[petsc-dev] Should pARMS converge in parallel?

[Jose E. Roman]

El 16/03/2011, a las 21:37, Jed Brown escribió:

> Jose, thanks for adding pARMS.
> 
> I wonder if there is something wrong or if I'm just not using it correctly. I'm testing with ksp ex2 and it works fine in serial:
> 
> $ mpiexec -n 1 ./ex2 -m 50 -n 50 -ksp_converged_reason -pc_type parms
> Linear solve converged due to CONVERGED_RTOL iterations 10
> Norm of error 9.34118e-05 iterations 10
> 
> but it diverges in parallel:
> 
> $ mpiexec -n 2 ./ex2 -m 50 -n 50 -ksp_converged_reason -pc_type parms
> Linear solve did not converge due to DIVERGED_DTOL iterations 630
> Norm of error 3.12589e+06 iterations 630
> 
> I can make it "converge" by turning off restart, but the algebraic residual is actually large indicating that the preconditioner is actually nonlinear.
> 
> $ mpiexec -n 2 ./ex2 -m 50 -n 50 -ksp_converged_reason -pc_type parms -ksp_gmres_restart 1000
> Linear solve converged due to CONVERGED_RTOL iterations 81
> Norm of error 30.4982 iterations 81
> 
> Indeed, using FGMRES makes it converge
> 
> $ mpiexec -n 2 ./ex2 -m 50 -n 50 -ksp_converged_reason -pc_type parms -ksp_gmres_restart 1000 -ksp_type fgmres
> Linear solve converged due to CONVERGED_RTOL iterations 71
> Norm of error 0.000150845 iterations 71
> 
> but avoiding restarts is really critical
> 
> $ mpiexec -n 2 ./ex2 -m 50 -n 50 -ksp_converged_reason -pc_type parms -ksp_gmres_restart 30 -ksp_type fgmres
> Linear solve converged due to CONVERGED_RTOL iterations 771
> Norm of error 0.00202382 iterations 771
> 
> 
> What do you think about making the preconditioner linear by default? Is there a way to make it more tolerant of restarts, at least for such a simple problem (2D Laplace, 5-point stencil, uniform grid)?


Yes, I am aware of this. I added a note to the PCPARMS manpage stating that this preconditioner should be used with flexible methods (fgmres, gcr). But it is true that it would be better to default to something more stable. Maybe it is better to make RAS the default global method, instead of the Schur complement. Anyway, I will think about this, and also ask for advice to the pARMS developers.

Please feel free to add fixes that you consider useful.

Thanks.
Jose