[petsc-users] Mat_CheckInode

Barry Smith bsmith at mcs.anl.gov
Mon Dec 5 20:47:45 CST 2011 

On Dec 5, 2011, at 8:42 PM, Debao Shao wrote:

> Yes, for the slow case, most of times, it will be diverged. But, the problem is it takes long runtime before it give an unconverged answer.
> 
>> From your experience, how large condition number shouldn't I use iterative solver?
> 
> The problem I'm solving is a QP problem(symmetry & semi-positive definite) with constraints.

   Direct solver. 

   By having the constraints this makes it much less likely that the "canned" iterative solvers will work. You need to read up on iterative solvers for your type of problem which likely requiring treating different variables differently before exploring iterative methods.

   Barry

> 
> Any suggestions?
> 
> Thanks,
> Debao
> -----Original Message-----
> From: petsc-users-bounces at mcs.anl.gov [mailto:petsc-users-bounces at mcs.anl.gov] On Behalf Of Barry Smith
> Sent: Tuesday, December 06, 2011 10:35 AM
> To: PETSc users list
> Subject: Re: [petsc-users] Mat_CheckInode
> 
> 
> On Dec 5, 2011, at 8:24 PM, Debao Shao wrote:
> 
>> Hi, Hong:
>> 
>> Thanks a lot for your suggestion.
>> The matrix scale of my case may vary from 10*10~1000000*1000000, so, I need both direct solver & iterative solver.
>> For example,
>> 1), <100*100, use direct dense solver;
>> 2), <10000*10000, use direct sparse solver;
>> 3), else, use iterative solver.
>> 
>> Iterative solver(ILU(1) & GMRES) is very efficient on many large scale problems, the issue I encounter now is its runtime's unstable. For a 50000*50000 matrix, it may only need dozens of seconds, but sometimes it also may take thousands of seconds.
> 
>  It shouldn't. There must be some issue with uncontrolled ill-conditioning on the matrix to it to take that long.  If it truly is that badly conditioned then you may want a direct solver even at that size. http://www.mcs.anl.gov/petsc/documentation/faq.html#kspdiverged
> 
> 
>   Barry
> 
>> 
>> Do you have any suggestion?
>> 
>> Thanks,
>> Debao
>> 
>> -----Original Message-----
>> From: petsc-users-bounces at mcs.anl.gov [mailto:petsc-users-bounces at mcs.anl.gov] On Behalf Of Hong Zhang
>> Sent: Monday, December 05, 2011 11:35 PM
>> To: PETSc users list
>> Subject: Re: [petsc-users] Mat_CheckInode
>> 
>> For
>>> The matrix size is around 50000*50000, nnz is ~2000000
>> 
>> You may also try direct solver '-pc_type lu' either Petsc lu (sequential)
>> or mumps, or superlu_dist.
>> They may be faster than ilu(1).
>> 
>> Hong
>> 
>> On Mon, Dec 5, 2011 at 8:54 AM, Matthew Knepley <knepley at gmail.com> wrote:
>>> On Mon, Dec 5, 2011 at 8:46 AM, Debao Shao <Debao.Shao at brion.com> wrote:
>>>> 
>>>> DA,
>>>> 
>>>> 1, Will check_inode affect the runtime performance? For example, in my
>>>> case, there are such different logs:
>>>> 
>>>>    [0] Mat_CheckInode(): Found 18602 nodes out of 18609 rows. Not using
>>>> Inode routines
>>>> 
>>>>    [0] Mat_CheckInode(): Found 0 nodes of 0. Limit used: 5. Using Inode
>>>> routines
>>>> 
>>>>    [0] Mat_CheckInode(): Found 14020 nodes out of 14020 rows. Not using
>>>> Inode routines
>>> 
>>> 
>>> This is intended to "discover" block structure. If you have it, MatMult
>>> should be faster.
>>> 
>>>> 
>>>> 2, Here is the log_summary, looks like PCSetup is big time-consuming
>>>> function, the method I'm using is ILU(1) & GMRES, may I improve it?
>>>> 
>>>>    MatMult            30733 1.0 8.9553e+01 1.0 3.41e+10 1.0 0.0e+00
>>>> 0.0e+00 0.0e+00  2  4  0  0  0   2  4  0  0  0   380
>>>> 
>>>>    MatMultAdd          9552 1.0 6.6610e+00 1.0 2.42e+09 1.0 0.0e+00
>>>> 0.0e+00 0.0e+00  0  0  0  0  0   0  0  0  0  0   363
>>>> 
>>>>    MatSolve           36236 1.0 2.4699e+02 1.0 9.44e+10 1.0 0.0e+00
>>>> 0.0e+00 0.0e+00  6 10  0  0  0   6 10  0  0  0   382
>>>> 
>>>>    MatLUFactorNum      2838 1.0 2.4328e+03 1.0 7.65e+11 1.0 0.0e+00
>>>> 0.0e+00 0.0e+00 61 85  0  0  0  61 85  0  0  0   315
>>>> 
>>>>    MatILUFactorSym      173 1.0 1.3486e+02 1.0 0.00e+00 0.0 0.0e+00
>>>> 0.0e+00 0.0e+00  3  0  0  0  0   3  0  0  0  0     0
>>>> 
>>>>    MatAssemblyBegin    5787 1.0 2.0547e-03 1.0 0.00e+00 0.0 0.0e+00
>>>> 0.0e+00 0.0e+00  0  0  0  0  0   0  0  0  0  0     0
>>>> 
>>>>    MatAssemblyEnd      5787 1.0 5.3559e+00 1.0 0.00e+00 0.0 0.0e+00
>>>> 0.0e+00 0.0e+00  0  0  0  0  0   0  0  0  0  0     0
>>>> 
>>>>    KSPGMRESOrthog     30679 1.0 5.5968e+00 1.0 4.06e+09 1.0 0.0e+00
>>>> 0.0e+00 0.0e+00  0  0  0  0  0   0  0  0  0  0   725
>>>> 
>>>>    KSPSetup            2838 1.0 1.8219e-02 1.0 0.00e+00 0.0 0.0e+00
>>>> 0.0e+00 0.0e+00  0  0  0  0  0   0  0  0  0  0     0
>>>> 
>>>>    KSPSolve            5503 1.0 2.9136e+03 1.0 8.99e+11 1.0 0.0e+00
>>>> 0.0e+00 0.0e+00 73100  0  0  0  73100  0  0  0   308
>>>> 
>>>>    PCSetUp             2838 1.0 2.5682e+03 1.0 7.65e+11 1.0 0.0e+00
>>>> 0.0e+00 0.0e+00 64 85  0  0  0  64 85  0  0  0   298
>>>> 
>>>>    PCApply            36236 1.0 2.4709e+02 1.0 9.44e+10 1.0 0.0e+00
>>>> 0.0e+00 0.0e+00  6 10  0  0  0   6 10  0  0  0   382
>>>> 
>>>> The matrix size is around 50000*50000, nnz is ~2000000
>>> 
>>> 
>>> ILU is expensive, and levels make it much more expensive. Maybe try AMG?
>>>> 
>>>> 3, Will the fill of ilu affect the runtime performance?
>>>> 
>>>>    [0] MatILUFactorSymbolic_SeqAIJ(): Reallocs 0 Fill ratio:given 1
>>>> needed 1.11111
>>>> 
>>>>    [0] MatILUFactorSymbolic_SeqAIJ(): Reallocs 1 Fill ratio:given 1
>>>> needed 5.05
>>>> 
>>>>    [0] MatILUFactorSymbolic_SeqAIJ(): Reallocs 1 Fill ratio:given 1
>>>> needed 8.3410
>>>> 
>>>> How to set a proper value for fill, >8?
>>> 
>>> 
>>> http://www.mcs.anl.gov/petsc/petsc-dev/docs/manualpages/PC/PCFactorSetFill.html
>>> 
>>> Use -pc_factor_fill
>>> 
>>> Matt
>>> 
>>>> 
>>>> Thanks,
>>>> 
>>>> Debao
>>>> 
>>>> 
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>>> 
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