[petsc-users] GAMG and zero pivots follow up
David Knezevic
david.knezevic at akselos.com
Tue Nov 10 21:28:10 CST 2015
On Tue, Nov 10, 2015 at 10:24 PM, Matthew Knepley <knepley at gmail.com> wrote:
> On Tue, Nov 10, 2015 at 9:21 PM, David Knezevic <
> david.knezevic at akselos.com> wrote:
>
>> 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.
>>
>
> Can you run this same example with -mat_no_inode? I think it may be a
> strange blocking that is causing this.
>
That works. The -ksp_view output is below.
Thanks,
David
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
not using I-node routines
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
not using I-node routines
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
not using I-node routines
Down solver (pre-smoother) on level 1 -------------------------------
KSP Object: (mg_levels_1_) 1 MPI processes
type: chebyshev
Chebyshev: eigenvalue estimates: min = -1.79769e+307, max = -inf
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: sor
SOR: type = local_symmetric, iterations = 1, local iterations = 1,
omega = 1
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
not using I-node routines
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 = -1.79769e+307, max = -inf
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: sor
SOR: type = local_symmetric, iterations = 1, local iterations = 1,
omega = 1
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
not using I-node routines
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 = -1.79769e+307, max = -inf
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: sor
SOR: type = local_symmetric, iterations = 1, local iterations = 1,
omega = 1
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
not using I-node routines
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 = 0.0998367, max = 1.0982
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: sor
SOR: type = local_symmetric, iterations = 1, local iterations = 1,
omega = 1
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
not using I-node routines
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
not using I-node routines
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