> On Oct 25, 2021, at 4:14 PM, Lionel CHENG <ch...@cerfacs.fr> wrote: > > The number of iterations at initialization (with rtol=1e-10) for both cg is > 11 for gmres and 12 for cg so roughly the same. Switching to bcgs the number > of iterations goes down to 6. So CG does not seem to fake it.
Yes, this sounds reasonable enough, maybe a touch of loss of orthogonality with the CG. > > Going back to the number of multi grid levels: how should I choose the number > of multi grid level depending on the problem at hand? How does GAMG evaluate > the number of grid levels required? Usually we just stick with the heuristic that GAMG comes up with. Maybe Mark has some better advice. Barry > > Lionel > > De: "Barry Smith" <bsm...@petsc.dev> > À: "cheng" <ch...@cerfacs.fr> > Cc: "petsc-users" <petsc-users@mcs.anl.gov> > Envoyé: Lundi 25 Octobre 2021 19:52:26 > Objet: Re: [petsc-users] Convergence on Axisymmetric Poisson matrix > > > > On Oct 25, 2021, at 1:01 PM, Lionel CHENG <ch...@cerfacs.fr > <mailto:ch...@cerfacs.fr>> wrote: > > We are running with the -ksp_norm_type unpreconditioned so the convergence is > done with the true residual for all the previous tests. I have a case with > 800 000 nodes that I have run for 200 iterations on 36 CPU cores (Intel Xeon > Gold 6140 - Skylake) and the Poisson solver gives me > > | Krylov Solver | Poisson running time [s] | > | `cg` | 3.9150E+00 | > | `gmres` | 4.6527E+00 | > | `bcgs` | 5.4416E+00 | > > Only the ksp_type has been changed in the following line: > mpirun -np $nb_cpu $exec -ksp_initial_guess_nonzero true \ > -ksp_type bcgs -ksp_norm_type unpreconditioned \ > -ksp_rtol 1e-10 \ > -pc_type gamg -mg_levels_pc_type sor -mg_levels_ksp_type richardson \ > > So CG is better than gmres (I have included the BiCGStab runs as well as I > have talked about them earlier). > > I was not interested in the runtime, I was interested in the convergence > behavior of CG vs GMRES for this problem. If CG is "faking it" then one would > see the GMRES converging faster (its residual would get smaller with fewer > iterations). > > Barry > > > I find it really weird that it behaves well with the preconditioner gamg I > can't really find an explanation why, it is really against my intuition. > > Apart from that I have also played around with the number of multi-grid > levels (-pc_mg_levels): > > | Number of MG levels | Poisson running time [s] | > | ------------------------------- | ------------------------ | > | 2 | 1.0385E+01 | > | 3 | 5.0015E+00 | > | 4 | 3.9150E+00 | > | 5 | 4.5015E+00 | > | 6 (default petsc for this case) | 4.5510E+00 | > > So that I find an optimum for 4 and not 6 as in the default PETSc > configuration and not specifying anything. How should I choose the number of > multi grid level depending on my problem? How does GAMG evaluate the number > of grid levels required? > > Lionel > > De: "Barry Smith" <bsm...@petsc.dev <mailto:bsm...@petsc.dev>> > À: "cheng" <ch...@cerfacs.fr <mailto:ch...@cerfacs.fr>> > Cc: "petsc-users" <petsc-users@mcs.anl.gov <mailto:petsc-users@mcs.anl.gov>> > Envoyé: Lundi 25 Octobre 2021 15:33:50 > Objet: Re: [petsc-users] Convergence on Axisymmetric Poisson matrix > > > Are you running with -ksp_monitor_true_residual to track the b - A*x > residual instead of just the preconditioned residual? > > GAMG definitely does not symmetrize the system but it is possible the > preconditioner results in the solve "not seeing" the unsymmetry during the > solution process and hence CG still converging; it would be dangerous to rely > on this in general I think. You could also run this case with GMRES to see if > that is better than the CG iterations. > > Barry > > On Oct 24, 2021, at 7:00 PM, Lionel CHENG <ch...@cerfacs.fr > <mailto:ch...@cerfacs.fr>> wrote: > > Hello everyone, > > I have some questions regarding a linear system that I am solving in my > plasma simulations. We have in this case a strongly non-symmetric matrix due > to the cylindrical coordinates for which the Laplacian cell is given by Fig. > 2 for two kinds of triangles. The different unstructured grids have from 300 > 000 nodes to 7 000 000 nodes. > > To my understanding, CG should not work properly on this matrix but > BiCGStab(1) should. When using SOR preconditioner it is indeed the case: > -ksp_type cg -pc_type sor yields solutions in 10 to 20 times more iterations > than -ksp_type bcgs -pc_type sor. > > However, when switching to -ksp_type cg -pc_type gamg the convergence is > great and even slightly better than -ksp_type bcgs. I do not understand how > CG is able to make the system converge when using GAMG although the matrix is > non-symmetric ? Is GAMG able to somehow symmetrize the system? I have the > impression that when using -pc_type gamg the Krylov solver is actually the > Pre-relaxation and post-relaxation of the initial grid, is that right? > > For GAMG since the matrix is non-symmetric -mg_levels_pc_type sor for and > -mg_levels_ksp_type richardson have been used and yields better results than > the original chebychev solver. > > Sincerely yours, > > Lionel Cheng > <main.pdf> > > > >
