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## Newmark algorithm in the finite-difference time-domain analysis of ferrite magnetized in an arbitrary direction

Wang Fei, Wei Bing, Yang Qian, Li Lin-Qian
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• #### 摘要

利用坐标系转换矩阵给出实验室坐标系中饱和磁化铁氧体的频域磁导系数张量，再通过频域到时域的转换关系jω→∂/∂t得到一个二阶微分方程形式的时域本构关系. 然后采用Newmark 方法求解时域本构关系从而给出一种适用于处理任意磁化方向铁氧体电磁问题的Newmark 时域有限差分算法. 利用此算法计算了饱和磁化铁氧体层的反(透) 射系数和饱和磁化铁氧体球的后向雷达散射截面，所获得的结果验证了此算法的正确有效性.

#### Abstract

The permeability tensor of saturated magnetized ferrite in frequency domain in the laboratory coordinate system is obtained by using the transformation matrix between the principal and laboratory system. The constitutive relation in time domain, which is a kind of second order differential equation, is derived by employing the transformation from the frequency domain jω to time domain ∂/∂t and solved by utilizing the Newmark algorithm. Consequently, a Newmark finite-difference time-domain method is proposed to deal with the problem of electromagnetic scattering by ferrite which is subjected to an external magnetic field in an arbitrary direction. The electromagnetic scattering by a magnetized ferrite layer and a sphere is simulated, and the numerical results demonstrate the validity and feasibility of the proposed method.

#### 作者及机构信息

###### 1. 西安电子科技大学物理与光电工程学院, 西安 710071
• 基金项目: 国家高技术研究发展计划（批准号：2012AA01A308）、国家自然科学基金重点项目（批准号：61231003）和中央高校基本科研业务费专项资金（批准号：JB140503）资助的课题.

#### Authors and contacts

###### 1. School of Physics and Optoelectronic Engineering, Xidian University, Xi'an 710071, China
• Funds: Project supported by the National High Technology Research and Development Program of China (Grant No. 2012AA01A308), the Key Program of the National Natural Science Foundation of China (Grant No. 61231003), and the Fundamental Research Funds for the Central Universities (Grant No. JB140503).

#### 参考文献

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#### 施引文献

•  [1] Zhou H M, Chen Q, Deng J H 2014 Chin. Phys. B 23 047502 [2] Wang W J, Zang C G, Jiao Q J 2013 Chin. Phys. B 22 128101 [3] Zhang H W, Li J, Su H, Zhou T C, Long Y, Zheng Z L 2013 Chin. Phys. B 22 117504 [4] Yasir Rafique M, Pan L Q, Javed Q, Zubair Iqbal M, Qiu H M, Hassan Farooq M, Guo Z G, Tanveer M 2013 Chin. Phys. B 22 107101 [5] Luebbers R J, Hunsberger F, Kunz K S 1991 IEEETrans. Antenn. Propag. 39 29 [6] Kelley D F, Lubbers R J 1996 IEEE Trans. Antenn. Propag. 44 792 [7] Chen Q, Katsurai M, Aoyagi P H 1998 IEEE Trans. Antenn. Propag. 46 1739 [8] Liu S B, Mo J J, Yuan N C 2004 Acta Phys. Sin. 53 778 (in Chinese) [刘少斌, 莫锦军, 袁乃昌 2004 物理学报 53 778] [9] Xu L J, Yuan N C 2005 IEEE Microw. Wireless Compon. Lett. 15 277 [10] Nickisch L J, Franke P M 1992 IEEE Trans. Antenn. Propag. Mag. 34 33 [11] Takayama Y, Klaus W 2002 IEEE Microw. Wireless Compon. Lett. 12 102 [12] Sullivan D M 1992 IEEE Trans. Antenn. Propag. 40 1223 [13] Sullivan D M 1995 IEEE Trans. Antenn. Propag. 43 676 [14] Sullivan D M 1996 IEEE Trans. Antenn. Propag. 44 28 [15] Ge D B, Wu Y L, Zhu X Q 2003 Chin. J. Radio Sci. 18 359 (in Chinese) [葛德彪, 吴跃丽, 朱湘琴 2003 电波科学学报 18 359] [16] Zhang Y Q, Ge D B 2009 Acta Phys. Sin. 58 4573 (in Chinese) [张玉强, 葛德彪 2009 物理学报 58 4573] [17] Yang L X, Ge D B 2006 Acta Phys. Sin. 55 1751 (in Chinese) [杨利霞, 葛德彪 2006 物理学报 55 1751] [18] Yang L X, Ge D B, Wang G, Yan S 2007 Acta Phys. Sin. 56 6937 (in Chinese) [杨利霞, 葛德彪, 王刚, 阎述 2007 物理学报 56 6937] [19] Yang L X, Ge D B, Zhao Y H, Wang G, Yan S 2008 Acta Phys. Sin. 57 2936 (in Chinese) [杨利霞, 葛德彪, 赵跃华, 王刚, 阎述 2008 物理学报 57 2936] [20] Wang F, Ge D B, Wei B 2009 Acta Phys. Sin. 58 6356 (in Chinese) [王飞, 葛德彪, 魏兵 2009 物理学报 58 6356] [21] Wang F, Wei B 2013 Acta Phys. Sin. 62 084106 (in Chinese) [王飞, 魏兵 2013 物理学报 62 084106] [22] Newmark N M 1959 J. Eng. Mech. Div. 85 67 [23] Zienkiewich O C 1977 Earthquate Eng. Struct. Dyn. 5 413 [24] Ge D B, Yan Y B 2011 Finite-Difference Time-Domain Method for Electromagnetic Waves (3rd Ed.) (Xi'an:Xidian University Press) p11 (in Chinese) [葛德彪, 闫玉波 2011 电磁波时域有限差分法 (第三版) (西安: 西安电子科技大学出版社) 第11页] [25] Bi D X 1985 Electromagnetic Field Theory (Beijing: Publishing House of Electronics Industry) (in Chinese) [毕德显 1985 电磁场理论 (北京: 电子工业出版社)] [26] Kong J A 2000 Electromagnetic Wave Theory (Cambridge: EMW Publishing) [27] Schuster J, Lubbers R 1996 IEEE Antennas and Propagation Society International Symposium 3 1648
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##### 出版历程
• 收稿日期:  2014-02-27
• 修回日期:  2014-04-04
• 刊出日期:  2014-08-05

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