Anyone out there doing anything with the extended finite element method?
Yes. We actually have a fairly large push in this direction right now. We got a proposal funded for this year (and probably the next two years) to do just this... XFEM with libMesh (well... with MOOSE, but of course that will mean putting the basic support into libMesh). We are working with John Dolbow from Duke (http://www.cee.duke.edu/faculty/john-e-dolbow) who is an XFEM expert.
We already have a few toy problems working.
We are simultaneously working on the two major ways of implementing XFEM:
1. Mesh cutting with "phantom cells".
2. "Enriched" finite element shape functions (like with a Heaviside for a crack).
I am heading up the the second one while Ben Spencer is doing the first. I have hacked a lot in the right direction (so far, I've added a new FE type where I've overloaded the idea of the P order for specifying whether or not an element should be "broken" so I can add enriched DoFs there). I know that what I've done is not the ultimate answer... but we were exploring whether or not we could dynamically add DoFs for the enrichment... and it seems like we can. Note that I don't have a working prototype of that code yet (I just got sidetracked on another project that's going to take a few more weeks to finish before I get back to XFEM).
We've been doing this work in preparation for talking to you and Roy so we would have our ducks in a row for intelligent conversation about what needs to be added to libMesh. It appears as if that time has now come ;-)
Let's put together a conference call on this to start a dialog this week. When are you available?
Does anyone else (Roy? Paul?) want to be on the conference call as well?