[petsc-users] [EXTERNAL] Re: Problem with PCFIELDSPLIT
Matthew Knepley
knepley at gmail.com
Wed Jul 14 10:09:50 CDT 2021
On Wed, Jul 14, 2021 at 11:01 AM Tang, Qi <tangqi at msu.edu> wrote:
> Thanks a lot for the explanation, Matt and Stefano. That helps a lot.
>
> Just to confirm, the comment in src/ts/impls/implicit/theta/theta.c seems
> to indicates TS solves U_{n+1} in its SNES/KSP solve, but it actually
> solves the update dU_n in U_{n+1} = U_n - lambda*dU_n in the solve. Right?
>
> It actually makes a lot sense, because KSPSolve in TSSolve reports it uses
> zero initial guess. So if what I said is true, that effectively means it
> uses U0 as the initial guess.
>
Yes, this makes it fit the SNES API.
Thanks,
Matt
> Qi
>
> On Jul 14, 2021, at 2:56 AM, Matthew Knepley <knepley at gmail.com> wrote:
>
> On Wed, Jul 14, 2021 at 4:43 AM Stefano Zampini <stefano.zampini at gmail.com>
> wrote:
>
>> Qi
>>
>> Backward Euler is a special case of Theta methods in PETSc (Theta=1).
>> In src/ts/impls/implicit/theta/theta.c on top of
>> SNESTSFormFunction_Theta you have some explanation of what is solved for at
>> each time step (see below). SNES then solves for the Newton update dy_n
>> and the next Newton iterate is computed as x_{n+1} = x_{n} - lambda *
>> dy_n. Hope this helps.
>>
>
> In other words, you should be able to match the initial residual to
>
> F(t + dt, 0, -Un / dt)
>
> for your IFunction. However, it is really not normal to use U = 0. The
> default is to use U = U0
> as the initial guess I think.
>
> Thanks,
>
> Matt
>
>
>> /*
>> This defines the nonlinear equation that is to be solved with SNES
>> G(U) = F[t0+Theta*dt, U, (U-U0)*shift] = 0
>>
>> Note that U here is the stage argument. This means that U = U_{n+1}
>> only if endpoint = true,
>> otherwise U = theta U_{n+1} + (1 - theta) U0, which for the case of
>> implicit midpoint is
>> U = (U_{n+1} + U0)/2
>> */
>> static PetscErrorCode SNESTSFormFunction_Theta(SNES snes,Vec x,Vec y,TS
>> ts)
>>
>>
>> On Jul 14, 2021, at 6:12 AM, Tang, Qi <tangqi at msu.edu> wrote:
>>
>> Hi,
>>
>> During the process to experiment the suggestion Matt made, we ran into
>> some questions regarding to TSSolve vs KSPSolve. We got different initial
>> unpreconditioned residual using two solvers. Let’s say we solve the problem
>> with backward Euler and there is no rhs. We guess TSSolve solves
>> (U^{n+1}-U^n)/dt = A U^{n+1}.
>> (We only provides IJacobian in this case and turn on TS_LINEAR.)
>> So we guess the initial unpreconditioned residual would be ||U^n/dt||_2,
>> which seems different from the residual we got from a backward Euler
>> stepping we implemented by ourself through KSPSolve.
>>
>> Do we have some misunderstanding on TSSolve?
>>
>> Thanks,
>> Qi
>> T5 at LANL
>>
>>
>>
>> On Jul 7, 2021, at 3:54 PM, Matthew Knepley <knepley at gmail.com> wrote:
>>
>> On Wed, Jul 7, 2021 at 2:33 PM Jorti, Zakariae <zjorti at lanl.gov> wrote:
>>
>>> Hi Matt,
>>>
>>>
>>> Thanks for your quick reply.
>>>
>>> I have not completely understood your suggestion, could you please
>>> elaborate a bit more?
>>>
>>> For your convenience, here is how I am proceeding for the moment in my
>>> code:
>>>
>>>
>>> TSGetKSP(ts,&ksp);
>>>
>>> KSPGetPC(ksp,&pc);
>>>
>>> PCSetType(pc,PCFIELDSPLIT);
>>>
>>> PCFieldSplitSetDetectSaddlePoint(pc,PETSC_TRUE);
>>>
>>> PCSetUp(pc);
>>>
>>> PCFieldSplitGetSubKSP(pc, &n, &subksp);
>>>
>>> KSPGetPC(subksp[1], &(subpc[1]));
>>>
>> I do not like the two lines above. We should not have to do this.
>>
>>> KSPSetOperators(subksp[1],T,T);
>>>
>> In the above line, I want you to use a separate preconditioning matrix
>> M, instead of T. That way, it will provide
>> the preconditioning matrix for your Schur complement problem.
>>
>> Thanks,
>>
>> Matt
>>
>>> KSPSetUp(subksp[1]);
>>>
>>> PetscFree(subksp);
>>>
>>> TSSolve(ts,X);
>>>
>>>
>>> Thank you.
>>>
>>> Best,
>>>
>>>
>>> Zakariae
>>> ------------------------------
>>> *From:* Matthew Knepley <knepley at gmail.com>
>>> *Sent:* Wednesday, July 7, 2021 12:11:10 PM
>>> *To:* Jorti, Zakariae
>>> *Cc:* petsc-users at mcs.anl.gov; Tang, Qi; Tang, Xianzhu
>>> *Subject:* [EXTERNAL] Re: [petsc-users] Problem with PCFIELDSPLIT
>>>
>>> On Wed, Jul 7, 2021 at 1:51 PM Jorti, Zakariae via petsc-users <
>>> petsc-users at mcs.anl.gov> wrote:
>>>
>>>> Hi,
>>>>
>>>>
>>>> I am trying to build a PCFIELDSPLIT preconditioner for a matrix
>>>>
>>>> J = [A00 A01]
>>>>
>>>> [A10 A11]
>>>>
>>>> that has the following shape:
>>>>
>>>>
>>>> M_{user}^{-1} = [I -ksp(A00) A01] [ksp(A00) 0] [I
>>>> 0]
>>>>
>>>> [0 I] [0
>>>> ksp(T)] [-A10 ksp(A00) I ]
>>>>
>>>>
>>>> where T is a user-defined Schur complement approximation that replaces
>>>> the true Schur complement S:= A11 - A10 ksp(A00) A01.
>>>>
>>>>
>>>> I am trying to do something similar to this example (lines 41--45 and
>>>> 116--121):
>>>> https://www.mcs.anl.gov/petsc/petsc-current/src/snes/tutorials/ex70.c.html
>>>> <https://urldefense.com/v3/__https://www.mcs.anl.gov/petsc/petsc-current/src/snes/tutorials/ex70.c.html__;!!HXCxUKc!hoEfgnaraTfQoSgAiplsc6GJ_HuPXN88m5AJVy1gb7WVMNkGENDnJ3zToOGlhw$>
>>>>
>>>>
>>>> The problem I have is that I manage to replace S with T on a
>>>> separate single linear system but not for the linear systems generated by
>>>> my time-dependent PDE. Even if I set the preconditioner M_{user}^{-1}
>>>> correctly, the T matrix gets replaced by S in the preconditioner once I
>>>> call TSSolve.
>>>>
>>>> Do you have any suggestions how to fix this knowing that the matrix J
>>>> does not change over time?
>>>>
>>>> I don't like how it is done in that example for this very reason.
>>>
>>> When I want to use a custom preconditioning matrix for the Schur
>>> complement, I always give a preconditioning matrix M to the outer solve.
>>> Then PCFIELDSPLIT automatically pulls the correct block from M, (1,1)
>>> for the Schur complement, for that preconditioning matrix without
>>> extra code. Can you do this?
>>>
>>> Thanks,
>>>
>>> Matt
>>>
>>>> Many thanks.
>>>>
>>>>
>>>> Best regards,
>>>>
>>>>
>>>> Zakariae
>>>>
>>>>
>>>
>>> --
>>> What most experimenters take for granted before they begin their
>>> experiments is infinitely more interesting than any results to which their
>>> experiments lead.
>>> -- Norbert Wiener
>>>
>>> https://www.cse.buffalo.edu/~knepley/
>>> <https://urldefense.com/v3/__http://www.cse.buffalo.edu/*knepley/__;fg!!HXCxUKc!hoEfgnaraTfQoSgAiplsc6GJ_HuPXN88m5AJVy1gb7WVMNkGENDnJ3wB3dcMFw$>
>>>
>>
>>
>> --
>> 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/
>> <https://urldefense.com/v3/__http://www.cse.buffalo.edu/*knepley/__;fg!!HXCxUKc!hoEfgnaraTfQoSgAiplsc6GJ_HuPXN88m5AJVy1gb7WVMNkGENDnJ3wB3dcMFw$>
>>
>>
>>
>>
>
> --
> What most experimenters take for granted before they begin their
> experiments is infinitely more interesting than any results to which their
> experiments lead.
> -- Norbert Wiener
>
> https://www.cse.buffalo.edu/~knepley/
> <https://urldefense.com/v3/__http://www.cse.buffalo.edu/*knepley/__;fg!!HXCxUKc!msQrz7__TrpOmaTVhvY1yLAlDQXNJ5jcYVAxF4lcpyLrZqt2lFe22bkbuJMizA$>
>
>
>
--
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.cse.buffalo.edu/~knepley/>
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