[petsc-users] Usage of AMG as preconditioner

[Jed Brown]

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.