The infinite dimensional Hamiltonian system of three-dimensional vector wave equation is given and a new numerical approximate scheme is proposed in this paper. Based on the Gauss-Lobatto-Legendre polynomial, the spatial discretization scheme for the proposed infinite dimensional system is established by virtue of the vector spectral element method, and then a finite dimensional Hamiltonian system is attained. Moreover, in order to preserve the structure and energy of the system, the full discretization scheme of the finite dimensional system is derived by utilizing the symplectic difference method. Finally, the stiff matrix and mass matrix are disposed by the diagonal techniques. High accuracy approximation scheme is thus obtained, and simultaneously the computing cost and storage capacity are reduced significantly.%本文给出了三维矢量波动方程的无穷维Hamilton系统形式并提出了一个新的数值逼近格式.基于Gauss-Lobatto-Legendre多项式,建立了该无穷维系统的矢量谱元方法空间离散格式,并得到一个有限维Hamilton系统.进而,利用辛差分方法对该有限维系统进行全离散,以期保持系统的结构和能量.最后,借助于对角化技巧处理刚度矩阵和质量矩阵,在得到高精度逼近格式的同时,大幅降低了计算量和存储量.
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