[petsc-users] Multigrid as a preconditioner

[coco at dmi.unict.it]

> Date: Fri, 17 Feb 2012 15:38:55 -0500
> From: Jed Brown <jedbrown at mcs.anl.gov>
> Subject: Re: [petsc-users] petsc-users Digest, Vol 38, Issue 41
> To: PETSc users list <petsc-users at mcs.anl.gov>
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> 	<CAM9tzSn+CaFbGRdRyc_bVQ8Wa1ACRn8LTRTg1EWxg0az9=YWEQ at mail.gmail.com>
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> On Fri, Feb 17, 2012 at 14:09, <coco at dmi.unict.it> wrote:
>
>> Indeed I would like to solve the whole linear system by a multigrid
>> approach and not by a lu factorization. Therefore I would like to use
>> -ksp_type richardson -pc_type mg.
>> In this case, the preconditioned problem P^(-1) (f-A x^n) is solved
>> exactly or it performs just a V-cycle iteration? In both cases, since I am
>> using a one-grid multigrid (just for debugging), it should anyway provide
>> the exact solution at the first iteration, but it is not so.
>>
>
> -pc_type mg with one level just applies a normal smoother. I've sometimes
> thought it should do a coarse-level solve instead, but I haven't messed
> with it. Barry, why doesn't it do a direct solve?
>

This explains why the residual decreases so slowly: because it applies  
the smoother instead of the coarse solver.

> In general -pc_type mg does one multigrid cycle (usually a V or W cycle).
> If you want to use multiple iterations, you can
>
> -pc_type ksp -ksp_pc_type mg
>
> which would use the default KSP (GMRES) as an iteration, preconditioned by
> multigrid. The "outer" problem will see the result of this converged
> iterative solve.

I've perfectly understood that. Thank you very much.
Armando