Acta mathematica scientia,Series B ›› 2012, Vol. 32 ›› Issue (6): 2341-2368.doi: 10.1016/S0252-9602(12)60184-2

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

 GAO Li-Ping   

  1. 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.

Abstract:

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.

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

CLC Number: 

  • 65M06
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