diff --git a/kalman/graphics/figure3.py b/kalman/graphics/figure3.py
index 9f76045..4e2b411 100644
--- a/kalman/graphics/figure3.py
+++ b/kalman/graphics/figure3.py
@@ -146,6 +146,17 @@ def plot_parameters(dat, input_file, deparameterize=False, ref=None):
 
 
     for i in range(len(ids)):
+
+        cur_key = ids[i]
+        rec_value = np.round(2**theta[-1, idx]*current_val[i],2)
+        curve = 2**theta[:, idx]*current_val[i]
+        std_down =  2**(-np.sqrt(P[:, idx, idx]))*curve
+        std_up =  2**np.sqrt(P[:, idx, idx])*curve
+        dash_curve = true_values[ids[i]]  + t*0
+
+
+
+
         if ids_type[i] == 'dirichlet':
             fig3, axes3 = plt.subplots(1,1,figsize=(12,5))
             axes3.plot(t, curve , '-', color=col_,label= legends_ + '= ' + str(rec_value) + '/' + str(true_values[cur_key])  + '$', linewidth = 4)
@@ -159,17 +170,9 @@ def plot_parameters(dat, input_file, deparameterize=False, ref=None):
             axes3.set_box_aspect(1/4)
             plt.xticks(fontsize=28)
             plt.yticks(fontsize=28)
-            plt.savefig('U.png')
-            plt.close(fig3)
+            plt.savefig('results/' + name_file + '/U.png')
         else:
 
-            cur_key = ids[i]
-            rec_value = np.round(2**theta[-1, idx]*current_val[i],2)
-            curve = 2**theta[:, idx]*current_val[i]
-            std_down =  2**(-np.sqrt(P[:, idx, idx]))*curve
-            std_up =  2**np.sqrt(P[:, idx, idx])*curve
-            dash_curve = true_values[ids[i]]  + t*0
-
             axes1.plot(t, curve , '-', color=col_,label= legends_ + '= ' + str(rec_value) + '/' + str(true_values[cur_key])  + '$', linewidth = 3)
             axes1.fill_between(t, std_down, std_up, alpha=0.3, color=col_)
             axes1.plot(t, dash_curve , color=col_,ls='--',linewidth = 3)
@@ -202,7 +205,7 @@ def plot_parameters(dat, input_file, deparameterize=False, ref=None):
     axes1.set_ylabel(r'$R_d$',fontsize=36)
     axes1.legend(fontsize=36,loc='upper right')
     axes1.set_xlim([-0.01,0.81])
-    axes1.set_ylim([1700,45000])
+    axes1.set_ylim([1700,55000])
     axes1.set_box_aspect(1/2)
     plt.xticks(fontsize=28)
     plt.yticks(fontsize=28)
@@ -220,7 +223,7 @@ def plot_parameters(dat, input_file, deparameterize=False, ref=None):
         axes2.set_xlabel(r'$t  (s)$',fontsize=36)
         fig2.savefig('C.png')
 
-    fig1.savefig('Rd.png')
+    fig1.savefig('results/' + name_file + '/Rd.png')
     if not is_ipython():
         plt.show()
 
diff --git a/kalman/graphics/figure_func.py b/kalman/graphics/figure_func.py
index d6f06de..5f5bd0b 100644
--- a/kalman/graphics/figure_func.py
+++ b/kalman/graphics/figure_func.py
@@ -33,5 +33,7 @@ ax1.legend(fontsize=20, loc= 'upper right')
 ax1.tick_params(axis='both', which='major', labelsize=22)
 ax1.set_yticks([])
 ax1.set_xlabel('$u$',fontsize=font_size)
+ax1.set_ylabel('$J(u)$',fontsize=font_size)
+
 plt.show()
 fig1.savefig('functionals.png', dpi=500, bbox_inches='tight')
\ No newline at end of file
diff --git a/kalman/graphics/figure_func2.py b/kalman/graphics/figure_func2.py
index 9afcd10..f30fa4a 100644
--- a/kalman/graphics/figure_func2.py
+++ b/kalman/graphics/figure_func2.py
@@ -10,9 +10,6 @@ from matplotlib import rc
 rc('font',**{'family':'sans-serif','sans-serif':['Helvetica']})
 rc('text', usetex=True)
 
-
-fig1, ax1 = plt.subplots(1,1,figsize=(8, 5))
-lwidth = 2
 font_size = 28
 
 ################ Flow Parameters
@@ -23,148 +20,150 @@ mu      =   0.5
 fac     =   1
 nr      =   50
 VENC    =   0.6
+VENC2    =   0.4
 
 gamma   =   267.513e6     #  rad/Tesla/sec   Gyromagnetic ratio for H nuclei
 Bo      =   1.5              #  Tesla           Magnetic Field Strenght
 TE      =   5e-3             #  Echo-time
-M       =   np.ones(nr)         #  Magnetization
 phi0    =   gamma*Bo*TE       # Reference phase
 phi02   =   phi0%3.14
-M1      =   np.pi/(gamma*VENC)
-ff      =   np.pi/(1000*gamma*M1)
-uv      =   np.arange(-4*VENC,4*VENC,ff)
-
-
 r       =   np.linspace(-Rd, Rd, nr)
 dr      =   r[2]-r[1]
 vmax    =   1
 v       =   vmax/Rt**2*( Rt**2 - r**2 )*(np.abs(r)<Rt);  # Poiseuille Formula
 ai      =   v/vmax
 
+
 theta       =   np.linspace(-4,5,2000)
 vtest       =   np.linspace(-5,5,2000)
-JF          =   0*theta
 jv          =   0*theta
 JV          =   0*theta
+JV2          =   0*theta
+
 Mjv         =   np.zeros([len(theta),len(ai)])
+Mjv2        =   np.zeros([len(theta),len(ai)])
 jv0         =   0*theta
 JV0         =   0*theta
 Mjv0        =   np.zeros([len(theta),len(ai)])
 #################################### MAGNETIZACION FROM V
 phiv    =   phi02 + v*np.pi/VENC
+phiv2    =   phi02 + v*np.pi/VENC2
+
 modv    =   np.ones(phiv.shape) 
 M1  =   modv*np.cos(phi02)  + 1j*modv*np.sin(phi02)
 M2  =   modv*np.cos(phiv)   + 1j*modv*np.sin(phiv)
+M2_2  =   modv*np.cos(phiv2)   + 1j*modv*np.sin(phiv2)
+
 
 ################################### FFT to COMPLEX M
 S1      =   np.fft.fft(M1)
 S2      =   np.fft.fft(M2)
-################################### SubSampling
-a1      =   0
-a2      =   1
-##### FILLED WITH ZEROS
-US1         =   S1
-US2         =   0*S2
-US2[a1::a2] =   S2[a1::a2]
+S2_2      =   np.fft.fft(M2_2)
+MR1         =   np.fft.ifft(S1)
+MR2         =   np.fft.ifft(S2)
+MR2_2         =   np.fft.ifft(S2_2)
 
-
-MR1         =   np.fft.ifft(US1)
-MR2         =   np.fft.ifft(US2)
 vrec1       =   (np.angle(MR2)-phi02)*VENC/(np.pi)
+vrec2       =   (np.angle(MR2_2)-phi02)*VENC2/(np.pi)
+
 
 
 for k in range(len(ai)):
-    jv0         =   1-np.cos(np.pi*(vrec1[k]-vtest)/VENC)
-    Mjv0[:,k]   =   jv0[:]
-    JV0         =   JV0 + jv0  
-
-for k in range(len(ai)):
-    jv          =   1-np.cos(np.pi*(vrec1[k]-theta*ai[k])/VENC)
-    Mjv[:,k]    =   jv[:]
-    JV          =   JV + jv 
-
-NJV1    =   JV*100/np.max(JV)
+    # v func
+    jv0 = 1-np.cos(np.pi*(vrec1[k]-vtest)/VENC)
+    Mjv0[:,k] = jv0[:]
+    JV0 += jv0  
+    
+    # theta func
+    jv = 1-np.cos(np.pi*(vrec1[k]-theta*ai[k])/VENC)
+    Mjv[:,k] = jv[:]
+    JV += jv
+    
+    jv2 = 1-np.cos(np.pi*(vrec2[k]-theta*ai[k])/VENC2)
+    Mjv2[:,k] = jv2[:]
+    JV2 += jv2 
 
+NJV1    =   JV#*100/np.max(JV)
+NJV2    =   JV2#*110/np.max(JV)
 MV = Mjv0
 V =NJV1
+V2 =NJV2
+
+
 
-left, bottom, width, height = [0.2, 0.2, 0.1, 0.1]
 
 fig     =   plt.figure(figsize=(12, 6), dpi=100)
 ax1     =   plt.subplot(1,2,1)
 
 ch1     =   20
 ch2     =   23
+color1 = 'xkcd:coral'
+color2 = 'xkcd:azure'
+color3 = 'darkviolet'
+lwidth = 2
 
+
+# Miniplot
+left, bottom, width, height = [0.18, 0.17, 0.1, 0.1]
 ax0 = fig.add_axes([left, bottom, width, height])
 ax0.plot(r,v,'b-')
-ax0.plot([r[ch1]],[v[ch1]],color='xkcd:coral',marker='o')
-ax0.plot([r[ch2]],[v[ch2]],color='xkcd:azure',marker='o')
+ax0.plot([r[ch1]],[v[ch1]],color=color1,marker='o')
+ax0.plot([r[ch2]],[v[ch2]],color=color2,marker='o')
 ax0.set_xlim((-1.5,1.5))
+ax0.set_xticks([])
+ax0.set_ylabel(r'$u$',fontsize=20)
 
 
 
-
-#for k in range(22,39):
-#   if k!=ch1 and k!=ch2 and np.sum(MV[:,k])!=0:        
-#       ax1.plot(vtest, MV[:,k],color='xkcd:beige',alpha=0.8)
-
-
-
-ax1.plot(vtest, MV[:,ch1],color='xkcd:coral',label='$v_1$')
-ax1.plot(vtest, MV[:,ch2],color='xkcd:azure',label='$v_2$')
-
+# Figure 1
+#ax1.plot(vtest, MV[:,ch1],color='xkcd:coral',label='$v_1$')
+#ax1.plot(vtest, MV[:,ch2],color='xkcd:azure',label='$v_2$')
+ax1.plot(vtest, MV[:,ch1],color=color1,linewidth=lwidth)
+ax1.plot(vtest, MV[:,ch2],color=color2,linewidth=lwidth)
 
 m1x     =   vtest[np.where( np.abs(MV[:,ch1] - np.min(MV[:,ch1]))<0.001  )]
-
 m1y     =   np.min(MV[:,ch1])
-
 m2x     =   vtest[np.where( np.abs(MV[:,ch2] - np.min(MV[:,ch2]))<0.001  )]
-#m2x    =   vtest[np.where(MV[:,ch2]==np.min(MV[:,ch2]))]
 m2y     =   np.min(MV[:,ch2])
 
-
-ax1.plot([m1x],[m1y],color='xkcd:coral',marker='o')
-ax1.plot([m2x],[m2y],color='xkcd:azure',marker='o')
-
-
-ax1.axvline(x=v[ch1], color='xkcd:coral', linestyle='--',label='$v_{1,true}$')
-ax1.axvline(x=v[ch2], color='xkcd:azure', linestyle='--',label='$v_{2,true}$')
-
-
-ax1.set_xlabel(r'$u$',fontsize=20)
-ax1.set_ylabel(r'$J_i(u)$',fontsize=20)
+#ax1.plot([m1x],[m1y],color='xkcd:coral',marker='o')
+#ax1.plot([m2x],[m2y],color='xkcd:azure',marker='o')
+ax1.axvline(x=v[ch1], color=color1, linestyle='--',label='$v_{1,true}$')
+ax1.axvline(x=v[ch2], color=color2, linestyle='--',label='$v_{2,true}$')
+ax1.set_ylabel('$individual \ functional$',fontsize=20)
 #ax1.legend(loc='upper right', bbox_to_anchor=(0.5, 1.05),ncol=2, fancybox=True, shadow=True,fontsize=15)
 ax1.set_yticks([])
-ax1.set_xticks([])
+ax1.tick_params(axis='both', which='major', labelsize=22)
+#ax1.set_xticks([])
+#ax1.legend(fontsize=20, loc= 'upper right')
 ax1.set_xlim((-3.5,3.5))
-ax1.set_ylim((-1.0,2.4))
-
-ax2     =   plt.subplot(1,2,2)
-ax2.plot(theta,V,'b-')
-ax2.axvline(x=1, color='k', linestyle='--')
-ax2.set_xlabel(r'$\theta$',fontsize=20)
-ax2.set_ylabel(r'$J_T(\theta)$',fontsize=20)
-plt.yticks([])
-ax2.set_xticks([])
-plt.title(r'$\theta_{true}=1$' + '\n' +'$venc < v_{max}$',fontsize=15)
-plt.xlim((-2,3))
-
-plt.show()
-
-
-
-
-
-
-#ax1.plot(u, J1, color = 'orangered', label = '$venc = 0.9 u_{true}$', linestyle='-',linewidth=lwidth)
-#ax1.plot(u, J2, color = 'dodgerblue', label = '$venc = 0.6 u_{true}$', linestyle='-',linewidth=lwidth)
-#ax1.axvline(x=1,color = 'black',linewidth = lwidth , label = '$u_{true}$')
-
-
-ax1.legend(fontsize=20, loc= 'upper right')
+ax1.set_ylim((-1.1,2.9))
+ax1.set_xlabel('$u$',fontsize=font_size)
 ax1.tick_params(axis='both', which='major', labelsize=22)
 ax1.set_yticks([])
-ax1.set_xlabel('$u$',fontsize=font_size)
+ax1.text(-1,2.4,'$u_{true}$',fontsize=22, color = color1)
+ax1.text(1.1,2.4,'$u_{true}$',fontsize=22, color = color2)
+
+
+# Figure 2
+ax2     =   plt.subplot(1,2,2)
+ax2.plot(theta,V,color=color3,linestyle = '-',linewidth=lwidth, label = '$venc=0.6u_{true}$')
+ax2.plot(theta,V2,color='darkorange',linestyle = '-',linewidth=lwidth, label = '$venc=0.4u_{true}$')
+
+ax2.axvline(x=1, color='black', linestyle='--')
+ax2.set_xlabel(r'$\theta$',fontsize=font_size)
+ax2.set_ylabel(r'$total \  functional$',fontsize=20)
+plt.yticks([])
+ax2.legend(fontsize=17, loc= 'upper left',frameon=False)
+ax2.set_ylim((-3,20))
+ax2.text(1.2,17,r'$ \theta _{true}$',fontsize=22, color = 'black')
+ax2.tick_params(axis='both', which='major', labelsize=22)
+#ax2.set_xticks([])
+#plt.title(r'$\theta_{true}=1$' + '\n' +'$venc < v_{max}$',fontsize=15)
+plt.xlim((-3.5,3.5))
+
+
+
+
 plt.show()
-#fig1.savefig('functionals.png', dpi=500, bbox_inches='tight')
\ No newline at end of file
+fig.savefig('functionals2.png', dpi=500, bbox_inches='tight')
\ No newline at end of file
diff --git a/kalman/input_files/aorta.yaml b/kalman/input_files/aorta.yaml
index aeefea3..63a4893 100755
--- a/kalman/input_files/aorta.yaml
+++ b/kalman/input_files/aorta.yaml
@@ -5,16 +5,15 @@ fluid:
     density: 1.2
     dynamic_viscosity: 0.035
     stokes: False
-    implicit_windkessel: True
     state_velocity: 'update'
 
 io:
-    write_path: 'results/updRz_Pb_wp0.5wm16.84'
+    write_path: 'results/Pb_Hz2.3_Hz5.7'
     restart:
         path: ''  # './projects/nse_coa3d/results/test_restart2/' 
         time: 0
     write_xdmf: True
-    write_checkpoints: True
+    write_checkpoints: True 
     write_hdf5_timeseries: False
     write_velocity: 'update'     # update or tentative
 
@@ -124,6 +123,13 @@ timemarching:
     checkpoint_dt:  0.03 # <= 0: only last; else value + last
     report: 1   # 0: print nothing, 1: print time step and writeout, 2: 1 + flux
 
+windkessel:
+    implicit: True
+    # low rank update formulation can run in parallel.
+    # note that fgmres or similar has to be selected for the pressure solve, as
+    # matrix is not explicitly formed.
+    low_rank_update: False
+
 # solver setup
 fem:
     velocity_space: p1  # p1 p1b/p1+ p2
@@ -154,6 +160,7 @@ fem:
 
 linear_solver:
     method: 'lu'
+    #inputfile: 'input_files/fracstep_p-gmres_u-LU_WK-LRC.yaml'
 
 estimation:
     boundary_conditions:
@@ -186,21 +193,35 @@ estimation:
 
     measurements:
         -
-            mesh: '/home/yeye/NuMRI/kalman/meshes/coaortaH3_leo2.0.h5'
-            #mesh: './meshes/coaortaH1.h5'
-            fe_degree: 1
-            xdmf_file: 'measurements/aorta_zdir/Perturbation/Mg15V120/u_all.xdmf'
-            file_root: 'measurements/aorta_zdir/Perturbation/Mg15V120/u{i}.h5'
-            #xdmf_file: 'measurements/aorta_exp_dt1ms/u_all.xdmf'
-            #file_root: 'measurements/aorta_exp_dt1ms/u{i}.h5'
+            #mesh: '/home/yeye/NuMRI/kalman/meshes/coaortaH3_leo2.0.h5'
+            mesh: '/home/yeye/Desktop/slices/slice_Hz2.3.h5'
+            fe_degree: 0
+            xdmf_file: 'measurements/slice_Hz2.3/Perturbation/Mg12V120/u_all.xdmf'
+            file_root: 'measurements/slice_Hz2.3/Perturbation/Mg12V120/u{i}.h5'
+            #xdmf_file: 'measurements/slice_Hz5.7/u_all.xdmf'
+            #file_root: 'measurements/slice_Hz5.7/u{i}.h5'
             indices: 0 # indices of checkpoints to be processed. 0 == all
             velocity_direction: [0,0,1]
-            noise_stddev: 16.84     # standard deviation of Gaussian noise
+            #noise_stddev: 0     # standard deviation of Gaussian noise
+            #noise_stddev: 22.39     # SNR 12 slice 5.7
+            #noise_stddev: 15.76     # SNR 15 slice 5.7
+            #noise_stddev: 8.75     # SNR 15 slice 2.3
+            noise_stddev: 12.15     # SNR 12 slice 2.3
+        -
+            mesh: '/home/yeye/Desktop/slices/slice_Hz5.7.h5'
+            fe_degree: 0
+            xdmf_file: 'measurements/slice_Hz5.7/Perturbation/Mg12V120/u_all.xdmf'
+            file_root: 'measurements/slice_Hz5.7/Perturbation/Mg12V120/u{i}.h5'
+            indices: 0 # indices of checkpoints to be processed. 0 == all
+            velocity_direction: [0,0,1]
+            noise_stddev: 22.39     # SNR 12 slice 5.7
+            
     
     roukf:
         particles: 'simplex' # unique or simplex
         observation_operator: 'postprocessing'         #state or postprocessing
         reparameterize: True
-        ODV_functional:
+        MAG_functional:
             enable: False
-            VENC: 138
\ No newline at end of file
+            VENC: 61
+            module_meas_file_root: 'measurements/aorta_zdir/Perturbation/Mg15V30/module/M{i}.h5'
\ No newline at end of file
diff --git a/kalman/input_files/aorta_reference.yaml b/kalman/input_files/aorta_reference.yaml
deleted file mode 100755
index 52425aa..0000000
--- a/kalman/input_files/aorta_reference.yaml
+++ /dev/null
@@ -1,178 +0,0 @@
-
-mesh: './meshes/coaortaH1.h5'
-# Physical parameters of the fluid
-fluid:
-    density: 1.2
-    dynamic_viscosity: 0.035
-    stokes: False
-    implicit_windkessel: True
-
-io:
-    write_path: 'results/aortaRR_Pa'
-    restart:
-        path: ''  # './projects/nse_coa3d/results/test_restart2/' 
-        time: 0
-    write_xdmf: True
-    write_checkpoints: True
-    write_hdf5_timeseries: False
-    write_velocity: 'update'     # update or tentative
-
-boundary_conditions:
-    - 
-        id: 2
-        type: 'dirichlet'
-        #value: ['0','0','-U*sin(DOLFIN_PI*t/Th)*(t<=Th) + (t<0.8)*(Th<t)*(U*DOLFIN_PI/Th*(t-Th)*exp(-(t-Th)*beta)) +
-        #                 -U*sin(DOLFIN_PI*(t-0.8)/Th)*(t<= 0.8+Th )*(t>0.8) + (t<1.6)*(0.8+Th<t)*(U*DOLFIN_PI/Th*(t-0.8-Th)*exp(-(t-0.8-Th)*beta)) +
-        #                 -U*sin(DOLFIN_PI*(t-1.6)/Th)*(t<= 1.6+Th )*(t>1.6) + (t<2.4)*(1.6+Th<t)*(U*DOLFIN_PI/Th*(t-1.6-Th)*exp(-(t-1.6-Th)*beta))' ]
-        value: ['0','0','-U*sin(DOLFIN_PI*t/Th)*(t<=Th) + (Th<t)*(U*DOLFIN_PI/Th*(t-Th)*exp(-(t-Th)*beta))']
-        parameters:
-            U: 75
-            Th: 0.36
-            beta: 70
-            t: 0
-    - 
-        id: 1
-        type: 'dirichlet'
-        value: ['0','0','0']
-    - 
-        id: 3
-        type: 'windkessel'
-        parameters:
-            R_p: 200
-            C: 0.0005
-            R_d: 4800
-            p0: 85
-            conv: 1333.223874   
-    - 
-        id: 4
-        type: 'windkessel'
-        parameters:
-            R_p: 480
-            C: 0.00045
-            R_d: 7200
-            p0: 85
-            conv: 1333.223874   
-    - 
-        id: 5
-        type: 'windkessel'
-        parameters:
-            R_p: 520
-            C: 0.00045
-            R_d: 11520
-            p0: 85
-            conv: 1333.223874   
-    - 
-        id: 6
-        type: 'windkessel'
-        parameters:
-            R_p: 520
-            C: 0.00045
-            R_d: 11520
-            p0: 85
-            conv: 1333.223874   
-
-timemarching:
-    velocity_pressure_coupling: 'fractionalstep'    # monolithic, fractionalstep
-
-    monolithic:
-        timescheme: 'gmp'   # generalized midpoint, steady FIXME TODO
-        theta: 1            # 1: Euler, 0.5: implicit midpoint rule (one-legged)
-        nonlinear:
-            method: 'constant_extrapolation'   # constant_extrapolation, linear_extrapolation, newton, picard, snes
-            maxit: 20
-            init_steps: 30
-            use_aitken: 1   #  0: False, 1: Picard only, 2: all
-            report: 1       # 0: None, 1: residuals, 2: residuals and energy (inflow/driving/forcing via ESSENTIAL Dbcs!)
-            atol: 1.e-6    # note: dot required!!
-            rtol: 1.e-16
-            stol: 0.0
-
-    fractionalstep:
-        scheme: 'CT'      # CT, IPCS
-        coupled_velocity: False     # False faster, True needed if robin_bc implicit
-        robin_bc_velocity_scheme: 'implicit' # explicit, semi-implicit, implicit
-        transpiration_bc_projection: 'robin'      # robin, dirichlet
-        flux_report_normalize_boundary: 1
-
-    T: 0.8       # end time
-    dt: 0.001
-    write_dt: 0.03
-    checkpoint_dt:  0.03 # <= 0: only last; else value + last
-    report: 1   # 0: print nothing, 1: print time step and writeout, 2: 1 + flux
-
-# solver setup
-fem:
-    velocity_space: p1  # p1 p1b/p1+ p2
-    pressure_space: p1  # p1 p0/dg0 dg1
-
-    strain_symmetric: False
-    convection_skew_symmetric: True    # aka Temam term
-    stabilization:
-        forced_normal:
-            enabled: True
-            boundaries: [3,4,5,6]
-            gamma: 20
-        backflow_boundaries: [3,4,5,6]
-        streamline_diffusion:
-            enabled: False
-            parameter: 'standard'   # standard, shakib, codina, klr
-            length_scale: 'metric' # average, max, metric
-            parameter_element_constant: True
-            Cinv: ~
-        monolithic:
-            infsup: 'pspg'    # pspg, pressure-stabilization
-            graddiv: False
-            consistent: False
-            pressure_stab_constant: 1.
-
-    fix_pressure: False
-    fix_pressure_point: [0., 0. , 0.]
-
-linear_solver:
-    method: 'lu'
-
-estimation:
-    boundary_conditions:
-        #- 
-        #    id: 3
-        #    type: 'windkessel'
-        #    initial_stddev: 1
-        - 
-            id: 4
-            type: 'windkessel'
-            initial_stddev: 1
-        - 
-            id: 5
-            type: 'windkessel'
-            initial_stddev: 1
-        - 
-            id: 6
-            type: 'windkessel'
-            initial_stddev: 1
-        - 
-            id: 2
-            type: 'dirichlet'
-            parameters: 'U'
-            initial_stddev: 1
-
-
-    measurements:
-        -
-            mesh: '/home/yeye/NuMRI/kalman/meshes/coaortaH3_leo2.0.h5'
-            #mesh: './meshes/coaortaH1.h5'
-            fe_degree: 1
-            xdmf_file: 'measurements/aortaRR/Perturbation/Mg15V120/u_all.xdmf'
-            file_root: 'measurements/aortaRR/Perturbation/Mg15V120/u{i}.h5'
-            #xdmf_file: 'measurements/aortaRR/u_all.xdmf'
-            #file_root: 'measurements/aortaRR/u{i}.h5'
-            indices: 0 # indices of checkpoints to be processed. 0 == all
-            velocity_direction: ~
-            noise_stddev: 55     # standard deviation of Gaussian noise
-    
-    roukf:
-        particles: 'simplex' # unique or simplex
-        observation_operator: 'postprocessing'         #state or postprocessing
-        reparameterize: True
-        ODV_functional:
-            enable: False
-            VENC: 102    #  102,120%   59,70%   42 50%,   21,25%
diff --git a/kalman/input_files/fracstep_p-gmres.yaml b/kalman/input_files/fracstep_p-gmres.yaml
new file mode 100644
index 0000000..16d1b61
--- /dev/null
+++ b/kalman/input_files/fracstep_p-gmres.yaml
@@ -0,0 +1,62 @@
+config_name: test
+petsc_options:
+    # - u_ten_ksp_view
+    - u_ten_ksp_converged_reason
+    - u_ten_ksp_monitor_true_residual
+    - u_ten_ksp_type bcgs
+    - u_ten_ksp_rtol 1.0e-6
+    - u_ten_ksp_initial_guess_nonzero
+
+    - u_ten_pc_type jacobi
+
+    - d_ksp_type cg
+    - d_ksp_rtol 1.0e-6
+
+    # - p_ksp_view
+    - p_ksp_converged_reason
+    - p_ksp_monitor_true_residual
+    - p_ksp_type fgmres
+    - p_ksp_rtol 1.0e-6
+    - p_ksp_initial_guess_nonzero
+
+    #- p_pc_type gamg
+    #- p_pc_gamg_type agg
+    #- p_pc_gamg_threshold 0.03
+    #- p_pc_gamg_square_graph 10     # no effect ??
+    #- p_pc_gamg_sym_graph
+    - p_mg_levels_ksp_type richardson
+    - p_mg_levels_pc_type sor
+
+    - p_mass_ksp_type cg
+    - p_mass_ksp_converged_reason
+    - p_mass_ksp_monitor_true_residual
+    - p_mass_ksp_rtol 1.0e-8
+    - p_mass_ksp_initial_guess_nonzero
+    - p_mass_pc_type jacobi
+
+    - u_upd_ksp_type cg
+    - u_upd_ksp_rtol 1.0e-8
+    - u_upd_ksp_initial_guess_nonzero
+    - u_upd_pc_type jacobi
+
+    - p_pc_type hypre
+    - p_pc_hypre_type boomeramg
+    - p_pc_hypre_boomeramg_strong_threshold 0.75
+    - p_pc_hypre_boomeramg_max_levels 25
+    - p_pc_hypre_boomeramg_smooth_type Euclid
+    - p_pc_hypre_boomeramg_eu_bj
+
+    # - p_pc_type hypre
+    # - p_pc_hypre_type boomeramg
+    # - p_pc_hypre_boomeramg_agg_nl 4
+    # - p_pc_hypre_boomeramg_agg_num_paths 2
+    # # Truncation factor for interpolation (note: increasing towrds 1
+    # # appears to reduce memory useage
+    # - p_pc_hypre_boomeramg_truncfactor 0.9
+    # # Max elements per row for interpolation operator
+    # - p_pc_hypre_boomeramg_P_max 5
+    # # - p_pc_hypre_boomeramg_max_levels 10
+    # # Strong threshold (BoomerAMG docs recommend 0.5-0.6 for 3D
+    # #   Poisson
+    # - p_pc_hypre_boomeramg_strong_threshold 0.5
+    
diff --git a/kalman/input_files/fracstep_p-gmres_u-LU_WK-LRC.yaml b/kalman/input_files/fracstep_p-gmres_u-LU_WK-LRC.yaml
new file mode 100644
index 0000000..fcc67bc
--- /dev/null
+++ b/kalman/input_files/fracstep_p-gmres_u-LU_WK-LRC.yaml
@@ -0,0 +1,82 @@
+config_name: test
+petsc_options:
+    # - u_ten_ksp_view
+    # - u_ten_ksp_converged_reason
+    # - u_ten_ksp_monitor_true_residual
+    - u_ten_ksp_type preonly
+    # - u_ten_ksp_rtol 1.0e-6
+    # - u_ten_ksp_initial_guess_nonzero
+
+    # - u_ten_pc_type jacobi
+
+     # - u_ten_pc_side right
+    - u_ten_pc_type lu
+    # - u_ten_pc_gamg_type agg
+    # - u_ten_pc_gamg_threshold 0.03
+    # - u_ten_pc_gamg_square_graph 10     # no effect ??
+    # - u_ten_pc_gamg_sym_graph
+    # - u_ten_mg_levels_ksp_type richardson
+    # - u_ten_mg_levels_pc_type sor
+    # # - u_ten_pc_gamg_coarse_eq_limit 50    # ignored !?!?!
+
+
+    # - p_ksp_view
+    - p_ksp_converged_reason
+    - p_ksp_monitor_true_residual
+    # - p_ksp_type gmres
+    # - p_ksp_norm_type unpreconditioned
+    - p_ksp_type fgmres
+    - p_ksp_rtol 1.0e-8
+    - p_ksp_initial_guess_nonzero
+    - p_pc_type gamg
+    - p_pc_gamg_type agg
+    - p_pc_gamg_threshold 0.03
+    - p_pc_gamg_square_graph 10     # no effect ??
+    - p_pc_gamg_sym_graph
+    - p_mg_levels_ksp_type richardson
+    - p_mg_levels_pc_type sor
+
+
+    - p_mass_ksp_type preonly
+    # - p_mass_ksp_rtol 1.0e-8
+    # - p_mass_ksp_initial_guess_nonzero
+    - p_mass_pc_type lu
+
+    # - p_pc_type hypre
+    # - p_pc_hypre_type boomeramg
+    # - p_pc_hypre_boomeramg_strong_threshold 0.75
+    # - p_pc_hypre_boomeramg_max_levels 25
+    # - p_pc_hypre_boomeramg_smooth_type Euclid
+    # - p_pc_hypre_boomeramg_eu_bj
+
+    # - p_ksp_type preonly
+    # - p_pc_type lu
+    # - p_pc_factor_mat_solver_package mumps
+    # - p_mat_mumps_icntl_14 80
+
+    # - p_ksp_type cg
+    # - p_ksp_converged_reason
+    # - p_ksp_monitor_true_residual
+    # - p_ksp_rtol 1.0e-8
+
+    # - p_pc_type hypre
+    # - p_pc_hypre_type boomeramg
+    # - p_pc_hypre_boomeramg_agg_nl 4
+    # - p_pc_hypre_boomeramg_agg_num_paths 2
+    # # Truncation factor for interpolation (note: increasing towrds 1
+    # # appears to reduce memory useage
+    # - p_pc_hypre_boomeramg_truncfactor 0.9
+    # # Max elements per row for interpolation operator
+    # - p_pc_hypre_boomeramg_P_max 5
+    # # - p_pc_hypre_boomeramg_max_levels 10
+    # # Strong threshold (BoomerAMG docs recommend 0.5-0.6 for 3D
+    # #   Poisson
+    # - p_pc_hypre_boomeramg_strong_threshold 0.5
+    
+    # - u_upd_ksp_converged_reason
+    # - u_upd_ksp_monitor_true_residual
+    # - u_upd_ksp_view
+    - u_upd_ksp_type preonly
+    # - u_upd_ksp_rtol 1.0e-8
+    # - u_upd_ksp_initial_guess_nonzero
+    - u_upd_pc_type lu
diff --git a/kalman/meshes/coaortaRH2.h5 b/kalman/meshes/coaortaRH2.h5
deleted file mode 100755
index 93f0e1b..0000000
Binary files a/kalman/meshes/coaortaRH2.h5 and /dev/null differ