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[Douglas Arnold <arnold@xxxxxxx>]

Using the default PETSc backend, we get an (UMFPACK) direct LU
factorization and solve via "Solve(A, x, b)".  But can we separate the
LU factorization from the backsolve, so that we can use the same
factorization with multiple right hand sides?  With the uBLAS backend,
this can be done with

  lusolver = LUSolver()
  lusolver.factorize(A)

and then

  lusolver.factorized_solve(x, b)

But these don't seem to be implemented with the PETSc backend.
Is there a way around this?