利用Hamilton函数的变分形式,将Maxwell方程表述为Hamilton正则方程形式。利用辛传播子技术结合高阶差分格式对方程进行离散以保持方程的内在结构,建立了求解Maxwell方程的辛时域有限差分(SFDTD)算法。对SFDTD算法的稳定性及数值色散性进行了探讨,并将辛SFDTD算法应用于时域电磁散射计算中,数值结果表明该方法的正确性及高精度性。
The Maxwell's equations are written as normal Hamilton equations using functional variation method. We discretize Maxwell's equations using sympletic propagation technique combined with fourth-order finite difference approximations to construct symplectic finite difference time domain (SFDTD) scheme. The stability and numerical dispersion analysis are presented. The applications of the scheme in electromagnetic scat- tering are also included. Numerical results are given to show the high efficiency and accuracy of the SFDTD scheme.