Introduce explicit interpolation operator instead of hidden interpolation

[Jan Blechta]

Following DOLFIN code

from dolfin import *

mesh1 = UnitIntervalMesh(1)
mesh2 = UnitIntervalMesh(2)

P1 = FiniteElement("P", mesh1.ufl_cell(), 1)
V2 = FunctionSpace(mesh2, P1)

u2 = Function(V2)
u2.vector()[:] = 1
DirichletBC(V2, 0, lambda x,b:b).apply(u2.vector())

print(assemble(u2*dx(mesh2)))  # Ok
print(assemble(u2*dx(mesh1)))  # Should raise

gives

0.5
0.0

which shows that hidden interpolation happens. (FFC generates code assuming u2 lives on ufl.FunctionSpace(mesh1, P1). This is not true and DOLFIN interpolates there by calling Function::restrict()). Arguably this should not happen behind the scene and the last line should raise. Current behaviour should be recovered by

# Explicit interpolation (gives current behaviour)
space_on_mesh1 = ufl.FunctionSpace(mesh1, P1)
interpolant_on_mesh1 = ufl.interpolate(u2, space_on_mesh1)
F = ufl.interpolate(interpolant_on_mesh1*dx(mesh1))
assert assemble(F) == 0

In conclusion ufl.interpolate(coefficient, space) needs to be added.

Furthermore, this operator will allow FC/FE library to implement further interpolation operators. FFC/DOLFIN currently has only interpolation from one mesh to another with the same element. Different elements are possible.