STABILITY AND SUPER CONVERGENCE ANALYSIS OF ADI-FDTD FOR THE 2D MAXWELL EQUATIONS IN A LOSSY MEDIUM

doi:10.1016/S0252-9602(12)60184-2

数学物理学报(英文版) ›› 2012, Vol. 32 ›› Issue (6): 2341-2368.doi: 10.1016/S0252-9602(12)60184-2

STABILITY AND SUPER CONVERGENCE ANALYSIS OF ADI-FDTD FOR THE 2D MAXWELL EQUATIONS IN A LOSSY MEDIUM

高理平

Department of Computational and Applied Mathematics, School of Sciences, China University of Petroleum, Qingdao 266580, China

收稿日期:2011-01-27 修回日期:2012-05-04 出版日期:2012-11-20 发布日期:2012-11-20
基金资助:
The work was supported by Shandong Provincial Natural Science Foundation (Y2008A19) and the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry.

STABILITY AND SUPER CONVERGENCE ANALYSIS OF ADI-FDTD FOR THE 2D MAXWELL EQUATIONS IN A LOSSY MEDIUM

GAO Li-Ping

Department of Computational and Applied Mathematics, School of Sciences, China University of Petroleum, Qingdao 266580, China

Received:2011-01-27 Revised:2012-05-04 Online:2012-11-20 Published:2012-11-20
Supported by:
The work was supported by Shandong Provincial Natural Science Foundation (Y2008A19) and the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry.

摘要/Abstract

摘要：

Several new energy identities of the two dimensional(2D) Maxwell equations in a lossy medium in the case of the perfectly electric conducting boundary conditions are proposed and proved. These identities show a new kind of energy conservation in the Maxwell system and provide a new energy method to analyze the alternating direction im-plicit finite difference time domain method for the 2D Maxwell equations (2D-ADI-FDTD). It is proved that 2D-ADI-FDTD is approximately energy conserved, unconditionally sta-ble and second order convergent in the discrete L2 and H1 norms, which implies that 2D-ADI-FDTD is super convergent. By this super convergence, it is simply proved that the error of the divergence of the solution of 2D-ADI-FDTD is second order accurate. It is also proved that the difference scheme of 2D-ADI-FDTD with respect to time t is second order convergent in the discrete H1 norm. Experimental results to confirm the theoretical
analysis on stability, convergence and energy conservation are presented.

关键词: stability, convergence, energy conservation, ADI-FDTD, Maxwell equations

Abstract:

Key words: stability, convergence, energy conservation, ADI-FDTD, Maxwell equations

中图分类号:

65M06

高理平. STABILITY AND SUPER CONVERGENCE ANALYSIS OF ADI-FDTD FOR THE 2D MAXWELL EQUATIONS IN A LOSSY MEDIUM[J]. 数学物理学报(英文版), 2012, 32(6): 2341-2368.

GAO Li-Ping. STABILITY AND SUPER CONVERGENCE ANALYSIS OF ADI-FDTD FOR THE 2D MAXWELL EQUATIONS IN A LOSSY MEDIUM[J]. Acta mathematica scientia,Series B, 2012, 32(6): 2341-2368.

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STABILITY AND SUPER CONVERGENCE ANALYSIS OF ADI-FDTD FOR THE 2D MAXWELL EQUATIONS IN A LOSSY MEDIUM

STABILITY AND SUPER CONVERGENCE ANALYSIS OF ADI-FDTD FOR THE 2D MAXWELL EQUATIONS IN A LOSSY MEDIUM

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