[petsc-users] Multigrid

[Matthew Knepley]

On Tue, May 1, 2012 at 6:12 PM, Karthik Duraisamy <dkarthik at stanford.edu>wrote:

> 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?
>

You only included one output, so I have no way of knowing what you used
before. However, this is running GMRES/ILU.


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

They are different algorithms. Its not possible to say generally that one
is better. Try them both.

   Matt


> 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
> > =======================================
>
>


-- 
What most experimenters take for granted before they begin their
experiments is infinitely more interesting than any results to which their
experiments lead.
-- Norbert Wiener
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