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Developing and Analyzing New Unconditionally Stable Finite Element Schemes for Maxwell’s Equations in Complex Media

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Abstract

In this paper we propose and analyze an unconditionally stable leapfrog method for Maxwell’s equations that removes the time step constraint for stability, which makes the proposed scheme more efficient in computation and easier in algorithm implementation compared to the same order Crank–Nicolson scheme. We also prove the unconditional stability and the optimal error estimate of the proposed scheme. To show the generality of our technique, we further develop similar unconditionally stable leapfrog schemes for other complicated Maxwell’s equations. Numerical results are presented to justify our theoretical analysis and demonstrate the practical applications in simulating wave propagation in metamaterials.

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Acknowledgements

The authors are very grateful to three referees for pointing out many interesting references and their insightful comments which improve our paper.

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Authors and Affiliations

  1. Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, Xiangtan, China

    Yunqing Huang & Meng Chen

  2. School of Mathematics and Information Science, Jiangxi Normal University, Nanchang, 330022, Jiangxi, China

    Meng Chen

  3. Department of Mathematical Sciences, University of Nevada Las Vegas, Nevada, 89154-4020, USA

    Jichun Li

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  1. Yunqing Huang
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  2. Meng Chen
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Correspondence to Jichun Li.

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Partially supported by NSF of China Project No. 11971410, and NSF Grant DMS-20-11943.

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Huang, Y., Chen, M. & Li, J. Developing and Analyzing New Unconditionally Stable Finite Element Schemes for Maxwell’s Equations in Complex Media. J Sci Comput 86, 35 (2021). https://doi.org/10.1007/s10915-020-01406-7

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  • DOI: https://doi.org/10.1007/s10915-020-01406-7

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