[petsc-users] GAMG and zero pivots follow up

Tue Nov 10 20:39:44 CST 2015

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.

2. Is there a way to set "-mg_levels_pc_type jacobi" programmatically,
rather than via the command line?

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
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