matrix_coefficient.py

'''
   Matrix coefficient example

   How to run:
      python <arguments>

   Example of arguments:
      coefficient_example.py

   Description:  This example code demonstrates how to use matrix coefficient,
                 which is defiend in Python.

'''
import mfem.ser as mfem
import numpy as np

class sigma(mfem.MatrixPyCoefficient):
    def __init__(self, dim):
       mfem.MatrixPyCoefficient.__init__(self, dim)
    def EvalValue(self, x):
       return np.array([[0.1, 0.], [0., 10.]])
   
# create sample mesh for square shape
mesh = mfem.Mesh(10, 10, "TRIANGLE")

# create finite element function space
fec = mfem.H1_FECollection(1, mesh.Dimension())   # H1 order=1
fespace = mfem.FiniteElementSpace(mesh, fec)      

# 
ess_tdof_list = mfem.intArray()
ess_bdr = mfem.intArray([1]*mesh.bdr_attributes.Size())
fespace.GetEssentialTrueDofs(ess_bdr, ess_tdof_list)

# constant coefficient 
one = mfem.ConstantCoefficient(1.0)

# define Bilinear and Linear operator
a = mfem.BilinearForm(fespace)
a.AddDomainIntegrator(mfem.DiffusionIntegrator(sigma(2)))
a.Assemble()
b = mfem.LinearForm(fespace)
b.AddDomainIntegrator(mfem.DomainLFIntegrator(one))
b.Assemble()

# create gridfunction, which is where the solution vector is stored
x = mfem.GridFunction(fespace);
x.Assign(0.0)

# form linear equation (AX=B)
A = mfem.OperatorPtr()
B = mfem.Vector()
X = mfem.Vector()
a.FormLinearSystem(ess_tdof_list, x, b, A, X, B);
print("Size of linear system: " + str(A.Height()))

# solve it using PCG solver and store the solution to x
AA = mfem.OperatorHandle2SparseMatrix(A)
M = mfem.GSSmoother(AA)
mfem.PCG(AA, M, B, X, 1, 200, 1e-12, 0.0)
a.RecoverFEMSolution(X, b, x)

# extract vertices and solution as numpy array
verts = mesh.GetVertexArray()
sol = x.GetDataArray()

# plot solution using Matplotlib

import matplotlib.pyplot as plt
import matplotlib.tri as tri

triang = tri.Triangulation(verts[:,0], verts[:,1])

fig1, ax1 = plt.subplots()
ax1.set_aspect('equal')
tpc = ax1.tripcolor(triang, sol, shading='gouraud')
fig1.colorbar(tpc)
plt.show()