Maxwell方程组的多辛算法

Multi-symplectic Integrators for Maxwell's Equations

Maxwell方程在线性、各向同性、均匀、无源的介质中具有自然的多辛结构,可以表示为多辛Hamilton系统。Maxwell方程的多辛算法即对Maxwell方程在时间、空间同时进行保辛离散得到相应的差分格式。文中给出了5种麦克斯韦方程的多辛算法,分析并比较了这5种方法的数值色散特性。数值计算结果表明这些算法能很好地保持Maxwell方程的离散全局能量守恒特性。

The source-less Maxwell's equations with constant scalar parameters have the symplectic property.The concept of multi-symplectic schemes for Maxwell equations,which can be viewed as the extension of symplectic schemes for Hamiltonian ODEs to Hamiltonian PDEs.In this paper,we introduce five multi-symplectic schemes for Maxwell's equations in a simple medium.Furthermore,we extend the discussion to several dispersion properties of the multi-symplectic schemes.Lastly,two-dimensional Maxwell's equations are simulated by five multi-symplectic schemes.Numerical results demonstrate that the five multi-symplectic schemes preserve the discrete globle energy of the Maxwell's equations exactly.