[petsc-dev] -pc_type gamg for vector PDE

[Jed Brown]

On Fri, Jan 20, 2012 at 08:19, Alexander Grayver <agrayver at gfz-potsdam.de>wrote:

> My initial motivation to try gamg was that paper:
> W.A. *Mulder*, A *multigrid solver for 3D* electromagnetic diffusion
>

This paper does entirely geometric coarse grids. You could use PCMG, but
you would have to write your own interpolation and restriction operators
(because even in the structured case, DMDA does not have specific support
for edge discretizations; you can use DMDA, but it won't automatically
build correct interpolants).

The smoother in this paper is node-centered overlapping relaxation. It
solves overlapping 6x6 problems (all edges connected to that node). I don't
know of a reliable way to extract these node connections from the matrix
alone, so you would have to implement this.

If you implement these two ingredients (interpolation and node-based
relaxation), then you can run the geometric multigrid method in this paper.


>
> Where it seems to work fine (on uniform grids only at least).
> I use MUMPS currently and it is very robust. It properly solves systems
> with extremely low \omega and \sigma for any stretched (which would 'kill'
> any multigrid I guess) grids.
> I don't expect iterative solvers to be that robust, but I would like to
> solve even simple models with ~uniform grid of the order 10^7
>
> So, I will try to look at HYPRE's approach for Maxwell equations.
>
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