[petsc-users] Help with ML/BoomerAMG

[Jed Brown]

Gaetan Kenway <gaetank at gmail.com> writes:

> Hello
>
> I am the process of trying out some of the multigrid functionality in PETSc
> and not having much luck. The simple system I am trying to solve is adjoint
> system of equations resulting from the finite volume discretization of the
> Euler equation on a 147,456 cell mesh resulting in a linear system of
> equations of size 5*147,456=737280. All of the test are done on a single
> processor and use petsc-3.2-p7.

Is this steady-state Euler?  Exterior or recirculating flow?
Conservative variables?  What Mach number?

The heuristics used in algebraic multigrid do not work for hyperbolic
systems like Euler.  There has been some research, but the multigrid
efficiency that we enjoy for elliptic problems continues to elude us.

For low Mach number, we can build preconditioners based on splitting,
reducing to an elliptic solve in the pressure space (changing variables
in the preconditioner if you use conservative variables for the full
problem).  Otherwise, we're currently stuck with geometric multigrid if
we want significant coarse-grid acceleration.  With finite volume
methods, this is done by agglomeration, leading to large cells with many
faces, but that exactly preserve the conservation statement of the
fine-grid problem.

The implementation effort required for such methods is why it's still
popular to use one-level domain decomposition.