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

作　　者：高理平 

机构地区：[1]Department of Computational and Applied Mathematics,School of Sciences,China University of Petroleum

出　　处：《Acta Mathematica Scientia》2012年第6期2341-2368,共28页数学物理学报（B辑英文版）

基　　金：supported by Shandong Provincial Natural Science Foundation(Y2008A19);the Scientific Research Foundation for the Returned Overseas Chinese Scholars,State Education Ministry

摘　　要：Several new energy identities of the two dimenslonal（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.Several new energy identities of the two dimenslonal（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 

分 类 号：O175[理学—数学]