Interpolation nonmatching mesh in parallel

With the function interpolate_nonmatching_mesh_any it is possible to interpolate from a Function on one mesh to a Function of the same space, but on a different mesh. An example for a Nedelec element is shown below.

    from dolfin import *
    from fenicstools import interpolate_nonmatching_mesh_any
    import numpy

    # Create two different meshes on the same domain
    mesh1 = UnitSquareMesh(2, 2)
    mesh2 = UnitSquareMesh(4, 4)

    V1 = FunctionSpace(mesh1, "Nedelec 1st kind H(curl)", 2)
    V2 = FunctionSpace(mesh2, "Nedelec 1st kind H(curl)", 2)

    f = Expression(("x[0]", "x[1]"))
    u1 = interpolate_nonmatching_mesh_any(f, V1)

    # Interpolate to nonmatching mesh
    u2 = interpolate_nonmatching_mesh_any(u1, V2)

    # Validation
    u3 = interpolate_nonmatching_mesh_any(f, V2)

    assert numpy.allclose(u2.vector().array(), u3.vector().array())

The interpolation function may also be used to interpolate between meshes of different dimensions. To illustrate, this code interpolates from a function in 3D to a 2D slice through the center of the 3D domain

    mesh1 = UnitCubeMesh(12, 12, 12)
    V1 = FunctionSpace(mesh1, "Nedelec 1st kind H(curl)", 2)
    f = Expression(("sin(x[0]*pi)", "cos(x[1]*pi)", "x[2]"))
    u1 = interpolate_nonmatching_mesh_any(f, V1)

    # Create a 2D unit square mesh from the boundary of mesh1
    mesh2 = BoundaryMesh(mesh1, "exterior")
    side = CellFunction("size_t", mesh2, 0)
    AutoSubDomain(lambda x: x[2] < 1e-8).mark(side, 1)
    mesh3 = SubMesh(mesh2, side, 1)
    x = mesh3.coordinates()
    x[:, 2] += 0.5

    # Interpolate from the 3D Function to the 2D Function
    V2 = FunctionSpace(mesh3, "Nedelec 1st kind H(curl)", 2)
    u2 = interpolate_nonmatching_mesh_any(u1, V2)

    plot(u1)
    plot(u2)
    interactive()