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

[Hong]

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

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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