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

被引：14
|
作者：
Gao LiPing [1 ]
Zhang Bo [2 ,3 ]
机构：
[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
来源：
SCIENCE CHINA-MATHEMATICS | 2011年 / 54卷 / 12期
基金：
中国国家自然科学基金;
关键词：
Maxwell equations; finite-difference time-domain method; stability; superconvergence; perfectly electric conducting boundary conditions; energy identities; ABSORBING BOUNDARY-CONDITIONS; CONVERGENCE ANALYSIS; NUMERICAL-SOLUTION; YEE SCHEME; GRIDS; LAYER;
D O I：
10.1007/s11425-011-4305-7
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
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.
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页码：2693 / 2712
页数：20
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