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_right_triangles():
  11     start = time.time()
  12     ### 2D FV right triangles mesh
  13     meshList=[10,20,50,100,150,200]
  14     #meshList=['squareWithRightTriangles_0','squareWithRightTriangles_1','squareWithRightTriangles_2','squareWithRightTriangles_3','squareWithRightTriangles_4','squareWithTriangles_5']
  15     mesh_path='../../../ressources/2DRightTriangles/'
  16     meshType="Regular_right_triangles"
  17     testColor="Green"
  18     nbMeshes=len(meshList)
  19     error_tab=[0]*nbMeshes
  20     mesh_size_tab=[0]*nbMeshes
  21     mesh_name='squareWithRightTriangles'
  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 nx in meshList:
  32         my_mesh=cdmath.Mesh(0,1,nx,0,1,nx,1)
  33         my_mesh.setGroupAtPlan(1,0,eps,"Bord1")
  34         my_mesh.setGroupAtPlan(0,0,eps,"Bord2")
  35         my_mesh.setGroupAtPlan(1,1,eps,"Bord3")
  36         my_mesh.setGroupAtPlan(0,1,eps,"Bord4")
  37         error_tab[i], mesh_size_tab[i], diag_data[i], min_sol_num, max_sol_num, time_tab[i] =FiniteVolumes2DPoisson_SQUARE.solve(my_mesh,str(nx)+'x'+str(nx),resolution,meshType,testColor)
  38 #        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)
  39         assert min_sol_num>-0.01
  40         assert max_sol_num<1.4
  41         plt.plot(curv_abs, diag_data[i], label= str(mesh_size_tab[i]) + ' cells')
  42         error_tab[i]=log10(error_tab[i])
  43         time_tab[i]=log10(time_tab[i])
  44         mesh_size_tab[i] = 0.5*log10(mesh_size_tab[i])
  45         i=i+1
  46
  47     end = time.time()
  48
  49     # Plot over diagonal line
  50     plt.legend()
  51     plt.xlabel('Position on diagonal line')
  52     plt.ylabel('Value on diagonal line')
  53     plt.title('Plot over diagonal line for finite volumes \n for Laplace operator on 2D right triangles meshes')
  54     plt.savefig(mesh_name+"_2DPoissonFV_PlotOverDiagonalLine.png")
  55
  56     # Least square linear regression
  57     # Find the best a,b such that f(x)=ax+b best approximates the convergence curve
  58     # The vector X=(a,b) solves a symmetric linear system AX=B with A=(a1,a2\\a2,a3), B=(b1,b2)
  59     a1=np.dot(mesh_size_tab,mesh_size_tab)
  60     a2=np.sum(mesh_size_tab)
  61     a3=nbMeshes
  62     b1=np.dot(error_tab,mesh_size_tab)
  63     b2=np.sum(error_tab)
  64
  65     det=a1*a3-a2*a2
  66     assert det!=0, 'test_validation2DVF_right_triangles() : Make sure you use distinct meshes and at least two meshes'
  67     a=( a3*b1-a2*b2)/det
  68     b=(-a2*b1+a1*b2)/det
  69
  70     print( "FV on 2D right triangles mesh : scheme order is ", -a)
  71     assert abs(a+0.04)<0.01
  72
  73     # Plot of convergence curve
  74     plt.close()
  75     plt.plot(mesh_size_tab, error_tab, label='log(|numerical-exact|)')
  76     plt.plot(mesh_size_tab, a*np.array(mesh_size_tab)+b,label='least square slope : '+'%.3f' % a)
  77     plt.legend()
  78     plt.plot(mesh_size_tab, error_tab)
  79     plt.xlabel('log(sqrt(number of cells))')
  80     plt.ylabel('log(error)')
  81     plt.title('Convergence of finite volumes for \n Laplace operator on 2D right triangles meshes')
  82     plt.savefig(mesh_name+"_2DPoissonFV_ConvergenceCurve.png")
  83
  84     # Plot of computational time
  85     plt.close()
  86     plt.plot(mesh_size_tab, time_tab, label='log(cpu time)')
  87     plt.legend()
  88     plt.xlabel('log(sqrt(number of cells))')
  89     plt.ylabel('log(cpu time)')
  90     plt.title('Computational time of finite volumes \n for Laplace operator on 2D right triangles meshes')
  91     plt.savefig(mesh_name+"_2DPoissonFV_ComputationalTime.png")
  92
  93     plt.close('all')
  94
  95     convergence_synthesis["Mesh_names"]=meshList
  96     convergence_synthesis["Mesh_type"]=meshType
  97     convergence_synthesis["Mesh_path"]=mesh_path
  98     convergence_synthesis["Mesh_description"]=mesh_name
  99     convergence_synthesis["Mesh_sizes"]=[10**x for x in mesh_size_tab]
 100     convergence_synthesis["Space_dimension"]=2
 101     convergence_synthesis["Mesh_dimension"]=2
 102     convergence_synthesis["Mesh_cell_type"]="Triangles"
 103     convergence_synthesis["Errors"]=[10**x for x in error_tab]
 104     convergence_synthesis["Scheme_order"]=-a
 105     convergence_synthesis["Test_color"]=testColor
 106     convergence_synthesis["Computational_time"]=end-start
 107
 108     with open('Convergence_Poisson_2DVF_'+mesh_name+'.json', 'w') as outfile:
 109         json.dump(convergence_synthesis, outfile)
 110
 111 if __name__ == """__main__""":
 112     test_validation2DVF_right_triangles()