The Hermite-Taylor Correction Function Method for Maxwell’s Equations

doi:10.1007/s42967-023-00287-5

Communications on Applied Mathematics and Computation ›› 2025, Vol. 7 ›› Issue (1): 347-371.doi: 10.1007/s42967-023-00287-5

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The Hermite-Taylor Correction Function Method for Maxwell’s Equations

Yann-Meing Law, Daniel Appel?

Department of CMSE, Michigan State University, East Lansing, USA

收稿日期:2022-10-13 修回日期:2023-03-18 接受日期:2023-05-15 出版日期:2025-04-21 发布日期:2025-04-21
通讯作者: Yann-Meing Law,lawkamci@msu.edu;Daniel Appel?,appeloda@msu.edu E-mail:lawkamci@msu.edu;appeloda@msu.edu
基金资助:
This work was supported in part by the Grant NSF-2208164 and 2210286. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the NSF.

The Hermite-Taylor Correction Function Method for Maxwell’s Equations

Yann-Meing Law, Daniel Appel?

Department of CMSE, Michigan State University, East Lansing, USA

Received:2022-10-13 Revised:2023-03-18 Accepted:2023-05-15 Online:2025-04-21 Published:2025-04-21
Supported by:
This work was supported in part by the Grant NSF-2208164 and 2210286. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the NSF.

摘要/Abstract

摘要： The Hermite-Taylor method, introduced in 2005 by Goodrich et al. is highly efficient and accurate when applied to linear hyperbolic systems on periodic domains. Unfortunately, its widespread use has been prevented by the lack of a systematic approach to implementing boundary conditions. In this paper we present the Hermite-Taylor correction function method (CFM), which provides exactly such a systematic approach for handling boundary conditions. Here we focus on Maxwell’s equations but note that the method is easily extended to other hyperbolic problems.

关键词: Hermite method, Correction function method (CFM), Maxwell's equations, High order, Boundary conditions

Abstract: The Hermite-Taylor method, introduced in 2005 by Goodrich et al. is highly efficient and accurate when applied to linear hyperbolic systems on periodic domains. Unfortunately, its widespread use has been prevented by the lack of a systematic approach to implementing boundary conditions. In this paper we present the Hermite-Taylor correction function method (CFM), which provides exactly such a systematic approach for handling boundary conditions. Here we focus on Maxwell’s equations but note that the method is easily extended to other hyperbolic problems.

Key words: Hermite method, Correction function method (CFM), Maxwell's equations, High order, Boundary conditions

中图分类号:

35Q61
65M70

Yann-Meing Law, Daniel Appel?. The Hermite-Taylor Correction Function Method for Maxwell’s Equations[J]. Communications on Applied Mathematics and Computation, 2025, 7(1): 347-371.

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The Hermite-Taylor Correction Function Method for Maxwell’s Equations

The Hermite-Taylor Correction Function Method for Maxwell’s Equations

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