On Wed, Feb 27, 2008 at 2:22 PM, <jens.madsen at risoe.dk> wrote: > Ok > > Thanks Matthew and Barry > > First I solve 2d boundary value problems of size 512^2 - 2048^2. > > Typically either kind of problem(solve for phi) > > I) poisson type equation: > > \nabla^2 \phi(x,y) = f(x,y) > > II) > > \nabla \cdot (g(x,y) \nabla\phi(x,y)) = f(x,y) > > Successively with new f and g functions > > > Do you know where to read about the smoothing properties of GMRES and > CG? All refs that I find are only describing smoothing with GS-RB etc. > > My vague idea on how a fast solver is to use a (preconditioned ILU?) > krylov (CG for spd ie. problem I, GMRES for II)) method with additional > MG preconditioning(GS-RB smoother, Krylov solver on coarsest level)? > > As my problems are not that big I fear that I will get no MG speedup if > I use krylov methods as smoothers?
Well, you might need to prove things, but I would not worry about that first. It is so easy to code up, just run everything and see what actually works. Then sit down and try to show it. Matt > Kind Regards Jens > > > -----Original Message----- > From: owner-petsc-users at mcs.anl.gov > [mailto:owner-petsc-users at mcs.anl.gov] On Behalf Of Barry Smith > Sent: Wednesday, February 27, 2008 8:49 PM > To: petsc-users at mcs.anl.gov > Subject: Re: MG question > > > The reason we default to these "very strong" (gmres + ILU(0)) > smoothers is robustness, we'd rather have > the solver "just work" for our users and be a little bit slower than > have it often fail but be optimal > for special cases. > > Most of the MG community has a mental block about using Krylov > methods, this is > why you find few papers that discuss their use with multigrid. Note > also that using several iterations > of GMRES (with or without ILU(0)) is still order n work so you still > get the optimal convergence of > mutligrid methods (when they work, of course). > > Barry > > > On Feb 27, 2008, at 1:40 PM, Matthew Knepley wrote: > > > On Wed, Feb 27, 2008 at 1:31 PM, <jens.madsen at risoe.dk> 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 > > robust. > > > > Matt > > > >> 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 > > > > > -- 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
