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

[Barry Smith]

> On Oct 15, 2017, at 11:59 AM, Jed Brown <jed at jedbrown.org> wrote:
> 
> 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.

   Yes, but since that is a huge involved process (they need to manage time discretization etc themselves) they will NEVER compare with reduced methods and that is a huge part of the problem. People do "research" in one or the other approach and never compare the two, leading to bad research. If we can combine them then one can actually compare the two approaches.

   Barry

I'm not saying it is possible to have a nice API that combines them.