[petsc-users] GAMG and zero pivots follow up

Tue Nov 10 21:00:17 CST 2015

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.

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.

> 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.

  Thanks,

    Matt

> Thanks,
> 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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