基于辛算法的二维电磁场散射问题的研究  

Study on the Scattering of Two-Dimensional Electromagnetic Field Based on Symplectic Integrator Method

作　　者：蒋乐乐[1] 吴先良[1] 

机构地区：[1]安徽大学智能计算和信号处理教育部重点实验室,安徽合肥230039

出　　处：《电子学报》2004年第12期1967-1970,共4页Acta Electronica Sinica

基　　金：国家自然科学基金 (No .60 371 0 4 1 );安徽省教育厅重点科研基金 (No .2 0 0 2kj32 )

摘　　要：辛算法是保持Hamilton系统辛结构的一种新的数值方法 ,由于Maxwell方程是一无穷维Hamilton系统 ,因此可将辛算法用于电磁场模拟中 .本文提出一种基于辛分块Runge Kutta(PRK)方法的显式辛算法 ,并将它成功应用于二维电磁散射问题的计算中 .通过对金属方柱散射场的数值模拟 ,比较了FDTD法和低阶辛算法 (一阶和二阶 ) ,结果表明低阶辛算法不仅与FDTD法精度相当 ,而且可以减少存储空间和计算时间 ,尤其是一阶辛算法节省了大约的CPU时间 ,提高了计算速度 。The symplectic integrator method is a new time-domain method which can preserve the symplectic structure of the Hamiltonian system. Maxwell Equations is in fact an infinite-dimensional Hamiltonian system, so this method can be used for electromagnetic field simulation. In this paper, A class of symplectic difference scheme which is based on an explicit symplectic partitioned Runge-Kutta (PRK) method is proposed, and it is demonstrated that the proposed method is applicable to the area of numerical computations for the scattering of electromagnetic waves by successful numerical simulation of the total field of a two-dimensional square metal conducting target. The results show that under the same mesh-point density, time steps and spatial discretization conditions, the accuracy of the low-order symplectic methods is equivalent to the standard FDTD method, but the symplectic methods can reduce the required memory and computational time, for it can describe the whole electromagnetic field with fewer functions compared with the standard FDTD method, especially the 1st-order symplectic method takesonly 60% of the computational time of the FDTD method, thus shows the symplectic PRK method is promising.

关 键 词：射域有限差与法 HAMILTON系统 辛算法 辛PRK方法 

分 类 号：TN8[电子电信—信息与通信工程]