[petsc-users] mg pre-conditioner default setup from PETSc-3.4 to PETSc-3.7

[Federico Golfrè Andreasi]

Dear PETSc users/developers,

I recently switched from PETSc-3.4 to PETSc-3.7 and found that some default
setup for the "mg" (mutigrid) preconditioner have changed.

We were solving a linear system passing, throug command line, the following
options:
-ksp_type      fgmres
-ksp_max_it    100000
-ksp_rtol      0.000001
-pc_type       mg
-ksp_view

The output of the KSP view is as follow:

KSP Object: 128 MPI processes
  type: fgmres
    GMRES: restart=30, using Classical (unmodified) Gram-Schmidt
Orthogonalization with no iterative refinement
    GMRES: happy breakdown tolerance 1e-30
  maximum iterations=100000, initial guess is zero
  tolerances:  relative=1e-06, absolute=1e-50, divergence=10000
  right preconditioning
  using UNPRECONDITIONED norm type for convergence test
PC Object: 128 MPI processes
  type: mg
    MG: type is MULTIPLICATIVE, levels=1 cycles=v
      Cycles per PCApply=1
      Not using Galerkin computed coarse grid matrices
  Coarse grid solver -- level -------------------------------
    KSP Object:    (mg_levels_0_)     128 MPI processes
      type: chebyshev
        Chebyshev: eigenvalue estimates:  min = 0.223549, max = 2.45903
        Chebyshev: estimated using:  [0 0.1; 0 1.1]
        KSP Object:        (mg_levels_0_est_)         128 MPI processes
          type: gmres
            GMRES: restart=30, using Classical (unmodified) Gram-Schmidt
Orthogonalization with no iterative refinement
            GMRES: happy breakdown tolerance 1e-30
          maximum iterations=10, initial guess is zero
          tolerances:  relative=1e-05, absolute=1e-50, divergence=10000
          left preconditioning
          using NONE norm type for convergence test
        PC Object:        (mg_levels_0_)         128 MPI processes
          type: sor
            SOR: type = local_symmetric, iterations = 1, local iterations =
1, omega = 1
          linear system matrix followed by preconditioner matrix:
          Matrix Object:           128 MPI processes
            type: mpiaij
            rows=279669, cols=279669
            total: nonzeros=6427943, allocated nonzeros=6427943
            total number of mallocs used during MatSetValues calls =0
              not using I-node (on process 0) routines
          Matrix Object:           128 MPI processes
            type: mpiaij
            rows=279669, cols=279669
            total: nonzeros=6427943, allocated nonzeros=6427943
            total number of mallocs used during MatSetValues calls =0
              not using I-node (on process 0) routines
      maximum iterations=1, initial guess is zero
      tolerances:  relative=1e-05, absolute=1e-50, divergence=10000
      left preconditioning
      using NONE norm type for convergence test
    PC Object:    (mg_levels_0_)     128 MPI processes
      type: sor
        SOR: type = local_symmetric, iterations = 1, local iterations = 1,
omega = 1
      linear system matrix followed by preconditioner matrix:
      Matrix Object:       128 MPI processes
        type: mpiaij
        rows=279669, cols=279669
        total: nonzeros=6427943, allocated nonzeros=6427943
        total number of mallocs used during MatSetValues calls =0
          not using I-node (on process 0) routines
      Matrix Object:       128 MPI processes
        type: mpiaij
        rows=279669, cols=279669
        total: nonzeros=6427943, allocated nonzeros=6427943
        total number of mallocs used during MatSetValues calls =0
          not using I-node (on process 0) routines
  linear system matrix followed by preconditioner matrix:
  Matrix Object:   128 MPI processes
    type: mpiaij
    rows=279669, cols=279669
    total: nonzeros=6427943, allocated nonzeros=6427943
    total number of mallocs used during MatSetValues calls =0
      not using I-node (on process 0) routines
  Matrix Object:   128 MPI processes
    type: mpiaij
    rows=279669, cols=279669
    total: nonzeros=6427943, allocated nonzeros=6427943
    total number of mallocs used during MatSetValues calls =0
      not using I-node (on process 0) routines

When I build the same program using PETSc-3.7 and run it with the same
options we observe that the runtime increases and the convergence is
slightly different. The output of the KSP view is:

KSP Object: 128 MPI processes
  type: fgmres
    GMRES: restart=30, using Classical (unmodified) Gram-Schmidt
Orthogonalization with no iterative refinement
    GMRES: happy breakdown tolerance 1e-30
  maximum iterations=100000, initial guess is zero
  tolerances:  relative=1e-06, absolute=1e-50, divergence=10000.
  right preconditioning
  using UNPRECONDITIONED norm type for convergence test
PC Object: 128 MPI processes
  type: mg
    MG: type is MULTIPLICATIVE, levels=1 cycles=v
      Cycles per PCApply=1
      Not using Galerkin computed coarse grid matrices
  Coarse grid solver -- level -------------------------------
    KSP Object:    (mg_levels_0_)     128 MPI processes
      type: chebyshev
        Chebyshev: eigenvalue estimates:  min = 0.223549, max = 2.45903
        Chebyshev: eigenvalues estimated using gmres with translations  [0.
0.1; 0. 1.1]
        KSP Object:        (mg_levels_0_esteig_)         128 MPI processes
          type: gmres
            GMRES: restart=30, using Classical (unmodified) Gram-Schmidt
Orthogonalization with no iterative refinement
            GMRES: happy breakdown tolerance 1e-30
          maximum iterations=10, initial guess is zero
          *tolerances:  relative=1e-12*, absolute=1e-50, divergence=10000.
          left preconditioning
          *using PRECONDITIONED norm type for convergence test*
      maximum iterations=2, initial guess is zero
      tolerances:  relative=1e-05, absolute=1e-50, divergence=10000.
      left preconditioning
      using NONE norm type for convergence test
    PC Object:    (mg_levels_0_)     128 MPI processes
      type: sor
        SOR: type = local_symmetric, iterations = 1, local iterations = 1,
omega = 1.
      linear system matrix followed by preconditioner matrix:
      Mat Object:       128 MPI processes
        type: mpiaij
        rows=279669, cols=279669
        total: nonzeros=6427943, allocated nonzeros=6427943
        total number of mallocs used during MatSetValues calls =0
          not using I-node (on process 0) routines
      Mat Object:       128 MPI processes
        type: mpiaij
        rows=279669, cols=279669
        total: nonzeros=6427943, allocated nonzeros=6427943
        total number of mallocs used during MatSetValues calls =0
          not using I-node (on process 0) routines
  linear system matrix followed by preconditioner matrix:
  Mat Object:   128 MPI processes
    type: mpiaij
    rows=279669, cols=279669
    total: nonzeros=6427943, allocated nonzeros=6427943
    total number of mallocs used during MatSetValues calls =0
      not using I-node (on process 0) routines
  Mat Object:   128 MPI processes
    type: mpiaij
    rows=279669, cols=279669
    total: nonzeros=6427943, allocated nonzeros=6427943
    total number of mallocs used during MatSetValues calls =0
      not using I-node (on process 0) routines

I was able to get a closer solution adding the following options:
-mg_levels_0_esteig_ksp_norm_type   none
-mg_levels_0_esteig_ksp_rtol        1.0e-5
-mg_levels_ksp_max_it               1

But I still can reach the same runtime we were observing with PETSc-3.4,
could you please advice me if I should specify any other options?

Thank you very much for your support,
Federico Golfre' Andreasi
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