Abstract: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.
白仲明, 赵彦珍, 马西奎. 子域精细积分方法在求解Maxwell方程组中的应用分析[J]. 电工技术学报, 2010, 25(4): 1-11.
Bai Zhongming, Zhao Yanzhen, Ma Xikui. Analysis and Application of Sub-Domain Precise Integration Method for Solving Maxwell’s Equations. Transactions of China Electrotechnical Society, 2010, 25(4): 1-11.
[1] 王秉中. 计算电磁学[M]. 北京:科学出版社, 2002.
[2] 谢德馨, 姚缨英, 白保东, 等. 三维涡流场的有限元分析[M]. 北京:机械工业出版社, 2001.
[3] 魏鸿磊, 顾元宪, 陈飚松. 瞬态电磁场问题求解的精细积分法[J]. 沈阳工业大学学报, 2003, 25(1): 44-46.
[4] 钟万勰, 朱建平. 对差分法时程积分的反思[J]. 应用数学和力学, 1995, 16(8): 663-668.
[5] 钟万勰. 单点子域积分与差分[J]. 力学学报, 1996, 28(2): 159-162.
[6] Richard L Stoll. The analysis of eddy currents[M]. Oxford: Clarendoon Press, 1974.
[7] 曾文平. 二维扩散方程的单点子域精细积分法[J]. 计算力学学报, 2000, 17(4): 492-495.
[8] Mohammed O A, Fuat G Uler. A state space technique for the solution of nonlinear 3-D transient eddy current problems[J]. IEEE Transactions on Magnetics, 1991, 27(6): 5520-5522.
[9] 钟万勰. 计算结构力学与最优控制[M]. 大连: 大连理工大学出版社, 1993.
[10] 孔向东, 钟万勰. 非线性动力系统刚性方程精细时程积分法[J]. 大连理工大学学报, 2002, 42(6): 654-658.
[11] 赵进全, 马西奎, 邱关源. 有损传输线时域响应的精细积分法[J]. 微电子学, 1997, 27(3): 181-185.
[12] 赵进全, 马西奎, 邱关源. 非均匀耦合传输线时域响应分析的精细积分法[J]. 光纤与电缆技术及其应用, 1999(3): 3-6.
[13] 赵进全, 马西奎, 邱关源. 变电站空载母线波过程的精细积分计算方法[J]. 电力系统自动化, 2002, 26(3): 52-55.
[14] Antonio C F, Williamson S. Time stepping finite element analysis of brushless doubly fed machine taking on loss and saturation into account[J]. IEEE Trans. on Industry Applications, 1999, 35(3): 583- 588.
[15] Boglietti A, Lazzari M, Pastorelli M. Predicting iron losses in soft magnetic materials with arbitrary voltage supply: An engineering approach[J]. IEEE Trans. on Magnetics, 2003, 39(2): 981-988.
[16] Yee K S. Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media[J]. IEEE Trans. on Antennas Propagat., 1966, 14(3): 302-307.
[17] Zheng F, Chen Z, Zhang J. Toward the development of a three-dimensional unconditionally stable finite-difference time-domain method[J]. IEEE Trans. on Microwave Theory Tech., 2000, 48(9): 1550-1558.
[18] 钟万勰. 子域精细积分及偏微分方程的数值解[J]. 计算结构力学及其应用, 1995, 12(3): 253-260.
[19] 唐旻, 马西奎. 一种用于分析高速VLSI中频变互连线瞬态响应的精细积分算法[J]. 电子学报, 2004, 32(5): 787-790.
[20] 杨梅, 马西奎. 板状铁磁材料中电磁脉冲传播特性计算的一种半积分方法[J]. 电工技术学报, 2005, 20(1): 89-94, 107.
[21] Ma X K, Zhao X T, Zhao Y Z. A 3-D precise integration time-domain method without the restraint of the Courant-Friedrich-Levy stability condition for the numerical solution of Maxwell’s equations[J]. IEEE Transactions on Microwave Theory and Techniques, 2006, 54(7): 3026-3037.
[22] 陈飚松, 顾元宪. 瞬态热传导方程的子结构精细积分法[J]. 应用力学学报, 2001, 18(1): 14-17.
[23] 葛德彪, 闫玉波. 电磁场时域有限差分法[M]. 西安: 西安电子科技大学出版社, 2005.
[24] 马西奎. 电磁场理论及应用[M]. 西安: 西安交通大学出版社, 2000.