[petsc-users] Apply operator to linearised system before solving?

[Asbjørn Nilsen Riseth]

Hi Matt,

1) K =
[               I                   0 ;
-A10*inv(diag(A00))     I  ]

There is a typo in my first email: S = Atilde11 = A11 -
A10*inv(diag(A00))*A01

2) I'd like to have the linear solver close to what these people currently
use. My ultimate goal is to look at nonlinear solver strategies, not
improve their linear solver. I already have a PC that seems to work fine
for my purposes, but was hoping I could implement this version of CPR to
get even closer to their current systems.

Ozzy

On Thu, 11 Jun 2015 at 00:54 Matthew Knepley <knepley at gmail.com> wrote:

> On Wed, Jun 10, 2015 at 6:30 PM, Asbjørn Nilsen Riseth <
> riseth at maths.ox.ac.uk> wrote:
>
>> Dear PETSc community,
>>
>> I'm trying to implement a preconditioner used in reservoir modelling,
>> called Constrained Pressure Residual.
>> They apply a transformation to the linearised system we get from each
>> Newton step, before solving it. Then a 2-stage multiplicative
>> preconditioner on the transformed system.
>>
>
> 1) What is K?
>
> 2) Do you care about the 2-stage thing, or would any Stokes solver do?
>
>   Thanks,
>
>     Matt
>
>
>> The main problem is implementing step 1 below.
>>
>> Let A be the Jacobian, b the residual and K my transformation.
>> A = [A00 A01; A10 A11].
>> The process is roughly like this:
>> 1) Set Atilde = KA,  btilde = Kb.
>>  - We want to solve Atilde x =  btilde
>>
>> 2) Create a 2-stage multiplicative preconditioner using Atilde, btilde
>> pc0: This is only applied to the "fieldsplit 1" block of my system.
>> B_1 = [0 0; 0 S^-1]
>> Where S is a selfp Schur approximation from Atilde
>> S =  Atilde11 - Atilde10 * inv(diag(Atilde00))* Atilde01
>> pc1: This is a standard ILU on the whole system Atilde
>>
>> Currently I'm doing something like this
>> Step 1:
>> -ksp_type richardson -ksp_max_it 1
>> -pc_type python
>> Then I create Atilde from KA in PCSetup, and a FGMRES ksp to take care of
>> step 2 with PCApply
>>
>> Step 2:
>> pc_type composite
>> pc_composite_type multiplicative
>> pc_composite_pcs python,ilu,
>>
>> Are there better ways of dealing with this transformation?
>> To me it looks similar to a 2-step right preconditioner on top of a left
>> preconditioner.
>>
>> Regards,
>> Ozzy
>>
>
>
>
> --
> 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
>
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