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

[Dave May]

On Wed, 25 Jul 2018 at 12:24, Buesing, Henrik <
hbuesing at eonerc.rwth-aachen.de> wrote:

> 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).
>

Have you just tried plain old multiplicative firldplit with LU as the
preconditioned for the diagonal blocks?

What are the iteration counts like?

I think that choice should not be terrible for this system. I'd try this
first before looking at Schur complements.

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>
> 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
>
>
>
> *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> 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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