BDDC Example

[jeremylt]

Nothing much to look at here yet. I'm just putting this here to make it easier to see/comment on what I'm doing.

[jeremylt]

There is some debugging to do after #744 merges, but this should be close. The open task is prolonging into the broken space - We don't really have a way to go from 1 qfunction output into a pair of target vectors

[jeremylt]

I have not started debugging yet, but all of the pieces I want are there. Here's to hoping

[jeremylt]

Huzzah - it compiles. Now to see what else is broken about it.

[jeremylt]

Oh cool, some memcheck backend change shows that we have a problem with how we are treating memory. That gives some direction to future debugging efforts here

[jeremylt]

ToDo: Fix assembly to use libCEED native assembly

[jeremylt]

Turns out the memcheck issue was unrelated - see the vector fix PR.

I wonder if the convergence issue can in part can be related to the loss of accuracy from using coloring to assemble the schur problem, which is part of why I want to switch to libCEED assembly (and it'll be faster) Nope, I assembled the way I assembled for good reasons since I'm assembling the action of several operators in sequence with other actions in between.

[jeremylt]

Note to self - I'm suspicious about possible pollution of helper function input vectors. Also, the addition of the preconditioning contributions back from the restricted problem looks funko