Dear Michal,
You mean because once you apply an inhomogeneous Dirichlet condition on
the velocity you also get a contribution because the divergence is not
zero? You could work around that by applying a function in the whole
domain that satisfies the Dirichlet constraints and is divergence free,
in which case you should not get a contribution to right right hand side
of the divergence equation but only the momentum equation. On the other
hand, I'm not sure how easy it would be to construct such a function...
Regarding the workaround: It could work by the modification you
suggested, but we cannot really fix that in the library because the
operators are meant for linear operators and not affine ones. The
problematic issue is that there are some cases where you want to apply
an operator with a non-zero constraint and others where you don't. For
example, all Krylov solvers expect you to provide a matrix-vector for
the linear operator, not the affine one as you would get when you have
inhomogeneous constraints inside the mat-vec. In particular, I do not
really understand the part in your second post where you talk about the
vmult_interface_{up,down} functions because those are only used for
multigrid where the library always assumes to work on homogeneous problems.
I have not gone down this route and as far as I know, nobody else has
previously - including the matrix-based solvers we have available in
deal.II whose way of operation resembles the setup I described in my
previous post, but do it inside the
ConstraintMatrix::distribute_local_to_global call - so I cannot say how
much work that would be. We would be happy to provide a solution that is
generic if you find one, but I'm not sure I will be able to help much
along this direction.
Best,
Martin
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