[petsc-users] Question concerning ilu and bcgs

Wed Feb 18 10:09:40 CST 2015

On Wed, Feb 18, 2015 at 10:02 AM, Sun, Hui <hus003 at ucsd.edu> wrote:

>  Yes I've tried other solvers, gmres/ilu does not work, neither does
> bcgs/ilu. Here are the options:
>
> -pc_type ilu -pc_factor_nonzeros_along_diagonal -pc_factor_levels 0
> -pc_factor_reuse_ordering -ksp_ty\
>
> pe bcgs -ksp_rtol 1e-6 -ksp_max_it 10 -ksp_monitor_short -ksp_view
>

Note here that ILU(0) is an unreliable and generally crappy preconditioner.
Have you looked in the
literature for the kinds of preconditioners that are effective for your
problem?

  Thanks,

     Matt

> Here is the output:
>
>   0 KSP Residual norm 211292
>
>   1 KSP Residual norm 13990.2
>
>   2 KSP Residual norm 9870.08
>
>   3 KSP Residual norm 9173.9
>
>   4 KSP Residual norm 9121.94
>
>   5 KSP Residual norm 7386.1
>
>   6 KSP Residual norm 6222.55
>
>   7 KSP Residual norm 7192.94
>
>   8 KSP Residual norm 33964
>
>   9 KSP Residual norm 33960.4
>
>  10 KSP Residual norm 1068.54
>
> KSP Object: 1 MPI processes
>
>   type: bcgs
>
>   maximum iterations=10, initial guess is zero
>
>   tolerances:  relative=1e-06, 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
>
>     ILU: Reusing reordering from past factorization
>
>     0 levels of fill
>
>     tolerance for zero pivot 2.22045e-14
>
>     using diagonal shift on blocks to prevent zero pivot [INBLOCKS]
>
>     matrix ordering: natural
>
>     factor fill ratio given 1, needed 1
>
>       Factored matrix follows:
>
>         Mat Object:         1 MPI processes
>
>           type: seqaij
>
>           rows=62500, cols=62500
>
>           package used to perform factorization: petsc
>
>           total: nonzeros=473355, allocated nonzeros=473355
>
>           total number of mallocs used during MatSetValues calls =0
>
>             not using I-node routines
>
>   linear system matrix = precond matrix:
>
>   Mat Object:   1 MPI processes
>
>     type: seqaij
>
>     rows=62500, cols=62500
>
>     total: nonzeros=473355, allocated nonzeros=7.8125e+06
>
>     total number of mallocs used during MatSetValues calls =0
>
>       not using I-node routines
>
>  Time cost: 0.307149,  0.268402,  0.0990018
>
>
>
>
>  ------------------------------
> *From:* hong at aspiritech.org [hong at aspiritech.org]
> *Sent:* Wednesday, February 18, 2015 7:49 AM
> *To:* Sun, Hui
> *Cc:* Matthew Knepley; petsc-users at mcs.anl.gov
> *Subject:* Re: [petsc-users] Question concerning ilu and bcgs
>
>    Have you tried other solvers, e.g., PETSc default gmres/ilu, bcgs/ilu
> etc.
> The matrix is small. If it is ill-conditioned, then pc_type lu would work
> the best.
>
>  Hong
>
> On Wed, Feb 18, 2015 at 9:34 AM, Sun, Hui <hus003 at ucsd.edu> wrote:
>
>>  With options:
>>
>>  -pc_type hypre -pc_hypre_type pilut -pc_hypre_pilut_maxiter 1000
>> -pc_hypre_pilut_tol 1e-3 -ksp_type bcgs -ksp_rtol 1e-10 -ksp_max_it 10
>> -ksp_monitor_short -ksp_converged_reason -ksp_view
>>
>>  Here is the full output:
>>
>>    0 KSP Residual norm 1404.62
>>
>>   1 KSP Residual norm 88.9068
>>
>>   2 KSP Residual norm 64.73
>>
>>   3 KSP Residual norm 71.0224
>>
>>   4 KSP Residual norm 69.5044
>>
>>   5 KSP Residual norm 455.458
>>
>>   6 KSP Residual norm 174.876
>>
>>   7 KSP Residual norm 183.031
>>
>>   8 KSP Residual norm 650.675
>>
>>   9 KSP Residual norm 79.2441
>>
>>  10 KSP Residual norm 84.1985
>>
>> Linear solve did not converge due to DIVERGED_ITS iterations 10
>>
>> KSP Object: 1 MPI processes
>>
>>   type: bcgs
>>
>>   maximum iterations=10, initial guess is zero
>>
>>   tolerances:  relative=1e-10, absolute=1e-50, divergence=10000
>>
>>   left preconditioning
>>
>>   using PRECONDITIONED norm type for convergence test
>>
>> PC Object: 1 MPI processes
>>
>>   type: hypre
>>
>>     HYPRE Pilut preconditioning
>>
>>     HYPRE Pilut: maximum number of iterations 1000
>>
>>     HYPRE Pilut: drop tolerance 0.001
>>
>>     HYPRE Pilut: default factor row size
>>
>>   linear system matrix = precond matrix:
>>
>>   Mat Object:   1 MPI processes
>>
>>     type: seqaij
>>
>>     rows=62500, cols=62500
>>
>>     total: nonzeros=473355, allocated nonzeros=7.8125e+06
>>
>>     total number of mallocs used during MatSetValues calls =0
>>
>>       not using I-node routines
>>
>> Time cost: 0.756198,  0.662984,  0.105672
>>
>>
>>
>>
>>  ------------------------------
>> *From:* Matthew Knepley [knepley at gmail.com]
>> *Sent:* Wednesday, February 18, 2015 3:30 AM
>> *To:* Sun, Hui
>> *Cc:* petsc-users at mcs.anl.gov
>> *Subject:* Re: [petsc-users] Question concerning ilu and bcgs
>>
>>     On Wed, Feb 18, 2015 at 12:33 AM, Sun, Hui <hus003 at ucsd.edu> wrote:
>>
>>>  I have a matrix system Ax = b, A is of type MatSeqAIJ or MatMPIAIJ,
>>> depending on the number of cores.
>>>
>>>  I try to solve this problem by pc_type ilu and ksp_type bcgs, it does
>>> not converge. The options I specify are:
>>>
>>> -pc_type hypre -pc_hypre_type pilut -pc_hypre_pilut_maxiter 1000
>>> -pc_hypre_pilut_tol 1e-3 -ksp_type b\
>>>
>>> cgs -ksp_rtol 1e-10 -ksp_max_it 1000 -ksp_monitor_short
>>> -ksp_converged_reason
>>>
>>
>>  1) Run with -ksp_view, so we can see exactly what was used
>>
>>  2) ILUT is unfortunately not a well-defined algorithm, and I believe
>> the parallel version makes different decisions
>>     than the serial version.
>>
>>    Thanks,
>>
>>      Matt
>>
>>
>>>   The first a few lines of the output are:
>>>
>>>   0 KSP Residual norm 1404.62
>>>
>>>   1 KSP Residual norm 88.9068
>>>
>>>   2 KSP Residual norm 64.73
>>>
>>>   3 KSP Residual norm 71.0224
>>>
>>>   4 KSP Residual norm 69.5044
>>>
>>>   5 KSP Residual norm 455.458
>>>
>>>   6 KSP Residual norm 174.876
>>>
>>>   7 KSP Residual norm 183.031
>>>
>>>   8 KSP Residual norm 650.675
>>>
>>>   9 KSP Residual norm 79.2441
>>>
>>>  10 KSP Residual norm 84.1985
>>>
>>>
>>>  This clearly indicates non-convergence. However, I output the sparse
>>> matrix A and vector b to MATLAB, and run the following command:
>>>
>>> [L,U] = ilu(A,struct('type','ilutp','droptol',1e-3));
>>>
>>> [ux1,fl1,rr1,it1,rv1] = bicgstab(A,b,1e-10,1000,L,U);
>>>
>>>
>>>  And it converges in MATLAB, with flag fl1=0, relative residue
>>> rr1=8.2725e-11, and iteration it1=89.5. I'm wondering how can I figure out
>>> what's wrong.
>>>
>>>
>>>  Best,
>>>
>>> Hui
>>>
>>
>>
>>
>>  --
>> 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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