[petsc-users] Preconditioner in multigrid solver

[Mark Adams]

You are giving all levels the same matrices (K & M). This code should not
work.

You are using LU as the smother. This will solve the problem immediately.
If MG is setup correctly then you will just have zero residuals and
corrections for the rest of the solve. And you set the relative tolerance
to 1.e-12, which will solve the problem with whatever smoother you use.

On Mon, Mar 11, 2019 at 10:42 AM Pietro Benedusi via petsc-users <
petsc-users at mcs.anl.gov> wrote:

> Dear Petsc team,
>
> I have a question about the setting up of a multigrid solver.
>
> I would like yo use a PCG smoother, preconditioned with a mass matrix,
> just on the fine level.
> But when add the line for preconditioning the CG with the mass matrix my
> MG diverges.
>
> I have implemented the same solver in MATLAB and it converges fine. Also
> the operators in PETSc are the same and the PCG applied directly on the
> problem (without MG) works the same in both PETSC and MATLAB.
>
> This is what I do in PETSC for 2 levels:
>
>
>     KSP space_solver;
>
>     ierr = KSPCreate(PETSC_COMM_WORLD,&space_solver);CHKERRQ(ierr);
>     ierr =
> KSPSetTolerances(space_solver,1e-8,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);CHKERRQ(ierr);
>
>     ierr = KSPSetOperators(space_solver, K, K);CHKERRQ(ierr);
>     ierr = KSPSetNormType(space_solver,  KSP_NORM_UNPRECONDITIONED
> );CHKERRQ(ierr);
>
>     ierr = KSPSetType(space_solver,KSPRICHARDSON);CHKERRQ(ierr);
>     ierr = KSPSetFromOptions(space_solver);CHKERRQ(ierr);
>     ierr = KSPSetUp(space_solver);CHKERRQ(ierr);
>
>     PC pcmg;
>     ierr = KSPGetPC(space_solver, &pcmg);
>     ierr = PCSetType(pcmg, PCMG);
>     ierr = PCMGSetLevels(pcmg,levels, NULL);CHKERRQ(ierr);
>     ierr = PCMGSetGalerkin(pcmg,PC_MG_GALERKIN_BOTH);CHKERRQ(ierr);
>
>     // smoothers
>     for (int i = 1; i < levels; ++i)
>     {
>         KSP smoother;
>         ierr = PCMGGetSmoother(pcmg, i, &smoother);CHKERRQ(ierr);
>
>             ierr = KSPSetType(smoother, KSPCG);CHKERRQ(ierr);
>             ierr = KSPSetOperators(smoother, K, M);CHKERRQ(ierr);
>
>
>             // ierr = KSPSetUp(smoother);CHKERRQ(ierr);
>
>             ierr =
> KSPSetTolerances(smoother,1e-12,PETSC_DEFAULT,PETSC_DEFAULT,s_p);CHKERRQ(ierr);
>
>             ierr = KSPSetNormType(smoother, KSP_NORM_NONE);CHKERRQ(ierr);
>
>             PC sm;
>             ierr = KSPGetPC(smoother, &sm);CHKERRQ(ierr);
>             ierr = PCSetType(sm,   PCLU);CHKERRQ(ierr);
>
>         ierr = PCMGSetInterpolation(pcmg, i,
> interpolation_operators[i-1]);CHKERRQ(ierr);
>     }
>
>
>
> I think there is a problem with the PETSc syntax, because I checked
> everything else and it is fine.
>
> Do you any ideas?
>
> Thank you very much!
>
> Best,
> Pietro
>
> ~~~~~~~~~~~~
> Pietro Benedusi
>
> Numerical Simulation in Science,
> Medicine and Engineering research group
> ICS, Institute of Computational Science
> USI, Università della Svizzera Italiana
> Via Giuseppe Buffi, 13
> CH - 6900 Lugano
> benedp at usi.ch
>
>
>
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