二维麦克斯韦方程改进的无条件稳定的时域有限差分方法

IMPROVED UNCONDITIONAL STABLE FDTD METHOD FOR 2D MAXWELL EQUATIONS

研究了麦克斯韦方程无条件稳定的有限差分格式US—FDTD（见MicrowaveOptTechnolLett38，2003），证明了该格式是耗散和一阶精度的．在此基础上，利用减少摄动误差的技巧，我们提出了二维麦克斯韦方程改进的无条件稳定的有限差分方法（IUS—FDTD），应用傅里叶方法证明了新格式IUS—FDTD是无条件稳定的和非耗散的．误差分析表明IUS—FDTD是二阶精度的，比原格式US—FDTD的精度高一阶．数值试验比较了这两种格式的模拟效果，计算结果证实：改进的格式IUS—FDTD比原格式uS—FDTD误差小、稳定性好、精度高．

This paper studies the unconditionally stable（US） finite difference time domain method（ named as US- FDTD,see Microwave Opt Technol Lett 38,2003） for the 2D Maxwell equations. It is proved that US- FDTD is dissipative and first order accurate. Based on this method, an improved unconditionally stable finite difference time domain method（ named as IUS -FDTD） is proved by using the technique to decrease the perturbation error. It is demonstrated by Fourier methods that IUS - FDTD is unconditionally stable, non - dissipative and second order accurate in both time and space, which is one order higher in accuracy than US - FDTD. Numerical experiments for solving the Maxwell equations with the perfectly electric conducting boundary conditions are carried out, and computational results confirm the theoretical analysis.