[petsc-users] Fieldsplit - Schur Complement Reduction - Efficient Preconditioner for Schur Complement

[Dave May]

On 25 July 2018 at 09:48, Matthew Knepley <knepley at gmail.com> wrote:

> On Wed, Jul 25, 2018 at 4:24 AM Buesing, Henrik <
> hbuesing at eonerc.rwth-aachen.de> wrote:
>
>> Dear all,
>>
>> I would like to improve the iterative solver [1]. As I understand it I
>> would need to improve the preconditioner for the Schur complement.
>>
>> How would I do that?
>>
>
> 1) I always start from the exact thing (full Schur factorization with
> exact solves and back off parts until I am happy)
>
> 2) Is the a11 block a good preconditioner for your Schur complement? If
> not, I would start by replacing that matrix
>     with something better.
>

Some additional info. If you want to pursue option 2, you need to do call

  PCFieldSplitSetSchurPre()

http://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/PC/
PCFieldSplitSetSchurPre.html#PCFieldSplitSetSchurPre

with PC_FIELDSPLIT_SCHUR_PRE_USER
<http://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/PC/PCFieldSplitSchurPreType.html#PCFieldSplitSchurPreType>
(second arg) and your user defined schur complement preconditioner (last
arg).

Thanks,
  Dave


>
>   Thanks,
>
>     Matt
>
>
>> Thank you for your help!
>> Henrik
>>
>>
>>
>> [1]
>> -ksp_max_it 100 -ksp_rtol 1e-6 -ksp_atol 1e-50 -ksp_type fgmres -pc_type
>> fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_precondition
>> a11 -fieldsplit_p_w_ksp_type preonly -fieldsplit_S_n_ksp_type gmres
>> -fieldsplit_p_w_pc_type hypre -fieldsplit_p_w_pc_hypre_type boomeramg
>> -fieldsplit_S_n_pc_type hypre -fieldsplit_S_n_pc_hypre_type boomeramg
>> -fieldsplit_S_n_ksp_max_it 100 fieldsplit_S_n_ksp_rtol 1e-2
>>
>>
>> --
>> Dipl.-Math. Henrik Büsing
>> Institute for Applied Geophysics and Geothermal Energy
>> E.ON Energy Research Center
>> RWTH Aachen University
>>
>> Mathieustr. 10
>> <https://maps.google.com/?q=Mathieustr.+10&entry=gmail&source=g>
>> | Tel +49 (0)241 80 49907
>> 52074 Aachen, Germany | Fax +49 (0)241 80 49889
>>
>> http://www.eonerc.rwth-aachen.de/GGE
>> hbuesing at eonerc.rwth-aachen.de
>>
>>
>
> --
> 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
>
> https://www.cse.buffalo.edu/~knepley/ <http://www.caam.rice.edu/~mk51/>
>
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