A discontinuous finite element time-domain solver for nanophotonic applications

Abstract

We present a discontinuous finite element time-domain solver for the computer simulation of the interaction of light with nanometer scale structures. The method relies on a compact stencil high order interpolation of the electromagnetic field components within each cell of an unstructured tetrahedral mesh. This piecewise polynomial numerical approximation is allowed to be discontinuous from one mesh cell to another, and the consistency of the global approximation is obtained thanks to the definition of appropriate numerical traces of the fields on a face shared by two neighboring cells. Time integration is achieved using an explicit scheme and no global mass matrix inversion is required to advance the solution at each time step. Moreover, the resulting time-domain solver is particularly well adapted to parallel computing. In this paper, we discuss about recent contributions for improving the accuracy, flexibility and efficiency of the method, as well as its adaptation to physical models relevant to nanophotonic applications.