Stability and superconvergence analysis of the FDTD scheme for the 2D Maxwell equations in a lossy medium

doi:10.1007/s11425-011-4305-7

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	Stability and superconvergence analysis of the FDTD scheme for the 2D Maxwell equations in a lossy medium
	Gao LiPing 1; Zhang Bo2,3
	2011-12-01
发表期刊	SCIENCE CHINA-MATHEMATICS
ISSN	1674-7283
卷号	54 期号:12 页码:2693-2712
摘要	This paper is concerned with the stability and superconvergence analysis of the famous finite-difference time-domain (FDTD) scheme for the 2D Maxwell equations in a lossy medium with a perfectly electric conducting (PEC) boundary condition, employing the energy method. To this end, we first establish some new energy identities for the 2D Maxwell equations in a lossy medium with a PEC boundary condition. Then by making use of these energy identities, it is proved that the FDTD scheme and its time difference scheme are stable in the discrete L (2) and H (1) norms when the CFL condition is satisfied. It is shown further that the solution to both the FDTD scheme and its time difference scheme is second-order convergent in both space and time in the discrete L (2) and H (1) norms under a slightly stricter condition than the CFL condition. This means that the solution to the FDTD scheme is superconvergent. Numerical results are also provided to confirm the theoretical analysis.
关键词	Maxwell equations finite-difference time-domain method stability superconvergence perfectly electric conducting boundary conditions energy identities
DOI	10.1007/s11425-011-4305-7
语种	英语
资助项目	Shandong Provincial Natural Science Foundation[Y2008A19] ; Research Reward for Excellent Young Scientists from Shandong Province[2007BS01020] ; Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry ; National Natural Science Foundation of China[11071244]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000297735900013
出版者	SCIENCE PRESS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/11879
专题	应用数学研究所
通讯作者	Gao LiPing
作者单位	1.China Univ Petr, Sch Sci, Dept Computat & Appl Math, Qingdao 266555, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Inst Appl Math, Beijing 100190, Peoples R China 3.Chinese Acad Sci, Acad Math & Syst Sci, LSEC, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Gao LiPing,Zhang Bo. Stability and superconvergence analysis of the FDTD scheme for the 2D Maxwell equations in a lossy medium[J]. SCIENCE CHINA-MATHEMATICS,2011,54(12):2693-2712.
APA	Gao LiPing,&Zhang Bo.(2011).Stability and superconvergence analysis of the FDTD scheme for the 2D Maxwell equations in a lossy medium.SCIENCE CHINA-MATHEMATICS,54(12),2693-2712.
MLA	Gao LiPing,et al."Stability and superconvergence analysis of the FDTD scheme for the 2D Maxwell equations in a lossy medium".SCIENCE CHINA-MATHEMATICS 54.12(2011):2693-2712.