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A Legendre Pseudospectral Penalty Scheme for Solving Time-Domain Maxwell’s Equations

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Abstract

In this paper we present a Legendre pseudospectral algorithm based on a tensor product formulation for solving the time-domain Maxwell equations. Our approach starts by conducting an analysis for finding well-posed boundary operators for the Maxwell equations. We then discuss equivalent characteristic boundary conditions for common physical boundary constraints. These theoretical results are then employed to construct a pseudospectral penalty scheme which is asymptotically stable at the semidiscrete level. Numerical computations based on the proposed scheme are also provided for different cases where exact solutions exist. By measuring the differences between the computed and exact solutions, we observe the expected convergence patterns of the scheme.

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Authors and Affiliations

  1. Department of Mathematics, National Cheng Kung University, No. 1 University Rd., Tainan, 701, Taiwan

    Chun-Hao Teng, Chien-Nan Lin & Ko-An Feng

  2. Graduate Institute of Communication Engineering, National Taiwan University, No. 1, Sec. 4, Roosevelt Rd., Taipei, 10617, Taiwan

    Bang-Yan Lin & Hung-Chun Chang

  3. Department of Electrical Engineering, National Taiwan University, No. 1, Sec. 4, Roosevelt Rd., Taipei, 10617, Taiwan

    Hung-Chun Chang

  4. Graduate Institute of Photonics and Optoelectronics, National Taiwan University, No. 1, Sec. 4, Roosevelt Rd., Taipei, 10617, Taiwan

    Hung-Chun Chang

  5. Institute of Atomic and Molecular Science, Academia Sinica, Taipei, Taiwan

    Hei-Chen Hsu

Authors
  1. Chun-Hao Teng
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  2. Bang-Yan Lin
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Correspondence to Chun-Hao Teng.

Additional information

This work is supported by National Science Council grant No. NSC 95-2120-M-001-003.

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Teng, CH., Lin, BY., Chang, HC. et al. A Legendre Pseudospectral Penalty Scheme for Solving Time-Domain Maxwell’s Equations. J Sci Comput 36, 351–390 (2008). https://doi.org/10.1007/s10915-008-9194-8

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  • DOI: https://doi.org/10.1007/s10915-008-9194-8

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