On Tue, Nov 10, 2015 at 8:39 PM, David Knezevic <[email protected]> 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. 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. > 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. Thanks, Matt > Thanks, > 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
