二维麦克斯韦方程分裂的高阶时域有限差分方法

Splitting High Order Finite-difference Time-domain Methods for Maxwell's Equations in Two Dimensions

将分裂算子的时域有限差分方法与高阶差分方法相结合,提出了二维麦克斯韦方程的分裂的高阶时域有限差分格式(SHO-FDTDⅠ)及其修正格式(SHO-FDTDⅡ)。用Fourier方法证明了这两种格式是无条件稳定的,其中格式Ⅰ是损耗(dissipative)的,格式Ⅱ是非损耗(non-dissipative)的。然后推导出了它们的数值弥散关系式,最后用数值算例验证了理论分析,并给出了数值弥散误差的计算和增长因子模的计算。

High-order finite difference time domain methods of 2D Maxwell＇ s equations by using the splitting and correcting techniques are considered. Two kinds of schemes, SHO-FDTD I and SHO-FDTD II are proposed and implemented. By using the Fourier method, the two schemes are proved to be unconditionally stable and their nu- merical dispersion relations are derived. It is found that SHO-FDTD II has smaller dispersion error than. SHO- FDTD, and that the former is non-dissipative, the latter is dissipative. Numerical experiments are carried out and show SHO-FDTDII is more accurate than SH-FDTD I .