[petsc-dev] Discussion about time-dependent optimization moved from PR

[Jed Brown]

Matthew Knepley <knepley at gmail.com> writes:

> Someone had to do it.
>
> I will not try to frame the entire discussion. Barry has already thrown
> down the "show me your interface" gauntlet. However, I want to emphasize
> one point that may have been lost in the prior discussion. Every example I
> have looked at so far is focused on the reduced space formulation of the
> optimization problem. However, I am interested in the full space
> formulation so that I can do multigrid on the entire optimal control
> problem. This is not a new idea, in particular Borzi does this in SIAM
> Review in 2009. I think we have a tremendous opportunity here since other
> codes cannot do this, it has the potential (I think) for much better
> globalization, and perhaps can be faster.
>
> So, when we come up with interface proposals, I think we should keep a full
> space solution method in mind.

I don't see how any of the present interfaces work for waveform
relaxation.  I also think that is rarely a desirable technique -- too
many awkward limitations.  My recollection is that Borzi only uses it
for parabolic problems, for which adaptivity would have given much
faster/cheaper solutions of equivalent accuracy.  The techniques are
theoretically interesting, but have not demonstrated sufficient
practicality to worry about.  Someone doing research on these full-space
methods can just discretize space-time using SNES.