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

   1 import FiniteVolumes2DDiffusion_SQUARE
   2 import matplotlib.pyplot as plt
   3 import numpy as np
   4 from math import log10, sqrt
   5 import time, json
   6
   7 convergence_synthesis=dict(FiniteVolumes2DDiffusion_SQUARE.test_desc)
   8
   9 def test_validation2DVF_checkerboard():
  10     start = time.time()
  11     ##### 2D FV checkerboard mesh
  12     meshList=['checkerboard_4x4','checkerboard_8x8','checkerboard_16x16','checkerboard_32x32','checkerboard_64x64','checkerboard_128x128']
  13     meshType="Non_conforming_checkerboard"
  14     testColor="Green"
  15     nbMeshes=len(meshList)
  16     error_tab=[0]*nbMeshes
  17     mesh_size_tab=[0]*nbMeshes
  18     mesh_path='../../../ressources/2DCheckerboard/'
  19     mesh_name='squareWithCheckerboard'
  20     diag_data=[0]*nbMeshes
  21     time_tab=[0]*nbMeshes
  22     resolution=100
  23     curv_abs=np.linspace(0,sqrt(2),resolution+1)
  24     plt.close('all')
  25     i=0
  26     # Storing of numerical errors, mesh sizes and diagonal values
  27     for filename in meshList:
  28         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)
  29         assert min_sol_num>-0.01
  30         assert max_sol_num<1.02
  31         plt.plot(curv_abs, diag_data[i], label= str(mesh_size_tab[i]) + ' cells')
  32         error_tab[i]=log10(error_tab[i])
  33         time_tab[i]=log10(time_tab[i])
  34         mesh_size_tab[i] = 0.5*log10(mesh_size_tab[i])
  35         i=i+1
  36
  37     end = time.time()
  38
  39     # Plot over diagonal line
  40     plt.legend()
  41     plt.xlabel('Position on diagonal line')
  42     plt.ylabel('Value on diagonal line')
  43     plt.title('Plot over diagonal line for finite volumes for \n the diffusion equation on 2D checkerboard meshes')
  44     plt.savefig(mesh_name+"_2DDiffusionVF_PlotOverDiagonalLine.png", dpi='figure')
  45
  46     # Least square linear regression
  47     # Find the best a,b such that f(x)=ax+b best approximates the convergence curve
  48     # The vector X=(a,b) solves a symmetric linear system AX=B with A=(a1,a2\\a2,a3), B=(b1,b2)
  49     a1=np.dot(mesh_size_tab,mesh_size_tab)
  50     a2=np.sum(mesh_size_tab)
  51     a3=nbMeshes
  52     b1=np.dot(error_tab,mesh_size_tab)
  53     b2=np.sum(error_tab)
  54
  55     det=a1*a3-a2*a2
  56     assert det!=0, 'test_validation2DVF_checkerboard() : Make sure you use distinct meshes and at least two meshes'
  57     a=( a3*b1-a2*b2)/det
  58     b=(-a2*b1+a1*b2)/det
  59
  60     print "FV for diffusion on 2D checkerboard meshes : scheme order is ", -a
  61     assert abs(a+0.5475)<0.001 #The scheme is not converging
  62
  63     # Plot of convergence curve
  64     plt.close()
  65     plt.plot(mesh_size_tab, error_tab, label='log(|numerical-exact|)')
  66     plt.plot(mesh_size_tab, a*np.array(mesh_size_tab)+b,label='least square slope : '+'%.3f' % a)
  67     plt.legend()
  68     plt.xlabel('log(sqrt(number of cells))')
  69     plt.ylabel('log(error)')
  70     plt.title('Convergence of finite volumes for \n the diffusion equation on 2D checkerboard meshes')
  71     plt.savefig(mesh_name+"_2DDiffusionVF_ConvergenceCurve.png", dpi='figure')
  72
  73     # Plot of computational time
  74     plt.close()
  75     plt.plot(mesh_size_tab, time_tab, label='log(cpu time)')
  76     plt.legend()
  77     plt.xlabel('log(sqrt(number of cells))')
  78     plt.ylabel('log(cpu time)')
  79     plt.title('Computational time of finite volumes for \n the diffusion equation on 2D checkerboard meshes')
  80     plt.savefig(mesh_name+"_2DDiffusionVF_ComputationalTime.png", dpi='figure')
  81
  82     plt.close('all')
  83
  84     convergence_synthesis["Mesh_names"]=meshList
  85     convergence_synthesis["Mesh_type"]=meshType
  86     convergence_synthesis["Mesh_path"]=mesh_path
  87     convergence_synthesis["Mesh_description"]=mesh_name
  88     convergence_synthesis["Mesh_sizes"]=[10**x for x in mesh_size_tab]
  89     convergence_synthesis["Space_dimension"]=2
  90     convergence_synthesis["Mesh_dimension"]=2
  91     convergence_synthesis["Mesh_cell_type"]="Squares"
  92     convergence_synthesis["Errors"]=[10**x for x in error_tab]
  93     convergence_synthesis["Scheme_order"]=-a
  94     convergence_synthesis["Test_color"]=testColor
  95     convergence_synthesis["Computational_time"]=end-start
  96
  97     with open('Convergence_Diffusion_2DVF_'+mesh_name+'.json', 'w') as outfile:
  98         json.dump(convergence_synthesis, outfile)
  99
 100 if __name__ == """__main__""":
 101     test_validation2DVF_checkerboard()