How to perform a matrix multiply

Question

I would like to construct something similar to a K M_L^{_1} K matrix. Is there a way of multiplying two spaces matrices to generate a third sparse matrix? Or is there some alternative method I should consider?

For background: I am using this in an eigenvalue solver. Solving in an outer product space is possible but inefficient.

Answer 1

There are tools to do this in fenicstools as well. Otherwise, it's quite straightforward to do it yourselves as Kent-Andrè suggests by, e.g.,

from dolfin import *
mesh = UnitSquareMesh(5, 5)
V = FunctionSpace(mesh, 'CG', 1)
A = assemble(TrialFunction(V)*TestFunction(V)*dx)
B = A.copy()
B._scale(2.)
am = as_backend_type(A).mat()
bm = as_backend_type(B).mat()
cm = am.matMult(bm)

# Now get it back into a dolfin matrix
C = Matrix(PETScMatrix(cm))
print C.getrow(0)

This works with development version, not quite sure about older versions.

Answer 2

There are tools that enable this in cbc.block. Furthermore,
the backends PETSC and Epetra have this functionality, but
you must cast the matrices to their underlying types and look up the
specific functions in the respective backends.