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

[Buesing, Henrik]

Dear Matt! Dear Dave!

Thank you for your messages! I pursued your option 1) and the solver I sent is what I ended up with. Thus, I would like to pursue option 2): Find a better preconditioner than the a11 block.

From a technical viewpoint I understand how I would build a matrix that is used as a preconditioner for the Schur complement.
But, from a mathematical viewpoint I do not know what to assemble. How do I find a good preconditioner for my problem? How would I tackle such a problem?

Thank you!
Henrik


--
Dipl.-Math. Henrik Büsing
Institute for Applied Geophysics and Geothermal Energy
E.ON Energy Research Center
RWTH Aachen University

Mathieustr. 10        | 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

Von: Dave May <dave.mayhem23 at gmail.com>
Gesendet: Mittwoch, 25. Juli 2018 11:14
An: Matthew Knepley <knepley at gmail.com>
Cc: Buesing, Henrik <hbuesing at eonerc.rwth-aachen.de>; PETSc <petsc-users at mcs.anl.gov>
Betreff: Re: [petsc-users] Fieldsplit - Schur Complement Reduction - Efficient Preconditioner for Schur Complement



On 25 July 2018 at 09:48, Matthew Knepley <knepley at gmail.com<mailto:knepley at gmail.com>> wrote:
On Wed, Jul 25, 2018 at 4:24 AM Buesing, Henrik <hbuesing at eonerc.rwth-aachen.de<mailto: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<mailto: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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