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Volume 25, Issue 1
A Conformal Energy-Conserved Method for Maxwell's Equations with Perfectly Matched Layers

Chaolong Jiang, Jin Cui & Yushun Wang

DOI: 10.4208/cicp.OA-2017-0219

Commun. Comput. Phys., 25 (2019), pp. 84-106.

Published online: 2018-09

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  • Abstract

In this paper, a conformal energy-conserved scheme is proposed for solving the Maxwell's equations with the perfectly matched layer. The equations are split as a Hamiltonian system and a dissipative system, respectively. The Hamiltonian system is solved by an energy-conserved method and the dissipative system is integrated exactly. With the aid of the Strang splitting, a fully-discretized scheme is obtained. The resulting scheme can preserve the five discrete conformal energy conservation laws and the discrete conformal symplectic conservation law. Based on the energy method, an optimal error estimate of the scheme is established in discrete L2-norm. Some numerical experiments are addressed to verify our theoretical analysis.

  • Keywords

Maxwell's equations, Fourier pseudo-spectral method, error estimate, conformal conservation law, PML.

  • AMS Subject Headings

65M12, 65M15, 65M70

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-25-84, author = {Chaolong Jiang, Jin Cui and Yushun Wang}, title = {A Conformal Energy-Conserved Method for Maxwell's Equations with Perfectly Matched Layers}, journal = {Communications in Computational Physics}, year = {2018}, volume = {25}, number = {1}, pages = {84--106}, abstract = {

In this paper, a conformal energy-conserved scheme is proposed for solving the Maxwell's equations with the perfectly matched layer. The equations are split as a Hamiltonian system and a dissipative system, respectively. The Hamiltonian system is solved by an energy-conserved method and the dissipative system is integrated exactly. With the aid of the Strang splitting, a fully-discretized scheme is obtained. The resulting scheme can preserve the five discrete conformal energy conservation laws and the discrete conformal symplectic conservation law. Based on the energy method, an optimal error estimate of the scheme is established in discrete L2-norm. Some numerical experiments are addressed to verify our theoretical analysis.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2017-0219}, url = {http://global-sci.org/intro/article_detail/cicp/12664.html} }
TY - JOUR T1 - A Conformal Energy-Conserved Method for Maxwell's Equations with Perfectly Matched Layers AU - Chaolong Jiang, Jin Cui & Yushun Wang JO - Communications in Computational Physics VL - 1 SP - 84 EP - 106 PY - 2018 DA - 2018/09 SN - 25 DO - http://doi.org/10.4208/cicp.OA-2017-0219 UR - https://global-sci.org/intro/article_detail/cicp/12664.html KW - Maxwell's equations, Fourier pseudo-spectral method, error estimate, conformal conservation law, PML. AB -

In this paper, a conformal energy-conserved scheme is proposed for solving the Maxwell's equations with the perfectly matched layer. The equations are split as a Hamiltonian system and a dissipative system, respectively. The Hamiltonian system is solved by an energy-conserved method and the dissipative system is integrated exactly. With the aid of the Strang splitting, a fully-discretized scheme is obtained. The resulting scheme can preserve the five discrete conformal energy conservation laws and the discrete conformal symplectic conservation law. Based on the energy method, an optimal error estimate of the scheme is established in discrete L2-norm. Some numerical experiments are addressed to verify our theoretical analysis.

Chaolong Jiang, Jin Cui and Yushun Wang. (2018). A Conformal Energy-Conserved Method for Maxwell's Equations with Perfectly Matched Layers. Communications in Computational Physics. 25 (1). 84-106. doi:10.4208/cicp.OA-2017-0219
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