[petsc-users] GAMG and zero pivots follow up

Wed Nov 11 12:36:19 CST 2015

On Wed, Nov 11, 2015 at 12:57 PM, David Knezevic <david.knezevic at akselos.com
> wrote:

> On Wed, Nov 11, 2015 at 12:24 PM, David Knezevic <
> david.knezevic at akselos.com> wrote:
>
>> On Tue, Nov 10, 2015 at 10:28 PM, David Knezevic <
>> david.knezevic at akselos.com> wrote:
>>
>>> 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.
>>>
>>
>>
>> I just wanted to follow up on this. I had a more careful look at the
>> matrix, and confirmed that there are no zero entries on the diagonal (as
>> expected for elasticity). The matrix is from one of libMesh's example
>> problems: a simple cantilever model using HEX8 elements.
>>
>> Do you have any further thoughts about what might cause the "strange
>> blocking" that you referred to? If there's something non-standard that
>> libMesh is doing with the blocks, I'd be interested to look into that. I
>> can send over the matrix if that would be helpful.
>>
>> Thanks,
>> David
>>
>>
> P.S. I was previously calling VecSetBlockSize and MatSetBlockSize to set
> the block size to 3. When I don't do that, I no longer need to call
> -mat_no_inodes. I've pasted the -ksp_view output below. Does it look like
> that's working OK?
>

Sorry for the multiple messages, but I think I found the issue. libMesh
internally sets the block size to 1 earlier on (in PetscMatrix::init()). I
guess it'll work fine if I get it to set the block size to 3 instead, so
I'll look into that. (libMesh has an enable-blocked-storage configure
option that should take care of this automatically.)

David
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