A comparison of three mixed methods for the time-dependent Maxwell's equations
SIAM Journal on Scientific and Statistical Computing
An analysis of operator splitting techniques in the stiff case
Journal of Computational Physics
A split step approach for the 3-D Maxwell's equations
Journal of Computational and Applied Mathematics
Finite Differences And Partial Differential Equations
Finite Differences And Partial Differential Equations
Energy-conserved splitting FDTD methods for Maxwell’s equations
Numerische Mathematik
Stability of FD-TD Schemes for Maxwell-Debye and Maxwell-Lorentz Equations
SIAM Journal on Numerical Analysis
Journal of Scientific Computing
DSP-Based ADI-PML formulations for truncating linear debye and lorentz dispersive FDTD domains
ICCSA'05 Proceedings of the 2005 international conference on Computational Science and Its Applications - Volume Part IV
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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.