Algebraically constrained extended edge element method (eXFEM-AC) for resolution of multi-material cells

Abstract

Surface effects are critical to the predictive simulation of electromagnetics as current tends to concentrate near material interfaces. There are two principal difficulties in the accurate representation of these effects in discrete models. First, many applications of interest operate at large deformations, where body-fitted meshes are impractical. Second, physics-compatible discretizations of the governing equations require curl-conforming edge elements, for which no practical alternatives to body-fitted meshes exist. The main purpose of this paper is to develop such an alternative that avoids remeshing the problem.Our approach uses the existing edge element basis to dynamically construct an interface-conforming basis. We show that in the case of triangular grids in two dimensions, our approach generates a basis that spans the same space as edge elements on an interface-fitted mesh. We also demonstrate the efficacy of the approach computationally.