[petsc-users] [petsc-maint] Monolithic AMG with fieldsplit as smoother

Matthew Knepley knepley at gmail.com
Thu Jul 27 00:09:32 CDT 2023

On Thu, Jul 27, 2023 at 12:48 AM Jed Brown <jed at jedbrown.org> wrote:

> AMG is subtle here. With AMG for systems, you typically feed it elements
> of the near null space. In the case of (smoothed) aggregation, the coarse
> space will have a regular block structure with block sizes equal to the
> number of near-null vectors. You can use pc_fieldsplit options to select
> which fields you want in each split.
> However, AMG also needs a strength of connection and if your system is so
> weird you need to fieldsplit the smoothers (e.g., a saddle point problem or
> a hyperbolic system) then it's likely that you'll also need a custom
> strength of connection to obtain reasonable coarsening.

For this reason, sometimes GMG is easier for systems since you just



> Barry Smith <bsmith at petsc.dev> writes:
> >   See the very end of the section
> https://petsc.org/release/manual/ksp/#multigrid-preconditioners on how to
> control the smoothers (and coarse grid solve) for multigrid in PETSc
> including for algebraic multigrid.
> >
> >    So, for example, -mg_levels_pc_type fieldsplit would be the starting
> point. Depending on the block size of the matrices it may automatically do
> simple splits, you can control the details  of the fieldsplit
> preconditioner with -mg_levels_pc_fieldsplit_...  and the details for each
> split with -mg_levels_fieldsplit_....
> >
> >    See src/ksp/ksp/tutorials/ex42.c for example, usage
> >
> >    Feel free to ask more specific questions once you get started.
> >
> >> On Jul 26, 2023, at 9:47 PM, Michael Wick <michael.wick.1980 at gmail.com>
> wrote:
> >>
> >> Hello PETSc team:
> >>
> >> I wonder if the current PETSc implementation supports using AMG
> monolithically for a multi-field problem and using fieldsplit in the
> smoother.
> >>
> >> Thank you very much,
> >>
> >> Mike

What most experimenters take for granted before they begin their
experiments is infinitely more interesting than any results to which their
experiments lead.
-- Norbert Wiener

https://www.cse.buffalo.edu/~knepley/ <http://www.cse.buffalo.edu/~knepley/>
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