Efficient Upwind Schemes for Linear and Nonlinear Dispersive Maxwell's Equations on Overset Grids

Overlapping grids are a powerful tool for representing the complex geometry inherent to many linear and nonlinear electromagnetic scattering problems. However, inter-grid interpolation is known to be potentially destabilizing in the context of wave phenomena. Upwind dissipation has become one of the most powerful tools to cure this instability, but unfortunately some of the original formulations were difficult to implement and expensive, particularly for complex material models. Here we present an optimized upwind scheme whose formulation enables a simple modular implementation so that it can be easily be applied even to complex models, and is computationally efficient in comparison to previous schemes.