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

Abstract

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

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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