[petsc-users] Questions about PCPATCH

[Lawrence Mitchell]

On Wed, 20 Sept 2023 at 12:17, Ce Qin <qince168 at gmail.com> wrote:
>
> Dear all,
>
> I am currently implementing a multigrid solver for Maxwell's equations in 3D.
> The AFW smoother has excellent convergence properties for Maxwell's equations. I
> noticed that PCPATCH provides such types of smoothers. However, I am using the
> deal.II library to build the patches. PCPATCH seems only to support the PETSc
> DMPlex data structure. Is there a way to use PCPATCH with user defined patches?

When we implemented, we didn't have a better idea about the callback
structure. If you can shoe-horn into the API PCPatch provides, then it
can work, but I guess deal.II doesn't use DMPlex for its mesh
management, so I don't think PCPatch is going to give you that much.

> Besides, I found that we can also use PCASM with user defined subdomains.
> Is there any performance difference between PCPATCH and PCASM?

For PCASM you have to assemble the global matrix and then extract the
subdomains, which might be expensive (in theory, pcpatch has a low
memory mode where you only assemble and factor one patch at a time,
but in most cases where you're using it, it's slower).

There are some other small optimisations in pcpatch that could be
ported to PCASM for small patches (for example, there's a mode where
the patch solver is just the application of an already factored
matrix, so you don't go through the KSP/PC/MatSolve callstack), but we
didn't do it.

But it likely depends a bit on your problem too (with pcpatch you
effectively assemble the operator twice if you're using sparse
matrices, rather than matrix-free, so that can be a bit more
expensive).

In summary: give it a go with PCASM.

Lawrence