[petsc-users] Setting a custom predictor in the generalized-alpha time stepper

[David Kamensky]

Hi Jed,

The current workaround I'm using is very minimal and basically just moves
the definition of `TS_Alpha` from `alpha2.c` up to `petsc/private/tsimpl.h`
(and renames it to avoid a conflict with `TS_Alpha` in `alpha1.c`), but I
gather that we're really still not "supposed to" include that header in
applications.  So, I don't know whether something like that would be
welcomed upstream.  The actual computation of the predictor is done on the
application side.

Having options like `-ts_alpha_same_velocity` and
`-ts_alpha_same_acceleration` could probably be implemented by analogy to
`-ts_theta_initial_guess_extrapolate`, although they wouldn't quite cover
my specific use-case, where I'm only setting the predictor on part of the
solution vector.  So, maybe something more general, like providing a
generalized-$\alpha$-specific option for a custom predictor callback that
takes `X0`, `V0`, and `A0` arguments would be the cleanest solution (and
some convenient shortcuts for full-solution same-velocity and
same-acceleration predictors could subsequently make use of that
infrastructure).  I've been working quickly over the past week, but I might
be able to take some time to implement a more sustainable solution soon.

Thanks again,
David

On Fri, Aug 4, 2023 at 9:23 AM Jed Brown <jed at jedbrown.org> wrote:

> Some other TS implementations have a concept of extrapolation as an
> initial guess. Such method-specific initial guesses sound like they fit
> that pattern and would be welcome to be included in alpha2.c. Would you be
> willing to make a merge request to bring your work upstream?
>
> David Kamensky <david at coreform.com> writes:
>
> > Hi Jed,
> >
> > What I'm trying to compute is basically a standard same-velocity or
> > same-acceleration predictor (although slightly more complicated, since
> I'm
> > restricting it to a sub-system).  I hadn't looked into
> > `SNESSetComputeInitialGuess` yet, although one difficulty is that it
> would
> > need access to the `X0`, `V0`, and `A0` members of the `TS_Alpha` struct,
> > which is only defined in `alpha2.c`, and thus not available through the
> > API.
> >
> > For now, we just worked around this by patching PETSc to move the
> > definition of `TS_Alpha` up into a header to make it accessible.
> > (Modifying the library obviously introduces a maintenance headache; I
> also
> > considered just casting the `ts->data` pointer to `(char*)`, calculating
> > memory offsets based on `sizeof` the struct members, and casting back to
> > `Vec`, but that relies on compiler-specific assumptions, and could also
> > break if the PETSc source code was updated.)  We also shuffled the order
> of
> > some calls to `VecCopy` and `TSPreStage` in the routine
> `TSAlpha_Restart`,
> > so that `TSPreStage` can set the initial guess, although that sounds like
> > it would be unnecessary if we instead used a callback in
> > `SNESSetComputeInitialGuess` that had access to the internals of
> > `TS_Alpha`.
> >
> > Thanks, David
> >
> > On Thu, Aug 3, 2023 at 11:28 PM Jed Brown <jed at jedbrown.org> wrote:
> >
> >> I think you can use TSGetSNES() and SNESSetComputeInitialGuess() to
> modify
> >> the initial guess for SNES. Would that serve your needs? Is there
> anything
> >> else you can say about how you'd like to compute this initial guess? Is
> >> there a paper or something?
> >>
> >> David Kamensky <david at coreform.com> writes:
> >>
> >> > Hi,
> >> >
> >> > My understanding is that the second-order generalized-alpha time
> stepper
> >> in
> >> > PETSc uses a same-displacement predictor as the initial guess for the
> >> > nonlinear solver that executes in each time step.  I'd like to be
> able to
> >> > set this to something else, to improve convergence.  However, my
> >> > (possibly-naive) attempts to use `TSSetPreStep` and `TSSetPreStage`
> >> haven't
> >> > worked out.  Is there any way to set a custom predictor?
> >> >
> >> > Thanks,
> >> > David Kamensky
> >>
>
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