[petsc-users] GAMG parallel convergence sensitivity

[Mark Lohry]

Thanks Jed, that's a good read.

I'm not too familiar with the Schur approach but I might give it a go in
the future. A primitive variable formulation is in the works though, at
least for pseudotime-derivative preconditioning.

It seems to me with these semi-implicit methods the CFL limit is still so
close to the explicit limit (that paper stops at 30), I don't really see
the purpose unless you're running purely incompressible? That's just my
ignorance speaking though. I'm currently running fully implicit for
everything, with CFLs around 1e3 - 1e5 or so.

On Wed, Mar 13, 2019 at 11:30 PM Jed Brown <jed at jedbrown.org> wrote:

> Mark Lohry via petsc-users <petsc-users at mcs.anl.gov> writes:
>
> > For what it's worth, I'm regularly solving much larger problems (1M-100M
> > unknowns, unsteady) with this discretization and AMG setup on 500+ cores
> > with impressively great convergence, dramatically better than ILU/ASM.
> This
> > just happens to be the first time I've experimented with this extremely
> low
> > Mach number, which is known to have a whole host of issues and generally
> > needs low-mach preconditioners, I was just a bit surprised by this
> specific
> > failure mechanism.
>
> A common technique for low-Mach preconditioning is to convert to
> primitive variables (much better conditioned for the solve) and use a
> Schur fieldsplit into the pressure space.  For modest time step, you can
> use SIMPLE-like method ("selfp" in PCFieldSplit lingo) to approximate
> that Schur complement.  You can also rediscretize to form that
> approximation.  This paper has a bunch of examples of choices for the
> state variables and derivation of the continuous pressure preconditioner
> each case.  (They present it as a classical semi-implicit method, but
> that would be the Schur complement preconditioner if using FieldSplit
> with a fully implicit or IMEX method.)
>
> https://doi.org/10.1137/090775889
>
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