Interpolating Test Function between Mismatched Meshes

[volkerk]

A working but propably very slow way to do this is setting up a function to act as the test function and assembling multiple vectors:

from dolfin import *

mesh_coarse = UnitSquareMesh(2, 2)
mesh_fine = refine(mesh_coarse)

coarse_space = FunctionSpace(mesh_coarse,"CG",1)
fine_space = FunctionSpace(mesh_fine,"CG",1)

fine_trial = TestFunction(fine_space)

A = []
for dof in range(coarse_space.dim()):
    coarse_test = Function(coarse_space)
    coarse_test.vector()[dof] = 1
    coarse_test_interpolated = interpolate(coarse_test, fine_space)
    assert( near( assemble( coarse_test**2 * dx ), assemble( coarse_test_interpolated**2 * dx ) ) )
    A.append( assemble(coarse_test_interpolated*fine_trial*dx ) )

print(A[0][:])

This post

How to create a Matrix (dolfin.cpp.la.Matrix) from Vectors (dolfin.cpp.la.Vector)?

As always, you should second-guess any procedure that results in a dense matrix, but, if it’s really necessary, one approach could be the following: from dolfin import * from petsc4py import PETSc from numpy import array # Get some dolfin.cpp.la.Vector objects: mesh = UnitIntervalMesh(10) V = FunctionSpace(mesh,"DG",0) v = TestFunction(V) v1 = assemble(Constant(1.0)*v*dx) v2 = assemble(Constant(2.0)*v*dx) v3 = assemble(Constant(3.0)*v*dx) # Put them all into a NumPy matrix: npMat = array([v1.…

describes how you can get a matrix from these vectors. You may have to transpose the matrix.

Note also that this works for this example, as the function spaces on the fine and coarse mesh are hierarchical, and thus the interpolated function acting as test function has the same shape as the original function (see the heuristic assert() test in the loop).