[petsc-users] Usage of AMG as preconditioner

[Mark Adams]

As Jed says hyperbolic dominated systems are hard.

For geometric papers you can look at Jameson papers and Adams, Samtaney &
Brandt (MHD).

But be prepared to work. Good stuff but hard.


On Fri, Sep 28, 2018 at 12:42 PM Jed Brown <jed at jedbrown.org> wrote:

> Michael Werner <michael.werner at dlr.de> writes:
>
> > A low-Mach preconditioner might help with the current test cases,
> > however I also intend to apply this code to high-Mach number
> > flows, so I need to find a more general solution. Actually, the
> > high-Mach number applications are more important, since so far all
> > the low-Mach cases are small enough to be solved with direct
> > solvers.
> >
> > I was also thinking about using a geometric multigrid approach via
> > DMPlex. As far as I understood, hyperbolic problems are difficult
> > to solve with AMG because the solver isn't aware of the underlying
> > structure of the problem. Therefore I would think that a geometric
> > multigrid approach should produce better results, right? Do you
> > think it would be worthwile to implement a DMPlex, or would I
> > still run into the same problems?
>
> Agglomeration-based geometric multigrid with block relaxation is a
> common technique for unstructured compressible CFD, but there are a lot
> of subtleties.  See FUN3D papers (Diskin, Thomas, sometimes Brandt) for
> examples of this approach.
>
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