[petsc-users] Multigrid

[Karthik Duraisamy]

Hello Barry,

    Thank you for your super quick response. I have attached the output of ksp_view and it is practically the same as that when I don't use PCMG. The part I don't understand is how PCMG able to function at the zero grid level and still produce a much better convergence than when using the default PC. Is there any additional smoothing or interpolation going on?

    Also, for Algebraic Multigrid, would you recommend BoomerAMG or ML ?

Best regards,
Karthik.

 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_)     8 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=1, initial guess is zero
      tolerances:  relative=1e-05, absolute=1e-50, divergence=10000
      left preconditioning
      using PRECONDITIONED norm type for convergence test
    PC Object:    (mg_levels_0_)     8 MPI processes
      type: bjacobi
        block Jacobi: number of blocks = 8
        Local solve is same for all blocks, in the following KSP and PC objects:
      KSP Object:      (mg_levels_0_sub_)       1 MPI processes
        type: preonly
        maximum iterations=10000, 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_sub_)       1 MPI processes
        type: ilu
          ILU: out-of-place factorization
          0 levels of fill
          tolerance for zero pivot 1e-12
          using diagonal shift to prevent zero pivot
          matrix ordering: natural
          factor fill ratio given 1, needed 1
            Factored matrix follows:
              Matrix Object:               1 MPI processes
                type: seqaij
                rows=9015, cols=9015
                package used to perform factorization: petsc
                total: nonzeros=517777, allocated nonzeros=517777
                total number of mallocs used during MatSetValues calls =0
                  using I-node routines: found 3476 nodes, limit used is 5
        linear system matrix = precond matrix:
        Matrix Object:         1 MPI processes
          type: seqaij
          rows=9015, cols=9015
          total: nonzeros=517777, allocated nonzeros=517777
          total number of mallocs used during MatSetValues calls =0
            using I-node routines: found 3476 nodes, limit used is 5
      linear system matrix = precond matrix:
      Matrix Object:       8 MPI processes
        type: mpiaij
        rows=75000, cols=75000
        total: nonzeros=4427800, allocated nonzeros=4427800
         total number of mallocs used during MatSetValues calls =0
          using I-node (on process 0) routines: found 3476 nodes, limit used is 5
  linear system matrix = precond matrix:
  Matrix Object:   8 MPI processes
    type: mpiaij
    rows=75000, cols=75000
    total: nonzeros=4427800, allocated nonzeros=4427800
    total number of mallocs used during MatSetValues calls =0
      using I-node (on process 0) routines: found 3476 nodes, limit used is 5



----- Original Message -----
From: "Barry Smith" <bsmith at mcs.anl.gov>
To: "PETSc users list" <petsc-users at mcs.anl.gov>
Sent: Tuesday, May 1, 2012 1:39:26 PM
Subject: Re: [petsc-users] Multigrid


On May 1, 2012, at 3:37 PM, Karthik Duraisamy wrote:

> Hello,
> 
>        I have been using PETSc for a couple of years with good success, but lately as my linear problems have become stiffer (condition numbers of the order of 1.e20), I am looking to use better preconditioners. I tried using PCMG with all the default options (i.e., I just specified my preconditioner as PCMG and did not add any options to it) and I am immediately seeing better convergence. 
> 
>        What I am not sure of is why? I would like to know more about the default parameters (the manual is not very explicit) and more importantly, want to know why it is working even when I haven't specified any grid levels and coarse grid operators. Any
> help in this regard will be appreciated.

   First run with -ksp_view to see what solver it is actually using.

   Barry

> 
>        Also, ultimately I want to use algebraic multigrid so is PCML a better option than BoomerAMG? I tried BoomerAMG with mixed results.
> 
> Thanks,
> Karthik
> 
> 
> 
> -- 
> 
> =======================================
> Karthik Duraisamy
> Assistant Professor (Consulting)
> Durand Building Rm 357
> Dept of Aeronautics and Astronautics
> Stanford University
> Stanford CA 94305
> 
> Phone: 650-721-2835
> Web:     www.stanford.edu/~dkarthik
> =======================================