Hamilton系统中Maxwell方程组的数值求解  

THE NUMERIC SOLUTION OF THE MAXWELL'S EQUATIONS IN THE HAMILTON SYSTEM

作　　者：刘双兵[1] 陈海波[1] 杨汉生[1] 

机构地区：[1]巢湖学院物理与电子科学系,安徽巢湖238000

出　　处：《巢湖学院学报》2010年第6期62-66,共5页Journal of Chaohu University

基　　金：巢湖学院自然科学研究资助项目(XLY-201010)

摘　　要：在详细阐述Hamilton系统中的辛算法的基础上,给出了Maxwell方程组的Hamilton的函数形式,将辛算法保持能量守恒和辛对称性的思想应用于Maxwell方程组的数值求解,结合传统的时域有限差分(FDTD)法,得到了电磁场时间和空间的离散迭代公式,即辛时域有限差分(SFDTD)法。最后扼要地分析了该数值计算方法的稳定性及数值色散性。The symplectic algorithm for Hamilton function is expatiated,the Maxwell＇s equations are written as Hamilton function.Then the idea of keeping conversation of energy and symmetry in the symplectic algorithm is used to solve the Maxwell＇s equations.Combining with the traditional Finite Difference Time Domain method,we obtain the discrete iterative equations of electromagnetism in time and space domain,named Symplectic Finite Difference Time Domain algorithm.Finally the stability and the numeric dispersion of the SFDTD algorithm are analyzed simply.

关 键 词：哈密尔顿系统 辛算法 时域有限差分 数值色散性 

分 类 号：O441[理学—电磁学]