Symplectic and multisymplectic numerical methods for Maxwell's equations

doi:10.1016/j.jcp.2010.12.006

	Symplectic and multisymplectic numerical methods for Maxwell's equations
	Sun, Y.; Tse, P. S. P.
	2011-03-01
发表期刊	JOURNAL OF COMPUTATIONAL PHYSICS
ISSN	0021-9991
卷号	230 期号:5 页码:2076-2094
摘要	In this paper, we compare the behaviour of one symplectic and three multisymplectic methods for Maxwell's equations in a simple medium. This is a system of PDEs with symplectic and multisymplectic structures. We give a theoretical discussion of how some numerical methods preserve the discrete versions of the local and global conservation laws and verify this behaviour in numerical experiments. We also show that these numerical methods preserve the divergence. Furthermore, we extend the discussion on dispersion for (multi)symplectic methods applied to PDEs with one spatial dimension, to include anisotropy when applying (multi)symplectic methods to Maxwell's equations in two spatial dimensions. Lastly, we demonstrate how varying the Courant-Friedrichs-Lewy (CFL) number can cause the (multi)symplectic methods in our comparison to behave differently, which can be explained by the study of backward error analysis for PDEs. (C) 2010 Elsevier Inc. All rights reserved.
关键词	Maxwell's equations Symplectic methods Multisymplectic methods Energy-preserving methods Dispersion relations Backward error analysis
DOI	10.1016/j.jcp.2010.12.006
语种	英语
资助项目	National Natural Science Foundation of China[60931002] ; National Basic Research Program of China[2010CB832702] ; Funds for Creative Research Groups of China[11021101] ; China Postdoctoral Science Foundation
WOS研究方向	Computer Science ; Physics
WOS类目	Computer Science, Interdisciplinary Applications ; Physics, Mathematical
WOS记录号	WOS:000287057900019
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/12482
专题	计算数学与科学工程计算研究所
通讯作者	Sun, Y.
作者单位	Chinese Acad Sci, Acad Math & Syst Sci, LSEC, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Sun, Y.,Tse, P. S. P.. Symplectic and multisymplectic numerical methods for Maxwell's equations[J]. JOURNAL OF COMPUTATIONAL PHYSICS,2011,230(5):2076-2094.
APA	Sun, Y.,&Tse, P. S. P..(2011).Symplectic and multisymplectic numerical methods for Maxwell's equations.JOURNAL OF COMPUTATIONAL PHYSICS,230(5),2076-2094.
MLA	Sun, Y.,et al."Symplectic and multisymplectic numerical methods for Maxwell's equations".JOURNAL OF COMPUTATIONAL PHYSICS 230.5(2011):2076-2094.