On Feb 17, 2012, at 2:38 PM, Jed Brown wrote:
> 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?
1) Because MG is an accelerator of the basic smoother, MG is not a deccelerator
of a direct solver. That is the action of adding a coarser level is suppose to
improve the convergence of the solver.
2) Because if you used a direct solver and the user switched from one to two
levels they would be dismayed at the worsening of the convergence. If the user
ran a large problem on one level it would run out of memory.
3) I don't think there is really a "correct" abstract or practical answer to
which it should be (hence my two snide answers above) I am happy with the
current default
>
> 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.
You can use -pc_mg_multiplicative_cycles 2 to use 2 V or W cycles as the
preconditioner etc.
Barry
