Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6422577 | Journal of Computational and Applied Mathematics | 2014 | 29 Pages |
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.