基于传播子技术的辛时域多分辨率方法

The Scheme of Symplectic MRTD Using Propagation Technique

数值求解三维时域Maxwell方程的过程中,保持方程的内在结构显得尤为重要.利用Hamilton函数的变分形式,将Maxwell方程表述为Hamilton正则方程形式.在时域方向,利用辛传播子技术对方程进行离散以保持方程的内在结构;在空域方向,采用时域多分辨率方法对三维旋度算符进行差分离散,建立了求解Maxwell方程的辛时域多分辨率(S-MRTD)方法.对S-MRTD方法的稳定性及数值色散性进行了系统的探讨,数值结果表明该方法的正确性及高精度性.

It is especially important to preserve some characters of the original system while numerical simulating three-di- mensional time domain Maxwell＇ s Equations. The Maxwell＇ s equations are written as normal Hamilton equations using functional variation method. We discretize Maxwell＇ s equations in the time direction using sympletic propagation technique and then evaluate the equations in the spatial direction with high-order nature of spatial multi-resolution approximations to construct symplectic Mtdti- Resolution Time Domain （S-MRTD） scheme. The stability and numerical dispersion analysis are also included. Numerical results are given to show the high efficiency and accuracy of the S-MRTD scheme.