Whitney Elements for Transient Maxwell Solvers

Zane Crawford, Michigan State University

The finite element method for computational electromagnetics has been extensively used to discretize the second-order vector wave equation. Curl-conforming elements are used to represent the electric and/or magnetic (E and H) fields, which also satisfies their respective tangential boundary conditions. They have been used with great success in solving Maxwell's equations without charged particles. Introduction of particles brings another set of challenges. Whereas the Whitney spaces permit tangential continuity of fields, normal components are discontinuous. This results in erratic motion of charged particles. To combat this, one may need to use both Whitney-1 and Whitney-2 elements to satisfy tangential E and normal D (or H and B) to solve Maxwell's equations.

Abstract Author(s): Z. Crawford, S. Balasubramaniam