[petsc-users] Question concerning ilu and bcgs

[Sun, Hui]

Yes I've tried other solvers, gmres/ilu does not work, neither does bcgs/ilu. Here are the options:

-pc_type ilu -pc_factor_nonzeros_along_diagonal -pc_factor_levels 0 -pc_factor_reuse_ordering -ksp_ty\

pe bcgs -ksp_rtol 1e-6 -ksp_max_it 10 -ksp_monitor_short -ksp_view


Here is the output:

  0 KSP Residual norm 211292

  1 KSP Residual norm 13990.2

  2 KSP Residual norm 9870.08

  3 KSP Residual norm 9173.9

  4 KSP Residual norm 9121.94

  5 KSP Residual norm 7386.1

  6 KSP Residual norm 6222.55

  7 KSP Residual norm 7192.94

  8 KSP Residual norm 33964

  9 KSP Residual norm 33960.4

 10 KSP Residual norm 1068.54

KSP Object: 1 MPI processes

  type: bcgs

  maximum iterations=10, initial guess is zero

  tolerances:  relative=1e-06, absolute=1e-50, divergence=10000

  left preconditioning

  using PRECONDITIONED norm type for convergence test

PC Object: 1 MPI processes

  type: ilu

    ILU: out-of-place factorization

    ILU: Reusing reordering from past factorization

    0 levels of fill

    tolerance for zero pivot 2.22045e-14

    using diagonal shift on blocks to prevent zero pivot [INBLOCKS]

    matrix ordering: natural

    factor fill ratio given 1, needed 1

      Factored matrix follows:

        Mat Object:         1 MPI processes

          type: seqaij

          rows=62500, cols=62500

          package used to perform factorization: petsc

          total: nonzeros=473355, allocated nonzeros=473355

          total number of mallocs used during MatSetValues calls =0

            not using I-node routines

  linear system matrix = precond matrix:

  Mat Object:   1 MPI processes

    type: seqaij

    rows=62500, cols=62500

    total: nonzeros=473355, allocated nonzeros=7.8125e+06

    total number of mallocs used during MatSetValues calls =0

      not using I-node routines

Time cost: 0.307149,  0.268402,  0.0990018



________________________________
From: hong at aspiritech.org [hong at aspiritech.org]
Sent: Wednesday, February 18, 2015 7:49 AM
To: Sun, Hui
Cc: Matthew Knepley; petsc-users at mcs.anl.gov
Subject: Re: [petsc-users] Question concerning ilu and bcgs

 Have you tried other solvers, e.g., PETSc default gmres/ilu, bcgs/ilu etc.
The matrix is small. If it is ill-conditioned, then pc_type lu would work the best.

Hong

On Wed, Feb 18, 2015 at 9:34 AM, Sun, Hui <hus003 at ucsd.edu<mailto:hus003 at ucsd.edu>> wrote:
With options:

-pc_type hypre -pc_hypre_type pilut -pc_hypre_pilut_maxiter 1000 -pc_hypre_pilut_tol 1e-3 -ksp_type bcgs -ksp_rtol 1e-10 -ksp_max_it 10 -ksp_monitor_short -ksp_converged_reason -ksp_view

Here is the full output:


  0 KSP Residual norm 1404.62

  1 KSP Residual norm 88.9068

  2 KSP Residual norm 64.73

  3 KSP Residual norm 71.0224

  4 KSP Residual norm 69.5044

  5 KSP Residual norm 455.458

  6 KSP Residual norm 174.876

  7 KSP Residual norm 183.031

  8 KSP Residual norm 650.675

  9 KSP Residual norm 79.2441

 10 KSP Residual norm 84.1985

Linear solve did not converge due to DIVERGED_ITS iterations 10

KSP Object: 1 MPI processes

  type: bcgs

  maximum iterations=10, initial guess is zero

  tolerances:  relative=1e-10, absolute=1e-50, divergence=10000

  left preconditioning

  using PRECONDITIONED norm type for convergence test

PC Object: 1 MPI processes

  type: hypre

    HYPRE Pilut preconditioning

    HYPRE Pilut: maximum number of iterations 1000

    HYPRE Pilut: drop tolerance 0.001

    HYPRE Pilut: default factor row size

  linear system matrix = precond matrix:

  Mat Object:   1 MPI processes

    type: seqaij

    rows=62500, cols=62500

    total: nonzeros=473355, allocated nonzeros=7.8125e+06

    total number of mallocs used during MatSetValues calls =0

      not using I-node routines

Time cost: 0.756198,  0.662984,  0.105672



________________________________
From: Matthew Knepley [knepley at gmail.com<mailto:knepley at gmail.com>]
Sent: Wednesday, February 18, 2015 3:30 AM
To: Sun, Hui
Cc: petsc-users at mcs.anl.gov<mailto:petsc-users at mcs.anl.gov>
Subject: Re: [petsc-users] Question concerning ilu and bcgs

On Wed, Feb 18, 2015 at 12:33 AM, Sun, Hui <hus003 at ucsd.edu<mailto:hus003 at ucsd.edu>> wrote:
I have a matrix system Ax = b, A is of type MatSeqAIJ or MatMPIAIJ, depending on the number of cores.

I try to solve this problem by pc_type ilu and ksp_type bcgs, it does not converge. The options I specify are:

-pc_type hypre -pc_hypre_type pilut -pc_hypre_pilut_maxiter 1000 -pc_hypre_pilut_tol 1e-3 -ksp_type b\

cgs -ksp_rtol 1e-10 -ksp_max_it 1000 -ksp_monitor_short -ksp_converged_reason

1) Run with -ksp_view, so we can see exactly what was used

2) ILUT is unfortunately not a well-defined algorithm, and I believe the parallel version makes different decisions
    than the serial version.

  Thanks,

    Matt


The first a few lines of the output are:

  0 KSP Residual norm 1404.62

  1 KSP Residual norm 88.9068

  2 KSP Residual norm 64.73

  3 KSP Residual norm 71.0224

  4 KSP Residual norm 69.5044

  5 KSP Residual norm 455.458

  6 KSP Residual norm 174.876

  7 KSP Residual norm 183.031

  8 KSP Residual norm 650.675

  9 KSP Residual norm 79.2441

 10 KSP Residual norm 84.1985


This clearly indicates non-convergence. However, I output the sparse matrix A and vector b to MATLAB, and run the following command:

[L,U] = ilu(A,struct('type','ilutp','droptol',1e-3));

[ux1,fl1,rr1,it1,rv1] = bicgstab(A,b,1e-10,1000,L,U);


And it converges in MATLAB, with flag fl1=0, relative residue rr1=8.2725e-11, and iteration it1=89.5. I'm wondering how can I figure out what's wrong.


Best,

Hui



--
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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