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

[Jed Brown]

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
>>