erdc-cm/proteus — pull request #171 by cekees (2014-12-12 16:06:14+00:00)
Title: [WIP] cekees/add nonlinear pod

@MajinSaha and @mfarthin this is my branch with the general nonlinear POD implemented as a special solver for the full system. I need to shelve this work for a couple of days at least some I'm going to leave this PR here as a work in progress unless Matthew wants me to merge it with his deim experiments. Here are the things I see that need thought/work on this branch.

- [ ] Decide on notation: our U is Sorenson's V, Sorenson's U is the reduced based for F, our u is the unknown
- [ ] Optimize loops for calculating U^t J U (this is just to speed up our planned sensitivity studies), current implementation is just a pure python prototype.
- [ ] Add DEIM to calculation P and modify F and J calculations (still using full F and J at first)
- [ ] Modify F and J API to allow efficient computation of U (P^t U)^-1 P^t F and U (P^t U)^-1 P^t J U