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

[Matthew Knepley]

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.
> 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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