SALOME platform Git repositories - tools/solverlab.git/blob

   1 import cdmath
   2 import FiniteVolumes2DDiffusion_SQUARE
   3 import matplotlib.pyplot as plt
   4 import numpy as np
   5 from math import log10, sqrt
   6 import time, json
   7
   8 convergence_synthesis=dict(FiniteVolumes2DDiffusion_SQUARE.test_desc)
   9
  10 def test_validation2DVF_skinny_triangles():
  11     start = time.time()
  12     ### 2D FV skinny triangles mesh
  13     meshList=[5,9,15,21,31]
  14     #meshList=['squareWithSkinnyTriangles_0','squareWithSkinnyTriangles_1','squareWithSkinnyTriangles_2','squareWithSkinnyTriangles_3','squareWithSkinnyTriangles_4','squareWithTriangles_5']
  15     mesh_path='../../../ressources/2DSkinnyTriangles/'
  16     meshType="Regular_skinny_triangles"
  17     testColor="Green"
  18     nbMeshes=len(meshList)
  19     error_tab=[0]*nbMeshes
  20     mesh_size_tab=[0]*nbMeshes
  21     mesh_name='squareWithSkinnyTriangles'
  22     diag_data=[0]*nbMeshes
  23     time_tab=[0]*nbMeshes
  24     resolution=100
  25     curv_abs=np.linspace(0,sqrt(2),resolution+1)
  26     plt.close('all')
  27     i=0
  28     # Storing of numerical errors, mesh sizes and diagonal values
  29     #for filename in meshList:
  30     for nx in meshList:
  31         my_mesh=cdmath.Mesh(0,1,nx,0,1,nx*nx,0)
  32         error_tab[i], mesh_size_tab[i], diag_data[i], min_sol_num, max_sol_num, time_tab[i] =FiniteVolumes2DDiffusion_SQUARE.solve(my_mesh,str(nx)+'x'+str(nx),resolution,meshType,testColor)
  33 #        error_tab[i], mesh_size_tab[i], diag_data[i], min_sol_num, max_sol_num, time_tab[i] =FiniteVolumes2DDiffusion_SQUARE.solve_file(mesh_path+filename,resolution,meshType,testColor)
  34         assert min_sol_num>-0.01
  35         assert max_sol_num<6.9
  36         plt.plot(curv_abs, diag_data[i], label= str(mesh_size_tab[i]) + ' cells')
  37         error_tab[i]=log10(error_tab[i])
  38         time_tab[i]=log10(time_tab[i])
  39         mesh_size_tab[i] = 0.5*log10(mesh_size_tab[i])
  40         i=i+1
  41
  42     end = time.time()
  43
  44     # Plot over diagonal line
  45     plt.legend()
  46     plt.xlabel('Position on diagonal line')
  47     plt.ylabel('Value on diagonal line')
  48     plt.title('Plot over diagonal line for finite volumes \n for the diffusion equation on 2D skinny triangles meshes')
  49     plt.savefig(mesh_name+"_2DDiffusionFV_PlotOverDiagonalLine.png", dpi='figure')
  50
  51     # Least square linear regression
  52     # Find the best a,b such that f(x)=ax+b best approximates the convergence curve
  53     # The vector X=(a,b) solves a symmetric linear system AX=B with A=(a1,a2\\a2,a3), B=(b1,b2)
  54     a1=np.dot(mesh_size_tab,mesh_size_tab)
  55     a2=np.sum(mesh_size_tab)
  56     a3=nbMeshes
  57     b1=np.dot(error_tab,mesh_size_tab)
  58     b2=np.sum(error_tab)
  59
  60     det=a1*a3-a2*a2
  61     assert det!=0, 'test_validation2DVF_skinny_triangles() : Make sure you use distinct meshes and at least two meshes'
  62     a=( a3*b1-a2*b2)/det
  63     b=(-a2*b1+a1*b2)/det
  64
  65     print "FV for diffusion on 2D skinny triangles meshes : scheme order is ", -a
  66     assert abs(a-0.442)<0.01
  67
  68     # Plot of convergence curve
  69     plt.close()
  70     plt.plot(mesh_size_tab, error_tab, label='log(|numerical-exact|)')
  71     plt.plot(mesh_size_tab, a*np.array(mesh_size_tab)+b,label='least square slope : '+'%.3f' % a)
  72     plt.legend()
  73     plt.plot(mesh_size_tab, error_tab)
  74     plt.xlabel('log(sqrt(number of cells))')
  75     plt.ylabel('log(error)')
  76     plt.title('Convergence of finite volumes for \n the diffusion equation on 2D skinny triangles meshes')
  77     plt.savefig(mesh_name+"_2DDiffusionFV_ConvergenceCurve.png", dpi='figure')
  78
  79     # Plot of computational time
  80     plt.close()
  81     plt.plot(mesh_size_tab, time_tab, label='log(cpu time)')
  82     plt.legend()
  83     plt.xlabel('log(sqrt(number of cells))')
  84     plt.ylabel('log(cpu time)')
  85     plt.title('Computational time of finite volumes \n for the diffusion equation on 2D skinny triangles meshes')
  86     plt.savefig(mesh_name+"_2DDiffusionFV_ComputationalTime.png", dpi='figure')
  87
  88     plt.close('all')
  89
  90     convergence_synthesis["Mesh_names"]=meshList
  91     convergence_synthesis["Mesh_type"]=meshType
  92     convergence_synthesis["Mesh_path"]=mesh_path
  93     convergence_synthesis["Mesh_description"]=mesh_name
  94     convergence_synthesis["Mesh_sizes"]=[10**x for x in mesh_size_tab]
  95     convergence_synthesis["Space_dimension"]=2
  96     convergence_synthesis["Mesh_dimension"]=2
  97     convergence_synthesis["Mesh_cell_type"]="Triangles"
  98     convergence_synthesis["Errors"]=[10**x for x in error_tab]
  99     convergence_synthesis["Scheme_order"]=-a
 100     convergence_synthesis["Test_color"]=testColor
 101     convergence_synthesis["Computational_time"]=end-start
 102
 103     with open('Convergence_Diffusion_2DVF_'+mesh_name+'.json', 'w') as outfile:
 104         json.dump(convergence_synthesis, outfile)
 105
 106 if __name__ == """__main__""":
 107     test_validation2DVF_skinny_triangles()