子域精细积分方法在求解Maxwell方程组中的应用分析  

Analysis and Application of Sub-Domain Precise Integration Method for Solving Maxwell’s Equations

作　　者：白仲明[1] 赵彦珍[1] 马西奎[1] 

机构地区：[1]西安交通大学电力设备电气绝缘国家重点实验室,西安710049

出　　处：《电工技术学报》2010年第4期1-9,共9页Transactions of China Electrotechnical Society

基　　金：国家自然科学基金资助项目(50877055)

摘　　要：采用子域精细积分方法求解Maxwell方程组。该方法将计算区域划分为多个子域,在每个时间步内,先使用精细积分算法对各个子域单独进行计算,再将各个子域的计算结果合成为全域结果。文中给出了子域的划分原则和对各个子域计算结果进行合成的处理方法,以及基于泰勒近似的子域边界处理方法和采用高斯积分求解非齐次项积分的方法。本文方法避免了矩阵求逆,降低了系数矩阵规模,因而减少了数据存储交换量,缩短了计算时间。算例结果表明了本文方法的实用性和有效性。In this paper, the sub-domain precise integration method is used to solve Maxwell’s equations. Firstly, the main domain is divided into sub-domains, and then for each time-step, the precise integration method is used to solve Maxwell’s equations in each sub-domain, lastly the main domain solution is derived by combining the results of all sub-domains. In detail discussion, the principle for dividing sub-domain is proposed and the combination method of sub-domain results is given. Furthermore, boundary condition of sub-domains is obtained based on Taylor’s series and the Gaussian integration is used to solve the inhomogeneous integration. Since the method presented avoids matrix inversion and reduces matrix order, data exchange and storage quantity and computing time are reduced. In conclusion, the practicality and effectiveness of these methods are illustrated by examples.

关 键 词：子域精细积分 子域边界 高斯积分 MAXWELL方程组 

分 类 号：TM15[电气工程—电工理论与新技术]