[petsc-users] Multigrid

Karthik Duraisamy dkarthik at stanford.edu
Tue May 1 17:18:34 CDT 2012

```Hello,

Sorry (and thanks for the reply). I've attached the no multigrid case. I didn't include it because (at least to the untrained eye, everything looks the same).

Regards,
Karthik

KSP Object: 8 MPI processes
type: gmres
GMRES: restart=100, using Classical (unmodified) Gram-Schmidt Orthogonalization with no iterative refinement
GMRES: happy breakdown tolerance 1e-30
maximum iterations=1
using preconditioner applied to right hand side for initial guess
tolerances:  relative=1e-05, absolute=1e-50, divergence=1e+10
left preconditioning
using nonzero initial guess
using PRECONDITIONED norm type for convergence test
PC Object: 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:  (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:  (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

----- Original Message -----
From: "Matthew Knepley" <knepley at gmail.com>
To: "PETSc users list" <petsc-users at mcs.anl.gov>
Sent: Tuesday, May 1, 2012 3:15:14 PM
Subject: Re: [petsc-users] Multigrid

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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