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.
/*
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 <[email protected]> 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@LANL
>
>
>
>> On Jul 7, 2021, at 3:54 PM, Matthew Knepley <[email protected]
>> <mailto:[email protected]>> wrote:
>>
>> On Wed, Jul 7, 2021 at 2:33 PM Jorti, Zakariae <[email protected]
>> <mailto:[email protected]>> 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 <[email protected] <mailto:[email protected]>>
>> Sent: Wednesday, July 7, 2021 12:11:10 PM
>> To: Jorti, Zakariae
>> Cc: [email protected] <mailto:[email protected]>; 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
>> <[email protected] <mailto:[email protected]>> 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$>
