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

[Barry Smith]

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