop)
% create tetrahedra
tet1 = delaunay(Xs);
tet = nodx(tet1);
else % no tetrahedra exists
tet = [];
end
end
% add new tetrahedra to list
Tetrahedra(el:el+size(tet,1)-1,:) = tet;
el = el+size(tet,1);
end
end
end
tets = Tetrahedra(1:el-1,:); % Delete extra preallocated rows.
clear Tetrahedra
disp([num2str(size(tets,1)), ' tetrahedra created'])
% Delete nodes which are not in any tetrahedra.
disp('Update mesh')
contr = zeros(size(nodes,1),1);
for i=1:size(tets,1)
for j=1:4
contr(tets(i,j))=1;
end
end
nodes = nodes(logical(contr),:);
% compute P
P = speye(Nnodes);
P = P(logical(contr),:);
disp([num2str(nnz(~contr)), ' unused nodes in triangulation deleted.'])
disp('Update tetrahedra')
% make tetrahedra compatible with new node indices
cumcon = cumsum(~contr)';
tets = tets - cumcon(tets);
% create triangles
if size(tets,1) == 0
warning('No tetrahedra created')
faces = zeros(0,3);
else
disp('Create Triangles')
faces = freeBoundary(triangulation(tets,nodes));
disp([num2str(size(faces,1)), ' triangles created'])
end
% checking the mesh by solving a Poisson problem
if check_mesh
% Builds the P1 stiffness matrix from tets and nodes
[A,volumes]=stifness_matrixP1_3D(tets,nodes);
% Check if element volumes may be negative
if any(volumes<=0)
warning('Some elements have zero or negative volume')
end
% solve the Poisson problem with Dirichlet BC
A(2:end,2:end)\ones(size(A(2:end,2:end),1),1);
disp('If there are no warnings, it probably means that the mesh is fine')
end
% Plots mesh
if plot_mesh
tetramesh(tets,nodes)
xlabel('x')
ylabel('y')
zlabel('z')
end
end

97
codes/MATLAB/leo/writemesh.m Executable file
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function writemesh(varargin)
%% writemesh(path, mesh)
% Save triangulation as path.xml and path.msh
% mesh is a struct with fields Pts, Tet, Tri
% alernatively one can use writemesh(path, Pts, Tet, Tri)
% Pts should by a n times 3 matrix consisting points of the mesh
% Tet is the m times 4 matrix consisting the tetrahedra
% Tri is the l times 3 matrix consisting the triangles at the boundary
if nargin > 3
mesh.Pts=varargin{2};
mesh.Tet=varargin{3};
mesh.Tri=varargin{4};
writemesh(varargin{1},mesh,varargin(nargin));
elseif isstruct(varargin{2})
rootMeshFile = varargin{1};
% NEW FILE
obj = [rootMeshFile,'.msh'];
meshfile = fopen(obj,'w');
obj2 = [rootMeshFile,'.xml'];
xmlfile = fopen(obj2,'w');
% MESH
fprintf(meshfile,['$MeshFormat','\n']);
fprintf(meshfile,['2.2 0 8','\n']);
fprintf(meshfile,['$EndMeshFormat','\n']);
fprintf(xmlfile,['<?xml version="1.0" encoding="UTF-8"?>','\n']);
fprintf(xmlfile,'\n');
fprintf(xmlfile,['<dolfin xmlns:dolfin="http://www.fenicsproject.org">','\n']);
mesh = varargin{2};
Nodes = mesh.('Pts');
mesh = rmfield(mesh,'Pts');
Nodes = [(1:size(Nodes,1))' Nodes(:,1:3)];
% POINTS
if ~strcmp(varargin{nargin},'mute')
disp('Write Points')
end
fprintf(meshfile,['$Nodes','\n']);
fprintf(meshfile,['%i','\n'],size(Nodes,1));
fprintf(xmlfile,[' <mesh celltype="tetrahedron" dim="3">','\n']);
fprintf(xmlfile,[' <vertices size="%i">','\n'],size(Nodes,1));
fprintf(meshfile,'%i %13.6f %13.6f %13.6f\n',Nodes');
Nodes(:,1) = Nodes(:,1) - 1;
fprintf(xmlfile,' <vertex index="%i" x="%0.16e" y="%0.16e" z="%0.16e"/>\n',Nodes');
fprintf(meshfile,['$EndNodes','\n']);
fprintf(meshfile,['$Elements','\n']);
fprintf(meshfile,['%i','\n'],size(mesh.Tet,1)+size(mesh.Tri,1));
fprintf(xmlfile,[' </vertices>','\n']);
fprintf(xmlfile,[' <cells size="%i">','\n'],size(mesh.Tet,1));
% Triangles
if ~strcmp(varargin{nargin},'mute')
disp('Write Triangles')
end
tri = mesh.('Tri');
tri = [(1:size(tri,1))' 2*ones(size(tri,1),1) 2*ones(size(tri,1),1) zeros(size(tri,1),1) 2*ones(size(tri,1),1) tri(:,1:3)];
fprintf(meshfile,'%i %i %i %i %i %i %i %i\n',tri');
% Tetrahedra
if ~strcmp(varargin{nargin},'mute')
disp('Write Tetrahedra')
end
tet = mesh.('Tet');
tet = [(size(tri,1)+1:size(tri,1)+size(tet,1))' 4*ones(size(tet,1),1) 2*ones(size(tet,1),1) zeros(size(tet,1),1) ones(size(tet,1),1) tet(:,1:4)];
fprintf(meshfile,'%i %i %i %i %i %i %i %i %i\n',tet');
tet = mesh.('Tet');
tet = [(0:size(tet,1)-1)' (tet(:,1:4)-1)];
fprintf(xmlfile,' <tetrahedron index="%i" v0="%i" v1="%i" v2="%i" v3="%i"/>\n',tet');
fprintf(meshfile,['$EndElements','\n']);
fprintf(xmlfile,' </cells>\n </mesh>\n</dolfin>\n');
fclose('all');
end