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.
Qi
On Jul 14, 2021, at 2:56 AM, Matthew Knepley
<[email protected]<mailto:[email protected]>> wrote:
On Wed, Jul 14, 2021 at 4:43 AM Stefano Zampini
<[email protected]<mailto:[email protected]>> 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 <[email protected]<mailto:[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$>
The problem I have is that I manage to replace S with T on a separate single
linear system but not for the linear systems generated by my time-dependent
PDE. Even if I set the preconditioner M_{user}^{-1} correctly, the T matrix
gets replaced by S in the preconditioner once I call TSSolve.
Do you have any suggestions how to fix this knowing that the matrix J does not
change over time?
I don't like how it is done in that example for this very reason.
When I want to use a custom preconditioning matrix for the Schur complement, I
always give a preconditioning matrix M to the outer solve.
Then PCFIELDSPLIT automatically pulls the correct block from M, (1,1) for the
Schur complement, for that preconditioning matrix without
extra code. Can you do this?
Thanks,
Matt
Many thanks.
Best regards,
Zakariae
--
What most experimenters take for granted before they begin their experiments is
infinitely more interesting than any results to which their experiments lead.
-- Norbert Wiener
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--
What most experimenters take for granted before they begin their experiments is
infinitely more interesting than any results to which their experiments lead.
-- Norbert Wiener
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--
What most experimenters take for granted before they begin their experiments is
infinitely more interesting than any results to which their experiments lead.
-- Norbert Wiener
https://www.cse.buffalo.edu/~knepley/<https://urldefense.com/v3/__http://www.cse.buffalo.edu/*knepley/__;fg!!HXCxUKc!msQrz7__TrpOmaTVhvY1yLAlDQXNJ5jcYVAxF4lcpyLrZqt2lFe22bkbuJMizA$>
