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

作　　者：GAO LiPing ZHANG Bo 

机构地区：[1]Department of Computational and Applied Mathematics, School of Sciences, China University of Petroleum, Qingdao 266555, China [2]LSEC and Institute of Applied Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China

出　　处：《Science China Mathematics》2011年第12期2693-2712,共20页中国科学：数学（英文版）

基　　金：supported by Shandong Provincial Natural Science Foundation (Grant No. Y2008A19);supported by Research Reward for Excellent Young Scientists from Shandong Province(Grant No. 2007BS01020) ;supported by Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry;supported by National Natural Science Foundation of China (Grant No. 11071244)

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 L2 and H1 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 L2 and H1 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.This paper is concerned with the stability and superconvergence analysis of the famous finitedifference 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 L2 and H1 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 L2 and H1 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 

分 类 号：O441[理学—电磁学] TN011[理学—物理]