[petsc-users] Question concerning ilu and bcgs

Matthew Knepley knepley at gmail.com
Wed Feb 18 10:33:44 CST 2015


On Wed, Feb 18, 2015 at 10:31 AM, Sun, Hui <hus003 at ucsd.edu> wrote:

>  So far I just try around, I haven't looked into literature yet.
>
>  However, both MATLAB's ilu+gmres and ilu+bcgs work. Is it possible that
> some parameter or options need to be tuned in using PETSc's ilu or hypre's
> ilu? Besides, is there a way to view how good the performance of the pc is
> and output the matrices L and U, so that I can do some test in MATLAB?
>

1) Its not clear exactly what Matlab is doing

2) PETSc uses ILU(0) by default (you can set it to use ILU(k))

3) I don't know what Hypre's ILU can do

I would really discourage from using ILU. I cannot imagine it is faster
than sparse direct factorization
for your system, such as from SuperLU or MUMPS.

  Thanks,

     Matt


> Hui
>
>
>  ------------------------------
> *From:* Matthew Knepley [knepley at gmail.com]
> *Sent:* Wednesday, February 18, 2015 8:09 AM
> *To:* Sun, Hui
> *Cc:* hong at aspiritech.org; petsc-users at mcs.anl.gov
> *Subject:* Re: [petsc-users] Question concerning ilu and bcgs
>
>    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
>



-- 
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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