[petsc-users] GAMG and zero pivots follow up

David Knezevic david.knezevic at akselos.com
Thu Nov 12 22:02:17 CST 2015


On Thu, Nov 12, 2015 at 9:58 AM, David Knezevic <david.knezevic at akselos.com>
wrote:

> On Thu, Nov 12, 2015 at 9:50 AM, Mark Adams <mfadams at lbl.gov> wrote:
>
>> Note, I suspect the zero pivot is coming from a coarse grid.  I don't
>> know why no-inode fixed it.  N.B., this might not be deterministic.
>>
>> If you run with -info and grep on 'GAMG' you will see the block sizes.
>> They should be 3 on the fine grid and the 6 on the coarse grids if you set
>> everything up correctly.
>>
>
> OK, thanks for the info, I'll look into this further.
>
> Though note that I got it to work now without needing no-inode now. The
> change I made was to make sure that I matched the order of function calls
> from the PETSc GAMG examples. The libMesh code I was using was doing things
> somewhat out of order, apparently.
>


As I mentioned above, GAMG seems to be working fine for me now. Thanks for
the help on this.

However, I wanted to ask about another 3D elasticity test case I ran in
which GAMG didn't converge. The "-ksp_view -ksp_monitor" output is below.
Any insights into what options I should set in order to get it to converge
in this case would be appreciated. (By the way, ML worked in this case with
the default options.)

Thanks,
David

--------------------------------------------

  0 KSP Residual norm 2.475892877233e-03
  1 KSP Residual norm 6.181785698923e-05
  2 KSP Residual norm 9.439050821656e-04
KSP Object: 8 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: 8 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_)     8 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_)     8 MPI processes
      type: bjacobi
        block Jacobi: number of blocks = 8
        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=6, cols=6, bs=6
                package used to perform factorization: petsc
                total: nonzeros=36, allocated nonzeros=36
                total number of mallocs used during MatSetValues calls =0
                  using I-node routines: found 2 nodes, limit used is 5
        linear system matrix = precond matrix:
        Mat Object:         1 MPI processes
          type: seqaij
          rows=6, cols=6, bs=6
          total: nonzeros=36, allocated nonzeros=36
          total number of mallocs used during MatSetValues calls =0
            using I-node routines: found 2 nodes, limit used is 5
      linear system matrix = precond matrix:
      Mat Object:       8 MPI processes
        type: mpiaij
        rows=6, cols=6, bs=6
        total: nonzeros=36, allocated nonzeros=36
        total number of mallocs used during MatSetValues calls =0
          using I-node (on process 0) routines: found 2 nodes, limit used
is 5
  Down solver (pre-smoother) on level 1 -------------------------------
    KSP Object:    (mg_levels_1_)     8 MPI processes
      type: chebyshev
        Chebyshev: eigenvalue estimates:  min = 0.146922, max = 1.61615
        Chebyshev: eigenvalues estimated using gmres with translations  [0
0.1; 0 1.1]
        KSP Object:        (mg_levels_1_esteig_)         8 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_)     8 MPI processes
      type: sor
        SOR: type = local_symmetric, iterations = 1, local iterations = 1,
omega = 1
      linear system matrix = precond matrix:
      Mat Object:       8 MPI processes
        type: mpiaij
        rows=162, cols=162, bs=6
        total: nonzeros=26244, allocated nonzeros=26244
        total number of mallocs used during MatSetValues calls =0
          using I-node (on process 0) routines: found 5 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_)     8 MPI processes
      type: chebyshev
        Chebyshev: eigenvalue estimates:  min = 0.143941, max = 1.58335
        Chebyshev: eigenvalues estimated using gmres with translations  [0
0.1; 0 1.1]
        KSP Object:        (mg_levels_2_esteig_)         8 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_)     8 MPI processes
      type: sor
        SOR: type = local_symmetric, iterations = 1, local iterations = 1,
omega = 1
      linear system matrix = precond matrix:
      Mat Object:       8 MPI processes
        type: mpiaij
        rows=4668, cols=4668, bs=6
        total: nonzeros=3.00254e+06, allocated nonzeros=3.00254e+06
        total number of mallocs used during MatSetValues calls =0
          using I-node (on process 0) routines: found 158 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_)     8 MPI processes
      type: chebyshev
        Chebyshev: eigenvalue estimates:  min = 0.128239, max = 1.41063
        Chebyshev: eigenvalues estimated using gmres with translations  [0
0.1; 0 1.1]
        KSP Object:        (mg_levels_3_esteig_)         8 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_)     8 MPI processes
      type: sor
        SOR: type = local_symmetric, iterations = 1, local iterations = 1,
omega = 1
      linear system matrix = precond matrix:
      Mat Object:       8 MPI processes
        type: mpiaij
        rows=66390, cols=66390, bs=6
        total: nonzeros=1.65982e+07, allocated nonzeros=1.65982e+07
        total number of mallocs used during MatSetValues calls =0
          using I-node (on process 0) routines: found 2668 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_)     8 MPI processes
      type: chebyshev
        Chebyshev: eigenvalue estimates:  min = 0.1, max = 1.1
        Chebyshev: eigenvalues estimated using gmres with translations  [0
0.1; 0 1.1]
        KSP Object:        (mg_levels_4_esteig_)         8 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_)     8 MPI processes
      type: sor
        SOR: type = local_symmetric, iterations = 1, local iterations = 1,
omega = 1
      linear system matrix = precond matrix:
      Mat Object:      ()       8 MPI processes
        type: mpiaij
        rows=1532187, cols=1532187, bs=3
        total: nonzeros=1.21304e+08, allocated nonzeros=1.21304e+08
        total number of mallocs used during MatSetValues calls =0
          has attached near null space
          using I-node (on process 0) routines: found 66403 nodes, limit
used is 5
  Up solver (post-smoother) same as down solver (pre-smoother)
  linear system matrix = precond matrix:
  Mat Object:  ()   8 MPI processes
    type: mpiaij
    rows=1532187, cols=1532187, bs=3
    total: nonzeros=1.21304e+08, allocated nonzeros=1.21304e+08
    total number of mallocs used during MatSetValues calls =0
      has attached near null space
      using I-node (on process 0) routines: found 66403 nodes, limit used
is 5
Error, conv_flag < 0!








>
>
>
>
>
> On Wed, Nov 11, 2015 at 1:36 PM, David Knezevic <
> david.knezevic at akselos.com> wrote:
>
>> 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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