MG question

Matthew Knepley knepley at
Wed Feb 27 13:40:59 CST 2008

On Wed, Feb 27, 2008 at 1:31 PM,  <jens.madsen at> wrote:
> Hi
> I hope that this question is not outside the scope of this mailinglist.
> As far as I understand PETSc uses preconditioned GMRES(or another KSP
> method) as pre- and postsmoother on all multigrid levels? I was just

This is the default. However, you can use any combination of KSP/PC on any
given level with options. For instance,

  -mg_level_ksp_type richardson -mg_level_pc_type sor

gives "regulation" MG. We default to GMRES because it is more robust.

> wondering why and where in the literature I can read about that method? I
> thought that a fast method would be to use MG (with Gauss-Seidel RB/zebra
> smothers) as a preconditioner for GMRES? I have looked at papers written by
> Oosterlee etc.

In order to prove something about GMRES/MG, you would need to prove something
about the convergence of GMRES on the operators at each level. Good luck. GMRES
is the enemy of all convergence proofs. See paper by Greenbaum, Strakos, & Ptak.
If SOR works, great and it is much faster. However, GMRES/ILU(0) tends
to be more


> Kind Regards
What most experimenters take for granted before they begin their
experiments is infinitely more interesting than any results to which
their experiments lead.
-- Norbert Wiener

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