Transformation optics based local mesh refinement for solving Maxwell's equations

Authors:
Jinjie Liu;Moysey Brio;Jerome V. Moloney
Affiliations:
Department of Mathematical Sciences, Delaware State University, Dover, DE 19901, United States;Arizona Center for Mathematical Sciences at Department of Mathematics, The University of Arizona, Tucson, AZ 85721, United States;Arizona Center for Mathematical Sciences at Department of Mathematics, The University of Arizona, Tucson, AZ 85721, United States
Venue:
Journal of Computational Physics
Year:
2014

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Abstract

In this paper, a novel local mesh refinement algorithm based on transformation optics (TO) has been developed for solving the Maxwell@?s equations of electrodynamics. The new algorithm applies transformation optics to enlarge a small region so that it can be resolved by larger grid cells. The transformed anisotropic Maxwell@?s equations can be stably solved by an anisotropic FDTD method, while other subgridding or adaptive mesh refinement FDTD methods require time-space field interpolations and often suffer from the late-time instability problem. To avoid small time steps introduced by the transformation optics approach, an additional application of the mapping of the material matrix to a dispersive material model is employed. Numerical examples on scattering problems of dielectric and dispersive objects illustrate the performance and the efficiency of the transformation optics based FDTD method.