<div dir="ltr"><div class="gmail_extra"><div class="gmail_quote">On Tue, Nov 10, 2015 at 8:39 PM, David Knezevic <span dir="ltr"><<a href="mailto:david.knezevic@akselos.com" target="_blank">david.knezevic@akselos.com</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="ltr"><div>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:</div><div><br></div><div>-----------------------------------------------------------------------</div><div><br></div><div><div>[0]PETSC ERROR: Zero pivot in LU factorization: <a href="http://www.mcs.anl.gov/petsc/documentation/faq.html#zeropivot" target="_blank">http://www.mcs.anl.gov/petsc/documentation/faq.html#zeropivot</a></div><div>[0]PETSC ERROR: Zero pivot, row 3</div><div>[0]PETSC ERROR: See <a href="http://www.mcs.anl.gov/petsc/documentation/faq.html" target="_blank">http://www.mcs.anl.gov/petsc/documentation/faq.html</a> for trouble shooting.</div><div>[0]PETSC ERROR: Petsc Release Version 3.6.1, Jul, 22, 2015 </div><div>[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</div><div>[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</div><div>[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</div><div>[0]PETSC ERROR: #2 MatSOR_SeqAIJ_Inode() line 2808 in /home/dknez/software/petsc-3.6.1/src/mat/impls/aij/seq/inode.c</div><div>[0]PETSC ERROR: #3 MatSOR() line 3697 in /home/dknez/software/petsc-3.6.1/src/mat/interface/matrix.c</div><div>[0]PETSC ERROR: #4 PCApply_SOR() line 37 in /home/dknez/software/petsc-3.6.1/src/ksp/pc/impls/sor/sor.c</div><div>[0]PETSC ERROR: #5 PCApply() line 482 in /home/dknez/software/petsc-3.6.1/src/ksp/pc/interface/precon.c</div><div>[0]PETSC ERROR: #6 KSP_PCApply() line 242 in /home/dknez/software/petsc-3.6.1/include/petsc/private/kspimpl.h</div><div>[0]PETSC ERROR: #7 KSPInitialResidual() line 63 in /home/dknez/software/petsc-3.6.1/src/ksp/ksp/interface/itres.c</div><div>[0]PETSC ERROR: #8 KSPSolve_GMRES() line 235 in /home/dknez/software/petsc-3.6.1/src/ksp/ksp/impls/gmres/gmres.c</div><div>[0]PETSC ERROR: #9 KSPSolve() line 604 in /home/dknez/software/petsc-3.6.1/src/ksp/ksp/interface/itfunc.c</div><div>[0]PETSC ERROR: #10 KSPSolve_Chebyshev() line 381 in /home/dknez/software/petsc-3.6.1/src/ksp/ksp/impls/cheby/cheby.c</div><div>[0]PETSC ERROR: #11 KSPSolve() line 604 in /home/dknez/software/petsc-3.6.1/src/ksp/ksp/interface/itfunc.c</div><div>[0]PETSC ERROR: #12 PCMGMCycle_Private() line 19 in /home/dknez/software/petsc-3.6.1/src/ksp/pc/impls/mg/mg.c</div><div>[0]PETSC ERROR: #13 PCMGMCycle_Private() line 48 in /home/dknez/software/petsc-3.6.1/src/ksp/pc/impls/mg/mg.c</div><div>[0]PETSC ERROR: #14 PCApply_MG() line 338 in /home/dknez/software/petsc-3.6.1/src/ksp/pc/impls/mg/mg.c</div><div>[0]PETSC ERROR: #15 PCApply() line 482 in /home/dknez/software/petsc-3.6.1/src/ksp/pc/interface/precon.c</div><div>[0]PETSC ERROR: #16 KSP_PCApply() line 242 in /home/dknez/software/petsc-3.6.1/include/petsc/private/kspimpl.h</div><div>[0]PETSC ERROR: #17 KSPSolve_CG() line 139 in /home/dknez/software/petsc-3.6.1/src/ksp/ksp/impls/cg/cg.c</div><div>[0]PETSC ERROR: #18 KSPSolve() line 604 in /home/dknez/software/petsc-3.6.1/src/ksp/ksp/interface/itfunc.c</div></div><div><br></div><div>-----------------------------------------------------------------------<br></div><div><br></div><div>I saw that there was a thread about this in September (subject: "gamg and zero pivots"), and that the fix is to use "<span style="color:rgb(0,0,0);white-space:pre-wrap">-mg_levels_pc_type jacobi." When I do that, the solve succeeds (I pasted the -ksp_view at the end of this email).</span></div><div><span style="color:rgb(0,0,0);white-space:pre-wrap"><br></span></div><div><span style="color:rgb(0,0,0);white-space:pre-wrap">So I have two questions about this:</span></div><div><span style="color:rgb(0,0,0);white-space:pre-wrap"><br></span></div><div>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.</div></div></blockquote><div><br></div><div>Yes, this seems like a bug, but it could be some strange BC thing I do not understand.</div><div><br></div><div>Naively, the elastic element matrix has a nonzero diagonal. I see that you are doing LU</div><div>of size 5. That seems strange for 3D elasticity. Am I missing something? I would expect</div><div>block size 3.</div><div> </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="ltr"><div>2. Is there a way to set "<span style="color:rgb(0,0,0);white-space:pre-wrap">-mg_levels_pc_type jacobi" programmatically, rather than via the command line?</span></div></div></blockquote><div><br></div><div>I would really discourage you from doing this. It makes your code fragile and inflexible.</div><div><br></div><div> Thanks,</div><div><br></div><div> Matt</div><div> </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="ltr"><div><span style="color:rgb(0,0,0);white-space:pre-wrap">Thanks,</span></div><div><span style="color:rgb(0,0,0);white-space:pre-wrap">David</span></div><div><span style="color:rgb(0,0,0);white-space:pre-wrap"><br></span></div><div>-----------------------------------------------------------------------<span style="color:rgb(0,0,0);white-space:pre-wrap"><br></span></div><div><span style="color:rgb(0,0,0);white-space:pre-wrap"><br></span></div><div><span style="color:rgb(0,0,0);white-space:pre-wrap">ksp_view output:</span></div><div><span style="color:rgb(0,0,0);white-space:pre-wrap"><br></span></div><div><span style="color:rgb(0,0,0);white-space:pre-wrap"><br></span></div><div><font color="#000000"><span style="white-space:pre-wrap">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</span></font><span style="color:rgb(0,0,0);white-space:pre-wrap">
</span></div><div><span style="color:rgb(0,0,0);white-space:pre-wrap"><br></span></div><div><span style="color:rgb(0,0,0);white-space:pre-wrap"><br></span></div></div>
</blockquote></div><br><br clear="all"><div><br></div>-- <br><div class="gmail_signature">What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead.<br>-- Norbert Wiener</div>
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