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

[Hong]

I did a quick test:
1) ilu with any shift type does not converge
2) gmres/4 bjacobi/ilu + shift_type nonzero does not converge
3) mpiexec -n 4 ./ex10 -f0 $D/mat.bin -rhs 0 -ksp_monitor -sub_pc_type lu
-sub_pc_factor_shift_type nonzero
...
0 KSP Residual norm 3.284826093129e+03
  1 KSP Residual norm 2.802972716423e+03
  2 KSP Residual norm 2.039112137210e+03
...
 24 KSP Residual norm 2.666350543810e-02
Number of iterations =  24
Residual norm 0.0179698

Hong

On Tue, Oct 27, 2015 at 1:50 PM, Barry Smith <bsmith at mcs.anl.gov> wrote:

>
> > 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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