[petsc-users] GAMG and zero pivots follow up

Tue Nov 10 21:24:31 CST 2015

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.

  Thanks,

     Matt

>
>>
>>> 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
>>
>

-- 
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
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.mcs.anl.gov/pipermail/petsc-users/attachments/20151110/26f6a9c5/attachment-0001.html>