色散介质电磁特性时域有限差分分析的Newmark方法

王飞; 魏兵; 李林茜

doi:10.7498/aps.63.104101

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摘要

根据Debye 模型、Drude 模型和Lorentz 模型3 种常见色散介质模型频域极化率的特点, 利用频域到时域的转换关系jω→∂/∂t, 将极化矢量P 与电场强度E 的频域关系转换成时域内关于P 的二阶微分方程, 其对3 种色散介质模型皆适用, 具有统一的形式. 然后采用相比于中心差分具有更高精度的Newmark 两步算法(Newmark-β-γ 法) 求解该方程, 进而得到E→P 的递推公式, 再结合本构关系得到D→E的时域递推式.实现了色散介质电磁场量的时域有限差分迭代计算. 数值计算结果表明该方法是适用于3 种色散介质模型的通用算法, 并且相比于移位算子时域有限差分方法等以中心差分为基础的离散方案具有更高的计算精度.

关键词:

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）和中央高等学校基本科研基金资助的课题.

参考文献

[1]	Yee K S 1966 IEEE Trans. Antennas Propag. AP-14 302
[2]	Li J, Guo L X, Zeng H, Han X B 2009 Chin. Phys. B 18 2757
[3]	Li X F, Pan S, Guo Y N, Wang Q 2011 Chin. Phys. B 20 015204
[4]	Bavil M A, Sun X D 2013 Chin. Phys. B 22 047808
[5]	Lu W F, Li C, Huang S H, Lin G Y, Wang C, Yan G M, Huang W, Lai H K, Chen S Y 2013 Chin. Phys. B 22 107703
[6]	Li Q B, Wu R X, Yang Y, Sun H L 2013 Chin. Phys. Lett. 30 074208
[7]	Taflove A, Hagness S C 2005 Computational Electrodynamics the Finite-Difference Time-Domain Method (3rd Ed.) (Boston London: Artech House) p374
[8]	Luebbers R J, Hunsberger F, Kunz K S 1990 IEEE Trans. Electromagn. Compat. 32 222
[9]	Luebbers R J, Hunsberger F, Kunz K S 1991 IEEE Trans. Antennas Propag. 39 29
[10]	Luebbers R J, Hunsberger F 1992 IEEE Trans. Antennas Propag. 40 1297
[11]	Pontalti R, Cristoforetti L, Antolini R, Cescatti L 1996 IEEE Trans. Microwave Theory Tech. 42 526
[12]	Kelley D F, Luebbers R J 1996 IEEE Trans. Antennas Propag. 44 792
[13]	Chen Q, Katsurai M, Aoyagi P H 1998 IEEE Trans. Antennas Propag. 46 1739
[14]	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]
[15]	Xu L J, Yuan N C 2005 IEEE Microwave Wireless Compon. Lett. 15 277
[16]	Nickisch L J, Franke P M 1992 IEEE Antennas Propag. Mag. 34 33
[17]	Takayama Y, Klaus W 2002 IEEE Microwave Wireless Compon. Lett. 12 102
[18]	Sullivan D M 1992 IEEE Trans. Antennas Propag. 40 1223
[19]	Sullivan D M 1995 IEEE Trans. Antennas Propag. 43 676
[20]	Sullivan D M 1996 IEEE Trans. Antennas Propag. 44 28
[21]	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]
[22]	Wei B, Ge D B, Wang F 2008 Acta Phys. Sin. 57 6290 (in Chinese)[魏兵, 葛德彪, 王飞 2008 物理学报 57 6290]
[23]	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]
[24]	NewMark N M 1959 J. Eng. Mech. Div. 85 67
[25]	Zienkiewich O C 1977 Earthquate Eng. Struct. Dyn. 5 413
[26]	Wood W L 1984 Int. J. Numer. Meth. Eng. 20 1009
[27]	Ge D B, Yan Y B 2011 Finite-Difference Time-Domain Method for Electromagnetic Waves (3rd Ed.) (Xi'an : Xidian University Press) p262 (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262页]

施引文献

[1]	Yee K S 1966 IEEE Trans. Antennas Propag. AP-14 302
[2]	Li J, Guo L X, Zeng H, Han X B 2009 Chin. Phys. B 18 2757
[3]	Li X F, Pan S, Guo Y N, Wang Q 2011 Chin. Phys. B 20 015204
[4]	Bavil M A, Sun X D 2013 Chin. Phys. B 22 047808
[5]	Lu W F, Li C, Huang S H, Lin G Y, Wang C, Yan G M, Huang W, Lai H K, Chen S Y 2013 Chin. Phys. B 22 107703
[6]	Li Q B, Wu R X, Yang Y, Sun H L 2013 Chin. Phys. Lett. 30 074208
[7]	Taflove A, Hagness S C 2005 Computational Electrodynamics the Finite-Difference Time-Domain Method (3rd Ed.) (Boston London: Artech House) p374
[8]	Luebbers R J, Hunsberger F, Kunz K S 1990 IEEE Trans. Electromagn. Compat. 32 222
[9]	Luebbers R J, Hunsberger F, Kunz K S 1991 IEEE Trans. Antennas Propag. 39 29
[10]	Luebbers R J, Hunsberger F 1992 IEEE Trans. Antennas Propag. 40 1297
[11]	Pontalti R, Cristoforetti L, Antolini R, Cescatti L 1996 IEEE Trans. Microwave Theory Tech. 42 526
[12]	Kelley D F, Luebbers R J 1996 IEEE Trans. Antennas Propag. 44 792
[13]	Chen Q, Katsurai M, Aoyagi P H 1998 IEEE Trans. Antennas Propag. 46 1739
[14]	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]
[15]	Xu L J, Yuan N C 2005 IEEE Microwave Wireless Compon. Lett. 15 277
[16]	Nickisch L J, Franke P M 1992 IEEE Antennas Propag. Mag. 34 33
[17]	Takayama Y, Klaus W 2002 IEEE Microwave Wireless Compon. Lett. 12 102
[18]	Sullivan D M 1992 IEEE Trans. Antennas Propag. 40 1223
[19]	Sullivan D M 1995 IEEE Trans. Antennas Propag. 43 676
[20]	Sullivan D M 1996 IEEE Trans. Antennas Propag. 44 28
[21]	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]
[22]	Wei B, Ge D B, Wang F 2008 Acta Phys. Sin. 57 6290 (in Chinese)[魏兵, 葛德彪, 王飞 2008 物理学报 57 6290]
[23]	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]
[24]	NewMark N M 1959 J. Eng. Mech. Div. 85 67
[25]	Zienkiewich O C 1977 Earthquate Eng. Struct. Dyn. 5 413
[26]	Wood W L 1984 Int. J. Numer. Meth. Eng. 20 1009
[27]	Ge D B, Yan Y B 2011 Finite-Difference Time-Domain Method for Electromagnetic Waves (3rd Ed.) (Xi'an : Xidian University Press) p262 (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262页]

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色散介质电磁特性时域有限差分分析的Newmark方法

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）和中央高等学校基本科研基金资助的课题.

收稿日期: 2013-12-17

修回日期: 2014-01-13

刊出日期: 2014-05-05

摘要: 根据Debye 模型、Drude 模型和Lorentz 模型3 种常见色散介质模型频域极化率的特点, 利用频域到时域的转换关系jω→∂/∂t, 将极化矢量P 与电场强度E 的频域关系转换成时域内关于P 的二阶微分方程, 其对3 种色散介质模型皆适用, 具有统一的形式. 然后采用相比于中心差分具有更高精度的Newmark 两步算法(Newmark-β-γ 法) 求解该方程, 进而得到E→P 的递推公式, 再结合本构关系得到D→E的时域递推式.实现了色散介质电磁场量的时域有限差分迭代计算. 数值计算结果表明该方法是适用于3 种色散介质模型的通用算法, 并且相比于移位算子时域有限差分方法等以中心差分为基础的离散方案具有更高的计算精度.

关键词:

Newmark method for finite-difference time-domain modeling of wave propagation in frequency-dispersive medium

1.
School of Physics and Optoelectronic Engineering, Xidian University, Xi'an 710071, China

Fund Project:

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 Scientific Research Foundation for the Central Universities of China.

Received Date: 17 December 2013

Accepted Date: 13 January 2014

Published Online: 05 May 2014

Abstract: The complex polarizations of three kinds of general dispersive medium models, i.e. Debye model, Lorentz model, Drude model, are described by rational polynomial fraction in jω. The relationship between the polarization vector P and the intensity of electric field E in time domain is obtained by utilizing the transformation relationship from frequency domain to time domain jω→∂/∂t. Then, the time domain second order equation is solved by using the Newmark β and γ method, which has higher accuracy than the traditional center difference method. Once the recursive formulations for E and P are obtained, the recursive formulations for D and E in time domain can be also obtained based on the constitutive relation. Therefore for a dispersive medium the iterative electromagnetic field calculation is conducted by finite-difference time-domain (FDTD) method. The present numerical results demonstrate that the proposed method is a general algorithm for three kinds of general dispersive medium models, and has higher accuracy than the shift operator-FDTD, which is based on the central difference discrete scheme.

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