[petsc-users] Discrete adjoint and adaptive time stepping

[Jed Brown]

Barry Smith <bsmith at mcs.anl.gov> writes:
>> If so, how is it done?
>
>    We just keep the history of the time-step sizes and then use those time-step sizes when doing the backward integration. Seems simple to me, am I missing something?

Barry, if you're using this for optimization, you might want the
gradient to be exactly consistent with the objective functional.  But
for that, you would need to differentiate the controller, which is
non-smooth in practice because the number of time steps can change and
stages could be rejected (solver failure).

One approach would be to save the timestep sequence and have the
controller use that in subsequent *forward* runs.  If the dynamical
system behaves similarly for those steps, it would be okay to use the
same timestep sequence.
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