High order discontinuous Galerkin methods for time-domain and frequency-domain nanophotonics

Abstract

The discontinuous Galerkin (DG) method is a general numerical modeling approach that has been extensively studied in the last 20 years for the solution of many systems of partial differential equations in physics. Its development for the numerical treatment of the system of Maxwell equations was initiated by the applied mathematics community in the early 2000s. It is now a very popular method for time-domain electromagnetics, which is increasingly used and further developed by the applied physics and electrical engineering communities. More recently, a specific variant of DG, referred to as hybridized DG (or HDG), has been proposed for frequency-domain electromagnetics. DG methods possess nice features that make them particularly attractive for dealing with heterogeneous media and irregularly shaped or curved geometries, and more generally with multiscale problems. Not surprisingly, the method has also been adopted by researchers in the nano-optics field. In this paper, we report on our recent efforts for extending the capabilities of this family of methods for the numerical modeling of nanoscale light-matter interactions.