[petsc-users] Reproducibility when restarting generalized-alpha

[David Kamensky]

Hi,

I've recently been helping some co-workers with restarting PETSc time
integrators from saved solution data.

It looks like the only supported path for restarting the generalized-alpha
integrator for 2nd-order-in-time systems (`TSALPHA2`) is to follow the same
procedure as initialization, in which two first-order-accurate half-steps
are used to estimate an acceleration from the given displacement and
velocity.  However, the resulting acceleration is not exactly equivalent to
the intermediate one that would have been used by the integrator if the
integration simply proceeded without restarting.  This prevents exact
reproducibility of computations from saved intermediate results.  (An
analogous issue would also affect `TSALPHA` for first-order-in-time
problems, where velocity is estimated on initialization/restart.)

Am I misunderstanding this, or missing a better method of restarting the
2nd-order generalized-alpha integrator?  If not, would there be interest in
adding an alternate initialization/restart option to the `TSALPHA2`
integrator that takes a user-provided `Vec` for the initial/intermediate
acceleration, and skips over the half-step estimation procedure?

Thanks, David
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