Solving Maxwell's Equations with a Generalized Dispersive Material Madel on Overset Grids

An efficient and high-order accurate time-domain (FDTD) scheme for solving Maxwell's equations in second-order form with a generalized dispersive material (GDM) model is described. The equations are discretized using finite-differences, and advanced in time with a single-stage, three-level, spacetime scheme which remains stable up to the usual explicit CFL-one restriction, as proven using mode analysis. Composite overlapping grids are used to treat complex geometries with boundary-conforming grids, and a high-order upwind dissipation is added to ensure robust and stable approximations on overlapping grids. Properties of the GDM model, which can represent arbitrary dispersive bahaviours, are analysed. Numerical results for some newly developed exact solutions confirm the accuracy and stability of the new scheme.