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

[Dave May]

On 25 July 2018 at 10:34, Buesing, Henrik 
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
> |
> Tel +49 (0)241 80 49907
>
> 52074 Aachen, Germany | Fax +49 (0)241 80 49889
>
>
>
> http://www.eonerc.rwth-aachen.de/GGE
>
> hbues...@eonerc.rwth-aachen.de
>
>
>
> *Von:* Dave May 
> *Gesendet:* Mittwoch, 25. Juli 2018 11:14
> *An:* Matthew Knepley 
> *Cc:* Buesing, Henrik ; PETSc <
> petsc-users@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  wrote:
>
> On Wed, Jul 25, 2018 at 4:24 AM Buesing, Henrik <
> hbues...@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
> 
> (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
> |
> Tel +49 (0)241 80 49907
> 52074 Aachen, Germany | Fax +49 (0)241 80 49889
>
> http://www.eonerc.rwth-aachen.de/GGE
> hbues...@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/ 
>
>
>

Re: [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
hbues...@eonerc.rwth-aachen.de

Von: Dave May 
Gesendet: Mittwoch, 25. Juli 2018 11:14
An: Matthew Knepley 
Cc: Buesing, Henrik ; PETSc 

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



On 25 July 2018 at 09:48, Matthew Knepley 
mailto:knep...@gmail.com>> wrote:
On Wed, Jul 25, 2018 at 4:24 AM Buesing, Henrik 
mailto:hbues...@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
  (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  
  | Tel +49 (0)241 80 49907
52074 Aachen, Germany | Fax +49 (0)241 80 49889

http://www.eonerc.rwth-aachen.de/GGE
hbues...@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/

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

[Dave May]

On 25 July 2018 at 09:48, Matthew Knepley  wrote:

> On Wed, Jul 25, 2018 at 4:24 AM Buesing, Henrik <
> hbues...@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

(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
>> 
>> | Tel +49 (0)241 80 49907
>> 52074 Aachen, Germany | Fax +49 (0)241 80 49889
>>
>> http://www.eonerc.rwth-aachen.de/GGE
>> hbues...@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/ 
>

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

[Matthew Knepley]

On Wed, Jul 25, 2018 at 4:24 AM Buesing, Henrik <
hbues...@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.

  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| Tel +49 (0)241 80 49907
> 52074 Aachen, Germany | Fax +49 (0)241 80 49889
>
> http://www.eonerc.rwth-aachen.de/GGE
> hbues...@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/ 

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

[Buesing, Henrik]

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? 

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| Tel +49 (0)241 80 49907
52074 Aachen, Germany | Fax +49 (0)241 80 49889

http://www.eonerc.rwth-aachen.de/GGE
hbues...@eonerc.rwth-aachen.de