A High-order Accurate Scheme for the Dispersive Maxwell's Equations and Material Interfaces on Overset Grids

An efficient and high-order accurate scheme for solving the time-domain dispersive Maxwell's equations and material interfaces is described. Maxwell's equations are solved in second-order form for the electric field. A generalized dispersive material (GDM) model is used to represent a general class of linear dispersive materials and this model is implemented in the time-domain with the auxiliary differential equation (ADE) approach. Fourth-order accuracy is achieved with a single-step three-level scheme. High-order accuracy at interfaces is obtained using locally conforming grids and compatibility conditions. Composite overlapping grids are used to treat complex geometry with Cartesian grids generally covering most of the domain and local conforming grids representing curved boundaries and interfaces.