[petsc-users] GAMG and zero pivots follow up

Tue Nov 10 21:21:54 CST 2015

On Tue, Nov 10, 2015 at 10:00 PM, Matthew Knepley <knepley at gmail.com> wrote:

> On Tue, Nov 10, 2015 at 8:39 PM, David Knezevic <
> david.knezevic at akselos.com> wrote:
>
>> I'm looking into using GAMG, so I wanted to start with a simple 3D
>> elasticity problem. When I first tried this, I got the following "zero
>> pivot" error:
>>
>> -----------------------------------------------------------------------
>>
>> [0]PETSC ERROR: Zero pivot in LU factorization:
>> http://www.mcs.anl.gov/petsc/documentation/faq.html#zeropivot
>> [0]PETSC ERROR: Zero pivot, row 3
>> [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, Jul, 22, 2015
>> [0]PETSC ERROR:
>> /home/dknez/akselos-dev/scrbe/build/bin/fe_solver-opt_real on a
>> arch-linux2-c-opt named david-Lenovo by dknez Tue Nov 10 21:26:39 2015
>> [0]PETSC ERROR: Configure options --with-shared-libraries=1
>> --with-debugging=0 --download-suitesparse --download-parmetis
>> --download-blacs
>> --with-blas-lapack-dir=/opt/intel/system_studio_2015.2.050/mkl
>> --CXXFLAGS=-Wl,--no-as-needed --download-scalapack --download-mumps
>> --download-metis --download-superlu_dist
>> --prefix=/home/dknez/software/libmesh_install/opt_real/petsc
>> --download-hypre --download-ml
>> [0]PETSC ERROR: #1 PetscKernel_A_gets_inverse_A_5() line 48 in
>> /home/dknez/software/petsc-3.6.1/src/mat/impls/baij/seq/dgefa5.c
>> [0]PETSC ERROR: #2 MatSOR_SeqAIJ_Inode() line 2808 in
>> /home/dknez/software/petsc-3.6.1/src/mat/impls/aij/seq/inode.c
>> [0]PETSC ERROR: #3 MatSOR() line 3697 in
>> /home/dknez/software/petsc-3.6.1/src/mat/interface/matrix.c
>> [0]PETSC ERROR: #4 PCApply_SOR() line 37 in
>> /home/dknez/software/petsc-3.6.1/src/ksp/pc/impls/sor/sor.c
>> [0]PETSC ERROR: #5 PCApply() line 482 in
>> /home/dknez/software/petsc-3.6.1/src/ksp/pc/interface/precon.c
>> [0]PETSC ERROR: #6 KSP_PCApply() line 242 in
>> /home/dknez/software/petsc-3.6.1/include/petsc/private/kspimpl.h
>> [0]PETSC ERROR: #7 KSPInitialResidual() line 63 in
>> /home/dknez/software/petsc-3.6.1/src/ksp/ksp/interface/itres.c
>> [0]PETSC ERROR: #8 KSPSolve_GMRES() line 235 in
>> /home/dknez/software/petsc-3.6.1/src/ksp/ksp/impls/gmres/gmres.c
>> [0]PETSC ERROR: #9 KSPSolve() line 604 in
>> /home/dknez/software/petsc-3.6.1/src/ksp/ksp/interface/itfunc.c
>> [0]PETSC ERROR: #10 KSPSolve_Chebyshev() line 381 in
>> /home/dknez/software/petsc-3.6.1/src/ksp/ksp/impls/cheby/cheby.c
>> [0]PETSC ERROR: #11 KSPSolve() line 604 in
>> /home/dknez/software/petsc-3.6.1/src/ksp/ksp/interface/itfunc.c
>> [0]PETSC ERROR: #12 PCMGMCycle_Private() line 19 in
>> /home/dknez/software/petsc-3.6.1/src/ksp/pc/impls/mg/mg.c
>> [0]PETSC ERROR: #13 PCMGMCycle_Private() line 48 in
>> /home/dknez/software/petsc-3.6.1/src/ksp/pc/impls/mg/mg.c
>> [0]PETSC ERROR: #14 PCApply_MG() line 338 in
>> /home/dknez/software/petsc-3.6.1/src/ksp/pc/impls/mg/mg.c
>> [0]PETSC ERROR: #15 PCApply() line 482 in
>> /home/dknez/software/petsc-3.6.1/src/ksp/pc/interface/precon.c
>> [0]PETSC ERROR: #16 KSP_PCApply() line 242 in
>> /home/dknez/software/petsc-3.6.1/include/petsc/private/kspimpl.h
>> [0]PETSC ERROR: #17 KSPSolve_CG() line 139 in
>> /home/dknez/software/petsc-3.6.1/src/ksp/ksp/impls/cg/cg.c
>> [0]PETSC ERROR: #18 KSPSolve() line 604 in
>> /home/dknez/software/petsc-3.6.1/src/ksp/ksp/interface/itfunc.c
>>
>> -----------------------------------------------------------------------
>>
>> I saw that there was a thread about this in September (subject: "gamg and
>> zero pivots"), and that the fix is to use "-mg_levels_pc_type jacobi."
>> When I do that, the solve succeeds (I pasted the -ksp_view at the end of
>> this email).
>>
>> So I have two questions about this:
>>
>> 1. Is it surprising that I hit this issue for a 3D elasticity problem?
>> Note that matrix assembly was done in libMesh, I can look into the
>> structure of the assembled matrix more carefully, if needed. Also, note
>> that I can solve this problem with direct solvers just fine.
>>
>
> Yes, this seems like a bug, but it could be some strange BC thing I do not
> understand.
>

OK, I can look into the matrix in more detail. I agree that it should have
a non-zero diagonal, so I'll have a look at what's happening with that.

> Naively, the elastic element matrix has a nonzero diagonal. I see that you
> are doing LU
> of size 5. That seems strange for 3D elasticity. Am I missing something? I
> would expect
> block size 3.
>

I'm not sure what is causing the LU of size 5. Is there a setting to
control that?

Regarding the block size: I set the vector and matrix block size to 3
via VecSetBlockSize and MatSetBlockSize. I also
used MatNullSpaceCreateRigidBody on a vector with block size of 3, and set
the matrix's near nullspace using that.

>
>
>> 2. Is there a way to set "-mg_levels_pc_type jacobi" programmatically,
>> rather than via the command line?
>>
>
> I would really discourage you from doing this. It makes your code fragile
> and inflexible.
>

OK. The reason I asked is that in this case I have to write a bunch of code
to set block sizes and the near nullspace, so I figured it'd be good to
also set the corresponding solver options required to make this work...
anyway, if I can fix the zero diagonal issue, I guess this will be moot.

David

> -----------------------------------------------------------------------
>>
>> ksp_view output:
>>
>>
>> KSP Object: 1 MPI processes type: cg maximum iterations=5000 tolerances:
>> relative=1e-12, absolute=1e-50, divergence=10000 left preconditioning using
>> nonzero initial guess using PRECONDITIONED norm type for convergence test
>> PC Object: 1 MPI processes type: gamg MG: type is MULTIPLICATIVE, levels=5
>> cycles=v Cycles per PCApply=1 Using Galerkin computed coarse grid matrices
>> GAMG specific options Threshold for dropping small values from graph 0 AGG
>> specific options Symmetric graph false Coarse grid solver -- level
>> ------------------------------- KSP Object: (mg_coarse_) 1 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
>> NONE norm type for convergence test PC Object: (mg_coarse_) 1 MPI processes
>> type: bjacobi block Jacobi: number of blocks = 1 Local solve is same for
>> all blocks, in the following KSP and PC objects: KSP Object:
>> (mg_coarse_sub_) 1 MPI processes type: preonly maximum iterations=1,
>> 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_coarse_sub_) 1 MPI processes type: lu LU: out-of-place
>> factorization tolerance for zero pivot 2.22045e-14 using diagonal shift on
>> blocks to prevent zero pivot [INBLOCKS] matrix ordering: nd factor fill
>> ratio given 5, needed 1 Factored matrix follows: Mat Object: 1 MPI
>> processes type: seqaij rows=30, cols=30, bs=6 package used to perform
>> factorization: petsc total: nonzeros=540, allocated nonzeros=540 total
>> number of mallocs used during MatSetValues calls =0 using I-node routines:
>> found 9 nodes, limit used is 5 linear system matrix = precond matrix: Mat
>> Object: 1 MPI processes type: seqaij rows=30, cols=30, bs=6 total:
>> nonzeros=540, allocated nonzeros=540 total number of mallocs used during
>> MatSetValues calls =0 using I-node routines: found 9 nodes, limit used is 5
>> linear system matrix = precond matrix: Mat Object: 1 MPI processes type:
>> seqaij rows=30, cols=30, bs=6 total: nonzeros=540, allocated nonzeros=540
>> total number of mallocs used during MatSetValues calls =0 using I-node
>> routines: found 9 nodes, limit used is 5 Down solver (pre-smoother) on
>> level 1 ------------------------------- KSP Object: (mg_levels_1_) 1 MPI
>> processes type: chebyshev Chebyshev: eigenvalue estimates: min = 0.335276,
>> max = 3.68804 Chebyshev: eigenvalues estimated using gmres with
>> translations [0 0.1; 0 1.1] KSP Object: (mg_levels_1_esteig_) 1 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=10, initial guess is zero
>> tolerances: relative=1e-05, absolute=1e-50, divergence=10000 left
>> preconditioning using NONE norm type for convergence test maximum
>> iterations=2 tolerances: relative=1e-05, absolute=1e-50, divergence=10000
>> left preconditioning using nonzero initial guess using NONE norm type for
>> convergence test PC Object: (mg_levels_1_) 1 MPI processes type: jacobi
>> linear system matrix = precond matrix: Mat Object: 1 MPI processes type:
>> seqaij rows=72, cols=72, bs=6 total: nonzeros=1728, allocated nonzeros=1728
>> total number of mallocs used during MatSetValues calls =0 using I-node
>> routines: found 23 nodes, limit used is 5 Up solver (post-smoother) same as
>> down solver (pre-smoother) Down solver (pre-smoother) on level 2
>> ------------------------------- KSP Object: (mg_levels_2_) 1 MPI processes
>> type: chebyshev Chebyshev: eigenvalue estimates: min = 0.260121, max =
>> 2.86133 Chebyshev: eigenvalues estimated using gmres with translations [0
>> 0.1; 0 1.1] KSP Object: (mg_levels_2_esteig_) 1 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=10, initial guess is zero tolerances:
>> relative=1e-05, absolute=1e-50, divergence=10000 left preconditioning using
>> NONE norm type for convergence test maximum iterations=2 tolerances:
>> relative=1e-05, absolute=1e-50, divergence=10000 left preconditioning using
>> nonzero initial guess using NONE norm type for convergence test PC Object:
>> (mg_levels_2_) 1 MPI processes type: jacobi linear system matrix = precond
>> matrix: Mat Object: 1 MPI processes type: seqaij rows=174, cols=174, bs=6
>> total: nonzeros=5796, allocated nonzeros=5796 total number of mallocs used
>> during MatSetValues calls =0 using I-node routines: found 57 nodes, limit
>> used is 5 Up solver (post-smoother) same as down solver (pre-smoother) Down
>> solver (pre-smoother) on level 3 ------------------------------- KSP
>> Object: (mg_levels_3_) 1 MPI processes type: chebyshev Chebyshev:
>> eigenvalue estimates: min = 0.267401, max = 2.94141 Chebyshev: eigenvalues
>> estimated using gmres with translations [0 0.1; 0 1.1] KSP Object:
>> (mg_levels_3_esteig_) 1 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=10,
>> initial guess is zero tolerances: relative=1e-05, absolute=1e-50,
>> divergence=10000 left preconditioning using NONE norm type for convergence
>> test maximum iterations=2 tolerances: relative=1e-05, absolute=1e-50,
>> divergence=10000 left preconditioning using nonzero initial guess using
>> NONE norm type for convergence test PC Object: (mg_levels_3_) 1 MPI
>> processes type: jacobi linear system matrix = precond matrix: Mat Object: 1
>> MPI processes type: seqaij rows=828, cols=828, bs=6 total: nonzeros=44496,
>> allocated nonzeros=44496 total number of mallocs used during MatSetValues
>> calls =0 using I-node routines: found 276 nodes, limit used is 5 Up solver
>> (post-smoother) same as down solver (pre-smoother) Down solver
>> (pre-smoother) on level 4 ------------------------------- KSP Object:
>> (mg_levels_4_) 1 MPI processes type: chebyshev Chebyshev: eigenvalue
>> estimates: min = 0.224361, max = 2.46797 Chebyshev: eigenvalues estimated
>> using gmres with translations [0 0.1; 0 1.1] KSP Object:
>> (mg_levels_4_esteig_) 1 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=10,
>> initial guess is zero tolerances: relative=1e-05, absolute=1e-50,
>> divergence=10000 left preconditioning using NONE norm type for convergence
>> test maximum iterations=2 tolerances: relative=1e-05, absolute=1e-50,
>> divergence=10000 left preconditioning using nonzero initial guess using
>> NONE norm type for convergence test PC Object: (mg_levels_4_) 1 MPI
>> processes type: jacobi linear system matrix = precond matrix: Mat Object:
>> () 1 MPI processes type: seqaij rows=2676, cols=2676, bs=3 total:
>> nonzeros=94014, allocated nonzeros=94014 total number of mallocs used
>> during MatSetValues calls =0 has attached near null space using I-node
>> routines: found 892 nodes, limit used is 5 Up solver (post-smoother) same
>> as down solver (pre-smoother) linear system matrix = precond matrix: Mat
>> Object: () 1 MPI processes type: seqaij rows=2676, cols=2676, bs=3 total:
>> nonzeros=94014, allocated nonzeros=94014 total number of mallocs used
>> during MatSetValues calls =0 has attached near null space using I-node
>> routines: found 892 nodes, limit used is 5
>>
>>
>>
>
>
> --
> 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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