[petsc-users] GAMG parallel convergence sensitivity

[Jed Brown]

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