高阶辛算法的稳定性与数值色散性分析

Stability and Numerical Dispersion of High Order Symplectic Schemes

利用Maxwell方程的哈密尔顿函数,导出对应的欧拉-哈密尔顿方程.利用辛积分技术与高阶交错差分技术,建立求解三维时域Maxwell方程的高阶辛算法;结合电磁场中的物理概念,借助矩阵分析和张量分析理论,获得高阶时域方法及高阶辛算法的稳定性和数值色散性的统一处理新方法.用数值结果证实方法的正确性,与FDTD算法和其它时域高阶方法相比,高阶辛算法具有较大的计算优势,为电磁计算提供了新的途径.

Euler-Hamilton equations are provided using Hamiltonian function of Maxwell＇ s equations. High order symplectic schemes of three-dimensional time-domain Maxwell＇ s equations are constructed with symplectic integrator technique combined with high order staggered difference. The method is used to analyzing stability and numerical dispersion of high order time-domain methods and symplectic schemes with matrix analysis and tensor nroduet. It confirms accuracy of the schema and super ability compared with other time-domain methods.