[petsc-users] gamg and zero pivots

Barry Smith bsmith at mcs.anl.gov
Sun Sep 20 12:57:05 CDT 2015 

> On Sep 20, 2015, at 12:40 PM, Gideon Simpson <gideon.simpson at gmail.com> wrote:
> 
> Point taken.  So this comes back to something that I began asking about in a previous thread, but took a detour as you guys identified other problems with my code.  The issue is that I have a DMComposite with two blocks.  One block is of size two, and couples certain pieces of the second block, which is, morally, a vector valued semilinear elliptic equation.  Using grid sequencing, the guesses for the SNES are now quite good, but I’m struggling with the issue of preconditioning the linear problem.  The second block would, presumably, benefit from multigrid, but jacobi doesn’t do such a good job on that. At the same time, the first block, as discussed, has these zeros on the diagonal, and can’t use SOR.

   I think we answered this before, this is what PCFIELDSPLIT is for.  If the matrix looks like (logically if you reorder rows and columns)

(A   B )
(C  0  )

  you should use something like -ksp_type fgmres -pc_type fieldsplit -pc_fieldsplit_detect_saddle_point -pc_fieldsplit_type schur  -fieldsplit_0_ksp_type gmres  -fieldsplit_0_pc_type gamg 

the detect saddle point flag automatically makes the first block fieldsplit_0 the block without the zeros on the diagonal and the second block fieldsplit_1 be the one with zeros on the diagonal.  You will likely need to play around a bit with sub options to get great convergence but 
start by running with -ksp_monitor -fieldsplit_0_ksp_monitor_true_residual and see how it converges.

  Barry

> 
> -gideon
> 
>> On Sep 19, 2015, at 10:43 PM, Barry Smith <bsmith at mcs.anl.gov> wrote:
>> 
>> 
>>> On Sep 19, 2015, at 9:14 PM, Gideon Simpson <gideon.simpson at gmail.com> wrote:
>>> 
>>> Yes, I know exactly where the zero diagonal entries are.  Is there a way to compensate for that?
>> 
>>  Not really. How can you update x_i if A_ii = 0 ?
>> 
>> 
>>> 
>>> -gideon
>>> 
>>>> On Sep 19, 2015, at 10:09 PM, Barry Smith <bsmith at mcs.anl.gov> wrote:
>>>> 
>>>> 
>>>> Oh, it is a different kind of zero pivot value. There is a zero on the diagonal while it is trying to do SOR.  Should there be zeros on the diagonal of your matrix? 
>>>> 
>>>>  You can use -mg_levels_pc_type jacobi  and it will ignore those zero values.
>>>> 
>>>>  Barry
>>>> 
>>>> 
>>>>> On Sep 19, 2015, at 7:12 PM, Gideon Simpson <gideon.simpson at gmail.com> wrote:
>>>>> 
>>>>> I never get to see the output.  When it runs, I get:
>>>>> 
>>>>> 0 SNES Function norm 8.405398322914e-02 
>>>>> [0]PETSC ERROR: --------------------- Error Message --------------------------------------------------------------
>>>>> [0]PETSC ERROR: Zero pivot in LU factorization: http://www.mcs.anl.gov/petsc/documentation/faq.html#zeropivot
>>>>> [0]PETSC ERROR: Zero pivot on row 0
>>>>> [0]PETSC ERROR: See http://www.mcs.anl.gov/petsc/documentation/faq.html for trouble shooting.
>>>>> [0]PETSC ERROR: Petsc Release Version 3.6.1, unknown 
>>>>> [0]PETSC ERROR: ./blowup_refine on a arch-darwin-c-debug named gs_air by gideon Sat Sep 19 20:11:44 2015
>>>>> [0]PETSC ERROR: Configure options --download-mpich=yes --download-suitesparse=yes --download-superlu=yes --download-superlu_dist=yes --download-mumps=yes --download-sprng=yes --with-cxx=clang++ --with-cc=clang --with-fc=gfortran --download-metis=yes --download-parmetis=yes --download-scalapack=yes
>>>>> [0]PETSC ERROR: #1 MatSOR_SeqAIJ_Inode() line 2795 in /opt/petsc/src/mat/impls/aij/seq/inode.c
>>>>> [0]PETSC ERROR: #2 MatSOR_MPIAIJ() line 1496 in /opt/petsc/src/mat/impls/aij/mpi/mpiaij.c
>>>>> [0]PETSC ERROR: #3 MatSOR() line 3697 in /opt/petsc/src/mat/interface/matrix.c
>>>>> [0]PETSC ERROR: #4 PCApply_SOR() line 37 in /opt/petsc/src/ksp/pc/impls/sor/sor.c
>>>>> [0]PETSC ERROR: #5 PCApply() line 483 in /opt/petsc/src/ksp/pc/interface/precon.c
>>>>> [0]PETSC ERROR: #6 KSP_PCApply() line 242 in /opt/petsc/include/petsc/private/kspimpl.h
>>>>> [0]PETSC ERROR: #7 KSPInitialResidual() line 63 in /opt/petsc/src/ksp/ksp/interface/itres.c
>>>>> [0]PETSC ERROR: #8 KSPSolve_GMRES() line 235 in /opt/petsc/src/ksp/ksp/impls/gmres/gmres.c
>>>>> [0]PETSC ERROR: #9 KSPSolve() line 604 in /opt/petsc/src/ksp/ksp/interface/itfunc.c
>>>>> [0]PETSC ERROR: #10 KSPSolve_Chebyshev() line 381 in /opt/petsc/src/ksp/ksp/impls/cheby/cheby.c
>>>>> [0]PETSC ERROR: #11 KSPSolve() line 604 in /opt/petsc/src/ksp/ksp/interface/itfunc.c
>>>>> [0]PETSC ERROR: #12 PCMGMCycle_Private() line 19 in /opt/petsc/src/ksp/pc/impls/mg/mg.c
>>>>> [0]PETSC ERROR: #13 PCApply_MG() line 340 in /opt/petsc/src/ksp/pc/impls/mg/mg.c
>>>>> [0]PETSC ERROR: #14 PCApply() line 483 in /opt/petsc/src/ksp/pc/interface/precon.c
>>>>> [0]PETSC ERROR: #15 KSP_PCApply() line 242 in /opt/petsc/include/petsc/private/kspimpl.h
>>>>> [0]PETSC ERROR: #16 KSPInitialResidual() line 63 in /opt/petsc/src/ksp/ksp/interface/itres.c
>>>>> [0]PETSC ERROR: #17 KSPSolve_GMRES() line 235 in /opt/petsc/src/ksp/ksp/impls/gmres/gmres.c
>>>>> [0]PETSC ERROR: #18 KSPSolve() line 604 in /opt/petsc/src/ksp/ksp/interface/itfunc.c
>>>>> [0]PETSC ERROR: #19 SNESSolve_NEWTONLS() line 233 in /opt/petsc/src/snes/impls/ls/ls.c
>>>>> [0]PETSC ERROR: #20 SNESSolve() line 3906 in /opt/petsc/src/snes/interface/snes.c
>>>>> [1]PETSC ERROR: #1 VecNorm_MPI() line 63 in /opt/petsc/src/vec/vec/impls/mpi/pvec2.c
>>>>> [1]PETSC ERROR: #2 VecNorm() line 242 in /opt/petsc/src/vec/vec/interface/rvector.c
>>>>> [1]PETSC ERROR: #3 VecNormalize() line 337 in /opt/petsc/src/vec/vec/interface/rvector.c
>>>>> [1]PETSC ERROR: #4 KSPGMRESCycle() line 127 in /opt/petsc/src/ksp/ksp/impls/gmres/gmres.c
>>>>> [1]PETSC ERROR: #5 KSPSolve_GMRES() line 236 in /opt/petsc/src/ksp/ksp/impls/gmres/gmres.c
>>>>> [1]PETSC ERROR: #6 KSPSolve() line 604 in /opt/petsc/src/ksp/ksp/interface/itfunc.c
>>>>> [1]PETSC ERROR: #7 KSPSolve_Chebyshev() line 381 in /opt/petsc/src/ksp/ksp/impls/cheby/cheby.c
>>>>> [1]PETSC ERROR: #8 KSPSolve() line 604 in /opt/petsc/src/ksp/ksp/interface/itfunc.c
>>>>> [1]PETSC ERROR: #9 PCMGMCycle_Private() line 19 in /opt/petsc/src/ksp/pc/impls/mg/mg.c
>>>>> [1]PETSC ERROR: #10 PCApply_MG() line 340 in /opt/petsc/src/ksp/pc/impls/mg/mg.c
>>>>> [1]PETSC ERROR: #11 PCApply() line 483 in /opt/petsc/src/ksp/pc/interface/precon.c
>>>>> [1]PETSC ERROR: #12 KSP_PCApply() line 242 in /opt/petsc/include/petsc/private/kspimpl.h
>>>>> [1]PETSC ERROR: #13 KSPInitialResidual() line 63 in /opt/petsc/src/ksp/ksp/interface/itres.c
>>>>> [1]PETSC ERROR: #14 KSPSolve_GMRES() line 235 in /opt/petsc/src/ksp/ksp/impls/gmres/gmres.c
>>>>> [1]PETSC ERROR: #15 KSPSolve() line 604 in /opt/petsc/src/ksp/ksp/interface/itfunc.c
>>>>> [1]PETSC ERROR: #16 SNESSolve_NEWTONLS() line 233 in /opt/petsc/src/snes/impls/ls/ls.c
>>>>> [1]PETSC ERROR: #17 SNESSolve() line 3906 in /opt/petsc/src/snes/interface/snes.c
>>>>> 
>>>>> and then it just sits there.
>>>>> 
>>>>> -gideon
>>>>> 
>>>>>> On Sep 19, 2015, at 7:18 PM, Matthew Knepley <knepley at gmail.com> wrote:
>>>>>> 
>>>>>> On Sat, Sep 19, 2015 at 6:10 PM, Gideon Simpson <gideon.simpson at gmail.com> wrote:
>>>>>> It gives zero pivots on:
>>>>>> 
>>>>>> Send -ksp_view
>>>>>> 
>>>>>> Matt
>>>>>> 
>>>>>> -ksp_type gmres -pc_type gamg -mg_coarse_sub_pc_factor_shift_type NONZERO
>>>>>> 
>>>>>> It has no problem with:
>>>>>> 
>>>>>> -ksp_type gmres -pc_type bjacobi -sub_pc_factor_shift_type NONZERO
>>>>>> 
>>>>>> -gideon
>>>>>> 
>>>>>>> On Sep 19, 2015, at 12:37 AM, Barry Smith <bsmith at mcs.anl.gov> wrote:
>>>>>>> 
>>>>>>> 
>>>>>>>> On Sep 18, 2015, at 10:42 PM, Gideon Simpson <gideon.simpson at gmail.com> wrote:
>>>>>>>> 
>>>>>>>> I’m getting a zero pivot in LU factorization error when I use the gamg preconditioner.  I know there is some issue with my matrix, as I get the same error if I use pc_type lu in serial, or if I use pc_type bjacobi in parallel, both of which are corrected by adding -pc_factor_shift_type NONZERO -sub_pc_factor_shift_type NONZERO, respectively.  However, I can’t quite seem to figure out the analogous command to use for the gamg preconditioner.
>>>>>>> 
>>>>>>> You need to figure out the prefix to the option that is added by gamg to set it. One way is to run with the gamg options and -help and grep for factor_shift.
>>>>>>> 
>>>>>>> The option is like something like -mg_coarse_pc_factor_shift_type nonzero or -mg_coarse_sub_pc_factor_shift_type
>>>>>>> 
>>>>>>> Barry
>>>>>>> 
>>>>>>>> 
>>>>>>>> -gideon
>>>>>>>> 
>>>>>>> 
>>>>>> 
>>>>>> 
>>>>>> 
>>>>>> 
>>>>>> -- 
>>>>>> 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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