On Tue, Nov 10, 2015 at 10:00 PM, Matthew Knepley <[email protected]> wrote:
> 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. > 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. > > >> 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 >
