Operator splitting methods for Maxwell’s equations in dispersive media with orientational polarization

Abstract

We present two operator splitting schemes for the numerical simulation of Maxwell’s equations in dispersive media of Debye type that exhibit orientational polarization (the Maxwell–Debye model). The splitting schemes separate the mechanisms of wave propagation and polarization to create simpler sub-steps that are easier to implement. In addition, dimensional splitting is used to propagate waves in different axial directions. We present a sequential operator splitting scheme and its symmetrized version for the Maxwell–Debye system in two dimensions. The splitting schemes are discretized using implicit finite difference methods that lead to unconditionally stable schemes. We prove that the fully discretized sequential scheme is a first order time perturbation, and the symmetrized scheme is a second order time perturbation of the Crank–Nicolson scheme for discretizing the Maxwell–Debye model. Numerical examples are presented that illustrate our theoretical results.