[petsc-users] Question on incomplete factorization level and fill

[Danyang Su]

Hi Matt,

Yes. The matrix is 450000x450000 sparse. The hypre takes hundreds of 
iterates, not for all but in most of the timesteps. The matrix is not 
well conditioned, with nonzero entries range from 1.0e-29 to 1.0e2. I 
also made double check if there is anything wrong in the parallel 
version, however, the matrix is the same with sequential version except 
some round error which is relatively very small. Usually for those not 
well conditioned matrix, direct solver should be faster than iterative 
solver, right? But when I use the sequential iterative solver with ILU 
prec developed almost 20 years go by others, the solver converge fast 
with appropriate factorization level. In other words, when I use 24 
processor using hypre, the speed is almost the same as as the old 
sequential iterative solver using 1 processor.

I use most of the default configuration for the general case with pretty 
good speedup. And I am not sure if I miss something for this problem.

Thanks,

Danyang


On 17-05-24 11:12 AM, Matthew Knepley wrote:
> On Wed, May 24, 2017 at 12:50 PM, Danyang Su <danyang.su at gmail.com 
> <mailto:danyang.su at gmail.com>> wrote:
>
>     Hi Matthew and Barry,
>
>     Thanks for the quick response.
>
>     I also tried superlu and mumps, both work but it is about four
>     times slower than ILU(dt) prec through hypre, with 24 processors I
>     have tested.
>
> You mean the total time is 4x? And you are taking hundreds of 
> iterates? That seems hard to believe, unless you are dropping
> a huge number of elements.
>
>     When I look into the convergence information, the method using
>     ILU(dt) still takes 200 to 3000 linear iterations for each newton
>     iteration. One reason is this equation is hard to solve. As for
>     the general cases, the same method works awesome and get very good
>     speedup.
>
> I do not understand what you mean here.
>
>     I also doubt if I use hypre correctly for this case. Is there
>     anyway to check this problem, or is it possible to increase the
>     factorization level through hypre?
>
> I don't know.
>
>   Matt
>
>     Thanks,
>
>     Danyang
>
>
>     On 17-05-24 04:59 AM, Matthew Knepley wrote:
>>     On Wed, May 24, 2017 at 2:21 AM, Danyang Su <danyang.su at gmail.com
>>     <mailto:danyang.su at gmail.com>> wrote:
>>
>>         Dear All,
>>
>>         I use PCFactorSetLevels for ILU and PCFactorSetFill for other
>>         preconditioning in my code to help solve the problems that
>>         the default option is hard to solve. However, I found the
>>         latter one, PCFactorSetFill does not take effect for my
>>         problem. The matrices and rhs as well as the solutions are
>>         attached from the link below. I obtain the solution using
>>         hypre preconditioner and it takes 7 and 38 iterations for
>>         matrix 1 and matrix 2. However, if I use other
>>         preconditioner, the solver just failed at the first matrix. I
>>         have tested this matrix using the native sequential solver
>>         (not PETSc) with ILU preconditioning. If I set the incomplete
>>         factorization level to 0, this sequential solver will take
>>         more than 100 iterations. If I increase the factorization
>>         level to 1 or more, it just takes several iterations. This
>>         remind me that the PC factor for this matrices should be
>>         increased. However, when I tried it in PETSc, it just does
>>         not work.
>>
>>         Matrix and rhs can be obtained from the link below.
>>
>>         https://eilinator.eos.ubc.ca:8443/index.php/s/CalUcq9CMeblk4R
>>         <https://eilinator.eos.ubc.ca:8443/index.php/s/CalUcq9CMeblk4R>
>>
>>         Would anyone help to check if you can make this work by
>>         increasing the PC factor level or fill?
>>
>>
>>     We have ILU(k) supported in serial. However ILU(dt) which takes a
>>     tolerance only works through Hypre
>>
>>     http://www.mcs.anl.gov/petsc/documentation/linearsolvertable.html
>>     <http://www.mcs.anl.gov/petsc/documentation/linearsolvertable.html>
>>
>>     I recommend you try SuperLU or MUMPS, which can both be
>>     downloaded automatically by configure, and
>>     do a full sparse LU.
>>
>>       Thanks,
>>
>>         Matt
>>
>>         Thanks and regards,
>>
>>         Danyang
>>
>>
>>
>>
>>
>>     -- 
>>     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
>>
>>     http://www.caam.rice.edu/~mk51/ <http://www.caam.rice.edu/%7Emk51/>
>
>
>
>
> -- 
> 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
>
> http://www.caam.rice.edu/~mk51/ <http://www.caam.rice.edu/%7Emk51/>

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