Computational Electromagnetics
The use of physics-compatible discretizations is critical for the accurate solution of computational electromagnetics problems. I focus on time-domain versions of the eddy current equations (neglecting polarization, magnetization and displacement currents), or problems that are close to, but not quite eddy current problems.
A recent focus of my work has been on techniques for approximating sub-cell interfaces in the context of electromagnetics. This includes XFEM-like techniques, as well as homogenization models for mixed material cells.
Collaborators
- Allen Robinson
- Richard Kramer
- Thomas Voth
Multilevel Solvers
Multilevel solvers in general, and algebraic multigrid (AMG) in particular, have been active areas of research in the last decade or so. These methods have the potential to provide nearly h-independent solvers for a variety of problems.
One area that has been the focus of my recent works is that of AMG solvers for Maxwell’s equations. Specifically, we consider problem reformulations that can make the system significantly easier for an AMG code to solve.
Collaborators
- Pavel Bochev
- Jonathan Hu
- Ray Tuminaro