[petsc-users] How to speed up geometric multigrid

[Barry Smith]

On Oct 2, 2013, at 12:28 AM, Jed Brown <jedbrown at mcs.anl.gov> wrote:

> "Mark F. Adams" <mfadams at lbl.gov> 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