[petsc-users] How to speed up geometric multigrid

[Michele Rosso]

Dave,

I am using a 2D decomposition, so if I increase the number of levels, I 
have to decrease the number of processors I am using
in order to have enough grid points per processor for the multigrid to work.

Michele

On 10/02/2013 03:05 PM, Dave May wrote:
> 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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