[petsc-users] How to speed up geometric multigrid

[Dave May]

And why are you fixed on 5 levels?

On Wednesday, 2 October 2013, Barry Smith wrote:

>
>   Something is wrong, you should be getting better convergence. Please
> answer my other email.
>
>
> On Oct 2, 2013, at 1:10 PM, Michele Rosso <mrosso at uci.edu <javascript:;>>
> wrote:
>
> > Thank you all for your contribution.
> > So far the fastest solution is still the initial one proposed by Jed in
> an earlier round:
> >
> > -ksp_atol 1e-9  -ksp_monitor_true_residual  -ksp_view  -log_summary
> -mg_coarse_pc_factor_mat_solver_package superlu_dist
> > -mg_coarse_pc_type lu    -mg_levels_ksp_max_it 3 -mg_levels_ksp_type
> richardson  -options_left -pc_mg_galerkin
> > -pc_mg_levels 5  -pc_mg_log  -pc_type mg
> >
> > where I used  -mg_levels_ksp_max_it 3  as Barry suggested instead of
>  -mg_levels_ksp_max_it 1.
> > I attached the diagnostics for this case. Any further idea?
> > Thank you,
> >
> > Michele
> >
> >
> > On 10/01/2013 11:44 PM, Barry Smith wrote:
> >> On Oct 2, 2013, at 12:28 AM, Jed Brown <jedbrown at mcs.anl.gov<javascript:;>>
> wrote:
> >>
> >>> "Mark F. Adams" <mfadams at lbl.gov <javascript:;>> writes:
> >>>> run3.txt uses:
> >>>>
> >>>> -ksp_type richardson
> >>>>
> >>>> This is bad and I doubt anyone recommended it intentionally.
> >>    Hell this is normal multigrid without a Krylov accelerator. Under
> normal circumstances with geometric multigrid this should be fine, often
> the best choice.
> >>
> >>> I would have expected FGMRES, but Barry likes Krylov smoothers and
> >>> Richardson is one of a few methods that can tolerate nonlinear
> >>> preconditioners.
> >>>
> >>>> You also have, in this file,
> >>>>
> >>>> -mg_levels_ksp_type gmres
> >>>>
> >>>> did you or the recommenders mean
> >>>>
> >>>> -mg_levels_ksp_type richardson  ???
> >>>>
> >>>> you are using gmres here, which forces you to use fgmres in the outer
> solver.  This is a safe thing to use you if you apply your BCa
> symmetrically with a low order discretization then
> >>>>
> >>>> -ksp_type cg
> >>>> -mg_levels_ksp_type richardson
> >>>> -mg_levels_pc_type sor
> >>>>
> >>>> is what I'd recommend.
> >>> I thought that was tried in an earlier round.
> >>>
> >>> I don't understand why SOR preconditioning in the Krylov smoother is so
> >>> drastically more expensive than BJacobi/ILU and why SOR is called so
> >>> many more times even though the number of outer iterations
> >>>
> >>> bjacobi: PCApply              322 1.0 4.1021e+01 1.0 6.44e+09 1.0
> 3.0e+07 1.6e+03 4.5e+04 74 86 98 88 92 28160064317351226 20106
> >>> bjacobi: KSPSolve              46 1.0 4.6268e+01 1.0 7.52e+09 1.0
> 3.0e+07 1.8e+03 4.8e+04 83100100 99 99 31670065158291309 20800
> >>>
> >>> sor:     PCApply             1132 1.0 1.5532e+02 1.0 2.30e+10 1.0
> 1.0e+08 1.6e+03 1.6e+05 69 88 99 88 93 21871774317301274 18987
> >>> sor:     KSPSolve             201 1.0 1.7101e+02 1.0 2.63e+10 1.0
> 1.1e+08 1.8e+03 1.7e+05 75100100 99 98 24081775248221352 19652
> >>
> >
> > <best.txt>
>
>
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