Developing and analyzing fourth-order difference methods for the metamaterial Maxwell’s equations

Developing and analyzing fourth-order difference methods for the metamaterial Maxwell’s equations Adv Comput Math https://doi.org/10.1007/s10444-018-9614-8 Developing and analyzing fourth-order difference methods for the metamaterial Maxwell’s equations 1 2 1 Jichun Li · Meng Chen · Min Chen Received: 26 November 2017 / Accepted: 17 May 2018 © Springer Science+Business Media, LLC, part of Springer Nature 2018 Abstract In this paper, we develop both a fourth order explicit scheme and a com- pact implicit scheme for solving the metamaterial Maxwell’s equations. A systematic technique is introduced to prove stability and error estimate for both schemes. Numerical results supporting our analysis are presented. To our best knowledge, our convergence theory and stability results are novel, and provide the first error estimate for the fourth order finite difference methods for Maxwell’s equations. Keywords Maxwell’s equations · Metamaterial · FDTD method · Fourth order method Mathematics Subject Classification (2010) 65N30 · 35L15 · 78-08 Communicated by: Aihui Zhou Work supported by NSF grant DMS-1416742 and NSFC project 11671340. Jichun Li jichun.li@unlv.edu Meng Chen pp756230872@126.com Min Chen chenm1@unlv.nevada.edu Department of Mathematical Sciences, University of Nevada Las Vegas, Las Vegas, NV 89154-4020, USA Hunan Key Laboratory for Computation and Simulation in Science and Engineering, School of Mathematics and Computational Science, Xiangtan University, Xiangtan, China J. Li http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Advances in Computational Mathematics Springer Journals

Developing and analyzing fourth-order difference methods for the metamaterial Maxwell’s equations

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Publisher
Springer US
Copyright
Copyright © 2018 by Springer Science+Business Media, LLC, part of Springer Nature
Subject
Mathematics; Computational Mathematics and Numerical Analysis; Mathematical Modeling and Industrial Mathematics; Mathematical and Computational Biology; Computational Science and Engineering; Visualization
ISSN
1019-7168
eISSN
1572-9044
D.O.I.
10.1007/s10444-018-9614-8
Publisher site
See Article on Publisher Site

Abstract

Adv Comput Math https://doi.org/10.1007/s10444-018-9614-8 Developing and analyzing fourth-order difference methods for the metamaterial Maxwell’s equations 1 2 1 Jichun Li · Meng Chen · Min Chen Received: 26 November 2017 / Accepted: 17 May 2018 © Springer Science+Business Media, LLC, part of Springer Nature 2018 Abstract In this paper, we develop both a fourth order explicit scheme and a com- pact implicit scheme for solving the metamaterial Maxwell’s equations. A systematic technique is introduced to prove stability and error estimate for both schemes. Numerical results supporting our analysis are presented. To our best knowledge, our convergence theory and stability results are novel, and provide the first error estimate for the fourth order finite difference methods for Maxwell’s equations. Keywords Maxwell’s equations · Metamaterial · FDTD method · Fourth order method Mathematics Subject Classification (2010) 65N30 · 35L15 · 78-08 Communicated by: Aihui Zhou Work supported by NSF grant DMS-1416742 and NSFC project 11671340. Jichun Li jichun.li@unlv.edu Meng Chen pp756230872@126.com Min Chen chenm1@unlv.nevada.edu Department of Mathematical Sciences, University of Nevada Las Vegas, Las Vegas, NV 89154-4020, USA Hunan Key Laboratory for Computation and Simulation in Science and Engineering, School of Mathematics and Computational Science, Xiangtan University, Xiangtan, China J. Li

Journal

Advances in Computational MathematicsSpringer Journals

Published: May 28, 2018

References

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