Assemble vector?

Question

I'm trying to integrate a vector function:

V = VectorFunctionSpace(mesh, 'Lagrange', 1)
f = Function(V)
# do stuff that defines f
result = assemble(f * dx)

I would have hoped that this would give me a three element result vector. Instead, it gives me an error:

UFLException: Trying to integrate expression of rank 1 with free indices ().

Evaluating the components one-by-one works fine:

result = [ assemble(f[0] * dx), assemble(f[1] * dx), assemble(f[2]* dx) ]

Is there a way to avoid the repeated calls to assemble?

Answer 1

You could do like this:

V = VectorFunctionSpace(mesh, 'Lagrange', 1)
R = VectorFunctionSpace(mesh, 'R', 0)
f = Function(V)
c = TestFunction(R)
result = assemble(dot(f, c)*dx)

Comments

Thanks! Could you explain how/why this works?

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It's explained here http://fenicsproject.org/pipermail/fenics/2013-July/000429.html

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Be advised however that Real spaces can lead, with the current implementation of dolfin (Jan 2014), to very bad performances with big meshes. See the thread starting at http://fenicsproject.org/pipermail/fenics/2013-September/000526.html and the follow-up thread http://fenicsproject.org/pipermail/fenics/2013-October/000657.html

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I don't think it will be case here. This happens for mixed spaces with R-space when reordering/insertion with dense row/column is costly. Here R-space is just a placeholder for small amount of DOFs. Nevertheless, I did not test it.