Assembling multilinear form from two function spaces

Question

Is it possible to assemble a multilinear form involving functions from different function spaces?
What I would like to do is something along these lines:

mesh = Mesh('mesh.xml')
bmesh = BoundaryMesh(mesh)
V = FunctionSpace(mesh, 'CG', 1)
V_b = FunctionSpace(bmesh, 'CG', 1)
f1 = TrialFunction(V)
f2 = TestFunction(V_b)
ml_form = f1 * f2 * ds
ml_tensor = assemble(ml_form)

where the integration is supposed to be carried out on the surface of the mesh (i.e. the ds of mesh, but the dx of bmesh), and the resulting tensor will not be square.

Is there a way to do this? Obviously the above code cannot work in this form...

Answer 1

Generally, yes, can assemble bilinear forms on $U \times V$ where $U$ and $V$ are different spaces, thus resulting in generally rectangular matrices. Nevertheless, for now you cannot currently combine different meshes in a single form. Removing this deficiency is one of highest priority of the developers.

Comments

Jan, Is it possible to project one Function space into another one to assembler forms
with different meshes?