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

[Jed Brown]

Yeah, we'd like the implementation to stay in alpha2.c. There could be a new interface TSAlpha2SetPredictorType (with -ts_alpha2_predictor_type [none,same_velocity,...]) or TSAlpha2SetPredictorFunction.

David Kamensky <david at coreform.com> writes:

> 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
>> >>
>>