This is really helpful, Jed! Thanks, Manav
> On Oct 29, 2018, at 1:57 PM, Jed Brown <j...@jedbrown.org> wrote: > > Manav Bhatia <bhatiama...@gmail.com> writes: > >> I am experimenting with the threshold parameter. >> >> As described in the manual: >> https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/PC/PCGAMGSetThreshold.html >> >> <https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/PC/PCGAMGSetThreshold.html> >> >> >> “ Conversely reducing the threshold increases the rate of coarsening >> (aggressive coarsening) and thereby reduces the complexity of the coarse >> grids, and generally results in slower solver converge rates." >> >> >> I did some experimentation for my problem: >> >> 1) -pc_mg_levels 3 -mg_levels_ksp_max_it 3 -pc_gamg_square_graph 1 >> -pc_gamg_threshold 0 : 22 KSP iterations, 39 seconds >> 2) -pc_mg_levels 3 -mg_levels_ksp_max_it 3 -pc_gamg_square_graph 1 >> -pc_gamg_threshold 0.5 : Did not converge in over 1000 KSP iterations > > 0.5 is enormous and likely results in "weird" aggregates. Try 0.001 to > 0.05 for example. You can see the coarsening rate and grid complexity > in -ksp_view output. > >> According to the manual reducing the threshold value would result in slower >> convergence rates. However, I am observing opposite behavior. >> >> Is this problem specific? Or maybe I am misunderstanding something here. >> >> Also, I am assuming that the threshold refers to some parameter in the >> connectivity graph, which is independent of the entries in the matrix. So, >> the value of threshold is independent of the magnitudes of the entries in >> the matrix (?). > > Yeah, the standard strength measure is > > |a_{ij}| / sqrt(|a_{ii}| |a_{jj}|) > >> I would appreciate some guidance here. >> >> Regards, >> Manav >> >>> On Oct 29, 2018, at 1:03 PM, Jed Brown <j...@jedbrown.org> wrote: >>> >>> Manav Bhatia <bhatiama...@gmail.com> writes: >>> >>>> I also observed that the number of KSP iterations increases with an >>>> increase in the levels of AMG. Is this true, in general, for all/most >>>> applications? >>> >>> Adding levels replaces a direct solve with a deeper V-cycle. When MG is >>> behaving well, this makes little difference because the coarse >>> approximations are no worse than the approximations made in the first >>> coarsening (from fine level to first coarsened level). But there are >>> many stubborn problems for which it does hurt, as you have seen.
