[petsc-users] ILU preconditioner hangs with some zero elements on the diagonal
Barry Smith
bsmith at mcs.anl.gov
Tue Oct 27 13:50:26 CDT 2015
> On Oct 27, 2015, at 12:40 PM, Hong <hzhang at mcs.anl.gov> wrote:
>
> Here is the reason why it does not converge:
> ./ex10 -f0 $D/mat.bin -rhs 0 -ksp_monitor_true_residual -ksp_view -ksp_converged_reason
> Linear solve did not converge due to DIVERGED_NANORINF iterations 0
This means it found a zero pivot either in the factorization or in the first attempt to do a triangular solve. You can try
-pc_factor_nonzeros_along_diagonal
and or
-pc_factor_shift_type nonzero
to generate a usable LU factorization but these are ad hoc fixes.
Barry
>
> KSP Object: 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=10000, initial guess is zero
> tolerances: relative=1e-05, absolute=1e-50, divergence=10000.
> left preconditioning
> using PRECONDITIONED norm type for convergence test
> PC Object: 1 MPI processes
> type: ilu
> ILU: out-of-place factorization
> ...
>
> Hong
>
> On Tue, Oct 27, 2015 at 12:36 PM, Hong <hzhang at mcs.anl.gov> wrote:
> Matt:
> On Tue, Oct 27, 2015 at 11:13 AM, Hong <hzhang at mcs.anl.gov> wrote:
> Gary :
> I tested your mat.bin using
> petsc/src/ksp/ksp/examples/tutorials/ex10.c
> ./ex10 -f0 $D/mat.bin -rhs 0 -ksp_monitor_true_residual -ksp_view
> ...
> Mat Object: 1 MPI processes
> type: seqaij
> rows=588, cols=588
> total: nonzeros=11274, allocated nonzeros=11274
> total number of mallocs used during MatSetValues calls =0
> using I-node routines: found 291 nodes, limit used is 5
> Number of iterations = 0
> Residual norm 24.2487
>
> It does not converge, neither hangs.
>
> This is the default GMRES/ILU.
> Hong
>
> As you said, matrix is non-singular, LU gives a solution
> ./ex10 -f0 $D/mat.bin -rhs 0 -ksp_monitor_true_residual -pc_type lu
> 0 KSP preconditioned resid norm 3.298891225772e+03 true resid norm 2.424871130596e+01 ||r(i)||/||b|| 1.000000000000e+00
> 1 KSP preconditioned resid norm 1.918157196467e-12 true resid norm 5.039404549028e-13 ||r(i)||/||b|| 2.078215409241e-14
> Number of iterations = 1
> Residual norm < 1.e-12
>
> Is this the same matrix as you mentioned?
>
> Hong, could you run ILU on it as well?
>
> Thanks,
>
> Matt
>
> Hong
>
>
>
>
> On Tue, Oct 27, 2015 at 9:10 AM, Matthew Knepley <knepley at gmail.com> wrote:
>
> On Tue, Oct 27, 2015 at 9:06 AM, Gary Rebt <gary.rebt at gmx.ch[gary.rebt at gmx.ch]> wrote:
>
> Dear petsc-users,
>
> While using the FEniCS package to Solve a simple Stokes' flow problem, I have run into problems with PETSc preconditioners. In particular, I would like to use ILU (no parallel version) along with GMRES to solve my linear system but the solver just hangs indefinitely at MatLUFactorNumeric_SeqAIJ_Inode without outputting anything. CPU usage is at 100% but even for a tiny system (59x59 for minimal test case), the solver does not seem to manage to push through it after 30 mins.
>
> PETSc version is 3.6 and the matrix for the minimal test case is as follows :
> http://pastebin.com/t3fvdkaS[http://pastebin.com/t3fvdkaS]
>
> Hanging is a bug. We will check it out.
>
> I do not have any way to read in this ASCII. Can you output a binary version
>
> -mat_view binary:mat.bin
>
> Thanks,
>
> Matt
>
>
> It contains zero diagonal entries, has a condition number of around 1e3 but is definitely non-singular. Direct solvers manage to solve the system as well as GMRES without preconditioner (although after many iterations for a 59x59 system..).
>
> This will never work. Direct solvers work because they pivot away the zeros, but ILU is defined by having no pivoting.
>
> Thanks,
>
> Matt
>
>
> Playing with the available options here http://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/PC/PCILU.html[http://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/PC/PCILU.html] did not seem to solve the issue (even after activating diagonal_fill and/or nonzeros_along_diagonal) although sometimes error 71 is returned which stands for zero pivot detected. Are there yet other options that I have not considered? The default ILU factorization in MATLAB returns satisfactory problems without errors so surely it must be possible with PETSc?
>
> As for the choice of ILU, I agree it might be suboptimal in this setting but I do need it for benchmarking purposes.
>
> Best regards,
>
> Gary
> --
> 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
> --
> 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
>
>
>
>
> --
> 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
>
>
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