High-Order BDDC Paper

[jeremylt]

This is the PR for the high-order BDDC paper

Currently it has the initial description of the LFA and validation against the LFA of low-order BDDC paper and a high-order BDDC paper I found for 2D Laplacian.

Pages: 13

Initial rough outline:

1. Intro
2. Definitions and Notation (done)
3. LFA of BDDC
   3.1) High-Order FEM (done)
   3.2) BDDC (done)
   3.3) Inexact subdomain solvers (ToDo)
   3.4) Extension to low-order macro-elements (ToDo)
4. Numerical Results
   4.1) Validation for low-order macro-elements (done)
   4.2) Validation for high-order single and macro-elements (done)
   4.3) Solid mechanics example
5. Conclusions

[jeremylt]

I would like to find a little bit of time to get this submitted somewhere.

I stalled out here

3. It might be interesting to add the histograms of the density of eigenvalue distribution like our BDDC paper of Figure 4. I also think the eigenvalue of one is dominated.
4. Following item 3, comparing the histograms between single element higher-order subdomains and macro-element case.

How were these histograms produced? I has having trouble getting Julia to reproduce those mix of bin sizes in the figure mentioned above.