Interpolate nonmatching mesh

The dolfin project or interpolate functions can not handle interpolation or projection from a FunctionSpace in one mesh to a FunctionSpace on a different mesh, at least not in parallel. Using the interpolate_nonmatching_mesh function this is now possible.

mesh1 = UnitSquareMesh(16, 16)
V1 = FunctionSpace(mesh1, 'CG', 2)
u1 = interpolate(Expression("sin(pi*x[0])*cos(pi*x[1])"), V1)
# Create a new _different_ mesh and FunctionSpace
mesh2 = UnitSquareMesh(10, 10)
x = mesh2.coordinates()
x[:, :] = x[:, :] * 0.5 + 0.25
V2 = FunctionSpace(mesh2, 'CG', 1)
u2 = interpolate_nonmatching_mesh(u1, V2)

The regular dolfin interpolate routine can handle this same interpolation problem, but only using one single processor. The code shown here works in parallel as well and as such it can be used for large scale applications. A ParaView plot of both u1 and u2 is shown below, where the colorscale has been reversed for the smaller mesh:

Interpolation from the small mesh onto the larger can be handled by dolfin's interpolate by setting parameters['allow_extrapolation'] = True. However, this will then extrapolate the solution from inside the small domain to the outside. Using interpolate_nonmatching_mesh the solution is simply set to zero outside the domain we are interpolating from:

u3 = interpolate_nonmatching_mesh(u2, V1)

leads to