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

• Autores: Vrushali Bokil, O. A. Keefer, A. C. -Y. Leung
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 263, Nº 1, 2014, págs. 160-188
• Idioma: inglés
• DOI: 10.1016/j.cam.2013.12.008
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• Resumen

  • 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.