[petsc-users] ILU preconditioner hangs with some zero elements on the diagonal

[Hong]

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.
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


>
>
> 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
>
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