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Energy-Conserved Splitting Multidomain Legendre-Tau Spectral Method for Two Dimensional Maxwell’s Equations

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Abstract

In this paper, the energy-conserved splitting multidomain Legendre-tau Chebyshev-collocation spectral method is proposed for solving two dimensional Maxwell’s equations. The method uses different degree polynomials to approximate the electric and magnetic fields respectively, and they can be decoupled in computation. Moreover, the error estimates are improved to the optimal order. In semi-discrete scheme, we apply the multidomain Legendre-tau Chebyshev-collocation spectral method. In fully discrete scheme, we use the energy-conserved splitting method in time step. The optimal error estimate is obtained for the homogeneous media. The multidomain spectral method is also applied to solve Maxwell’s equations with discontinuous solutions. Numerical results indicate that the spectral accuracy is not affected by the discontinuity of solutions. With the multidomain method, the computation can be implemented in parallel.

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Acknowledgements

Heping Ma’s and Cuixia Niu’s works were supported by the NSF of China(11971016). Dong Liang’s work was supported partially by Natural Sciences and Engineering Research Council of Canada.

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Authors and Affiliations

  1. Department of Mathematics, Shanghai University, Shanghai, 200444, China

    Cuixia Niu & Heping Ma

  2. School of Computer Science and Technology, Shandong Institute of Business and Technology, Yantai, 264000, China

    Cuixia Niu

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

    Dong Liang

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  1. Cuixia Niu
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  2. Heping Ma
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  3. Dong Liang
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Correspondence to Heping Ma.

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Niu, C., Ma, H. & Liang, D. Energy-Conserved Splitting Multidomain Legendre-Tau Spectral Method for Two Dimensional Maxwell’s Equations. J Sci Comput 90, 77 (2022). https://doi.org/10.1007/s10915-021-01744-0

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