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

Wed Jul 25 05:24:03 CDT 2018

The problem is from two-phase flow in porous media. I have written down the equations and the operators from the 2x2 block Jacobian (see attachment).
The J11 block of the Jacobian is made elliptic.

Maybe someone could tell me how to go on from there to build a good preconditioner?

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 11:37
An: Buesing, Henrik <hbuesing at eonerc.rwth-aachen.de>
Cc: Matthew Knepley <knepley at gmail.com>; 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 10:34, Buesing, Henrik <hbuesing at eonerc.rwth-aachen.de<mailto:hbuesing at eonerc.rwth-aachen.de>> wrote:
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?

Where does your discrete saddle point system come from?
Stokes? Navier Stokes? Something else?
Maybe someone on the list can advise you.

Thank you!
Henrik

--
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>

Von: Dave May <dave.mayhem23 at gmail.com<mailto:dave.mayhem23 at gmail.com>>
Gesendet: Mittwoch, 25. Juli 2018 11:14
An: Matthew Knepley <knepley at gmail.com<mailto:knepley at gmail.com>>
Cc: Buesing, Henrik <hbuesing at eonerc.rwth-aachen.de<mailto:hbuesing at eonerc.rwth-aachen.de>>; PETSc <petsc-users at mcs.anl.gov<mailto: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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