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

[Hong]

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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