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Symmetric Energy-Conserved S-FDTD Scheme for Two-Dimensional Maxwell’s Equations in Negative Index Metamaterials

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Abstract

A new time second-order symmetric energy-conserved splitting FDTD scheme is proposed for solving the two-dimensional Maxwell’s equations in negative index metamaterials with Drude model. The scheme is proved to preserve the discrete electromagnetic energies in metamaterials and is of second order accuracy both in time and space. The proposed scheme also possesses the superconvergence and the second-order convergence for the discrete divergence. Numerical experiments confirm the theoretical results. Simulations of CW Gaussian beam interactions with double negative matematerials slabs and the electromagnetic waves propagating in metamaterials excited by sinusoidal point source are carried out to show supernormal phenomena in negative index metamaterials.

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Acknowledgments

We would like to thank Professor Chi-Wang Shu and the referees for their valuable suggestions which have helped to improve the paper. D. Liang’s work was partly supported by Natural Sciences and Engineering Research Council of Canada.

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Authors and Affiliations

  1. School of Science, Nanjing University of Science and Technology, Nanjing, 210094, China

    Wanshan Li

  2. School of Mathematics, Shandong University, Jinan, 250199, China

    Wanshan Li

  3. Department of Mathematics and Statistics, York University, Toronto, ON, M3J 1P3, Canada

    Dong Liang

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  1. Wanshan Li
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  2. Dong Liang
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Correspondence to Wanshan Li.

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Li, W., Liang, D. Symmetric Energy-Conserved S-FDTD Scheme for Two-Dimensional Maxwell’s Equations in Negative Index Metamaterials. J Sci Comput 69, 696–735 (2016). https://doi.org/10.1007/s10915-016-0214-9

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  • DOI: https://doi.org/10.1007/s10915-016-0214-9

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