基于传播子技术的辛时域多分辨率方法

摘要

It is especially important to preserve some characters of the original system while numerical simulating three-dimensional 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-older nature of spatial multi-resolution approximations to construct symplectic Multi-Resolution Tune 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.%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.