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

   1 import cdmath
   2 import FiniteVolumes2DPoisson_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(FiniteVolumes2DPoisson_SQUARE.test_desc)
   9
  10 def test_validation2DVF_equilateral_triangles():
  11     start = time.time()
  12     ### 2D FV equilateral triangles mesh
  13     #meshList=[5,20,50,100,200]
  14     meshList=['squareWithEquilateralTriangles5','squareWithEquilateralTriangles20','squareWithEquilateralTriangles50','squareWithEquilateralTriangles100','squareWithEquilateralTriangles200']
  15     mesh_path='../../../ressources/2DEquilateralTriangles/'
  16     meshType="Regular_equilateral_triangles"
  17     testColor="Green"
  18     nbMeshes=len(meshList)
  19     error_tab=[0]*nbMeshes
  20     mesh_size_tab=[0]*nbMeshes
  21     mesh_name='squareWithEquilateralTriangles'
  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     eps=1e-6;
  29     # Storing of numerical errors, mesh sizes and diagonal values
  30     #for filename in meshList:
  31     for filename in meshList:
  32         error_tab[i], mesh_size_tab[i], diag_data[i], min_sol_num, max_sol_num, time_tab[i] =FiniteVolumes2DPoisson_SQUARE.solve_file(mesh_path+filename,resolution,meshType,testColor)
  33         assert min_sol_num>-0.01
  34         assert max_sol_num<1.4
  35         plt.plot(curv_abs, diag_data[i], label= str(mesh_size_tab[i]) + ' cells')
  36         error_tab[i]=log10(error_tab[i])
  37         time_tab[i]=log10(time_tab[i])
  38         mesh_size_tab[i] = 0.5*log10(mesh_size_tab[i])
  39         i=i+1
  40
  41     end = time.time()
  42
  43     # Plot over diagonal line
  44     plt.legend()
  45     plt.xlabel('Position on diagonal line')
  46     plt.ylabel('Value on diagonal line')
  47     plt.title('Plot over diagonal line for finite volumes \n for Laplace operator on 2D equilateral triangles meshes')
  48     plt.savefig(mesh_name+"_2DPoissonFV_PlotOverDiagonalLine.png")
  49
  50     # Least square linear regression
  51     # Find the best a,b such that f(x)=ax+b best approximates the convergence curve
  52     # The vector X=(a,b) solves a symmetric linear system AX=B with A=(a1,a2\\a2,a3), B=(b1,b2)
  53     a1=np.dot(mesh_size_tab,mesh_size_tab)
  54     a2=np.sum(mesh_size_tab)
  55     a3=nbMeshes
  56     b1=np.dot(error_tab,mesh_size_tab)
  57     b2=np.sum(error_tab)
  58
  59     det=a1*a3-a2*a2
  60     assert det!=0, 'test_validation2DVF_equilateral_triangles() : Make sure you use distinct meshes and at least two meshes'
  61     a=( a3*b1-a2*b2)/det
  62     b=(-a2*b1+a1*b2)/det
  63
  64     print( "FV on 2D equilateral triangles mesh : scheme order is ", -a)
  65     assert abs(a+1.98)<0.01
  66
  67     # Plot of convergence curve
  68     plt.close()
  69     plt.plot(mesh_size_tab, error_tab, label='log(|numerical-exact|)')
  70     plt.plot(mesh_size_tab, a*np.array(mesh_size_tab)+b,label='least square slope : '+'%.3f' % a)
  71     plt.legend()
  72     plt.plot(mesh_size_tab, error_tab)
  73     plt.xlabel('log(sqrt(number of cells))')
  74     plt.ylabel('log(error)')
  75     plt.title('Convergence of finite volumes for \n Laplace operator on 2D equilateral triangles meshes')
  76     plt.savefig(mesh_name+"_2DPoissonFV_ConvergenceCurve.png")
  77
  78     # Plot of computational time
  79     plt.close()
  80     plt.plot(mesh_size_tab, time_tab, label='log(cpu time)')
  81     plt.legend()
  82     plt.xlabel('log(sqrt(number of cells))')
  83     plt.ylabel('log(cpu time)')
  84     plt.title('Computational time of finite volumes \n for Laplace operator on 2D equilateral triangles meshes')
  85     plt.savefig(mesh_name+"_2DPoissonFV_ComputationalTime.png")
  86
  87     plt.close('all')
  88
  89     convergence_synthesis["Mesh_names"]=meshList
  90     convergence_synthesis["Mesh_type"]=meshType
  91     convergence_synthesis["Mesh_path"]=mesh_path
  92     convergence_synthesis["Mesh_description"]=mesh_name
  93     convergence_synthesis["Mesh_sizes"]=[10**x for x in mesh_size_tab]
  94     convergence_synthesis["Space_dimension"]=2
  95     convergence_synthesis["Mesh_dimension"]=2
  96     convergence_synthesis["Mesh_cell_type"]="Triangles"
  97     convergence_synthesis["Errors"]=[10**x for x in error_tab]
  98     convergence_synthesis["Scheme_order"]=-a
  99     convergence_synthesis["Test_color"]=testColor
 100     convergence_synthesis["Computational_time"]=end-start
 101
 102     with open('Convergence_Poisson_2DVF_'+mesh_name+'.json', 'w') as outfile:
 103         json.dump(convergence_synthesis, outfile)
 104
 105 if __name__ == """__main__""":
 106     test_validation2DVF_equilateral_triangles()