[petsc-users] petsc-users Digest, Vol 38, Issue 41

[Jed Brown]

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?

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.
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