基于DSP的色散介质FDTD算法及相关问题研究
|
摘要
鉴于色散介质瞬态电磁问题在隐身技术、生物电磁学等许多领域中的重要性,结合数字信号处理(DSP)理论和技术,对色散介质瞬态电磁问题的FDTD算法及相关问题进行了深入研究,并应用所提出的新方法对一些实际问题进行了分析。
结合DSP理论中的半解析递归卷积(SARC)算法提出了一种用于色散介质的半解析递归卷积时域有限差分(SARC-FDTD)方法。SARC算法是建立在数值逼近理论基础上的一种卷积递归计算方法,具有绝对稳定、高精度、低内存、高效率等优点。将SARC引入色散介质FDTD,在保留RC方法优点的基础上,提高了算法的通用性,使得在应用时只需给出色散介质模型的极点及其留数,即可进行计算,无需再针对色散模型计算更新公式的系数。解决了现有色散介质RC-FDTD方法对于各种色散介质模型需要单独处理,公式推导复杂、不具有通用性的问题。
结合DSP技术中的IIR数字滤波器级联思想,研究了一种高阶有理分式模型色散介质的级联SARC FDTD算法。有理分式是描述介质色散特性的精确、高效的模型之一,常用于复杂介质的色散特性描述。在该方法中,通过先将高阶有理分式频域模型表示为一系列低阶有理分式之积,再将各低阶有理分式表示为时域复指数函数形式,使得高阶色散模型转化为一系列时域复指数函数的卷积,然后通过SARC-FDTD得到求解。解决了现有RC方法处理高阶有理分式模型和渐进稳定色散介质电磁问题时的困难,并将所提算法应用于宽带Lorentz介质、窄带Lorentz介质及其临界情况的分析,表明了算法的有效性。
研究并实现了一种改进的Z变换方法。DSP理论中的脉冲响应不变法当脉冲响应h ( t )在t = 0时刻不连续时是不精确的。如果将传统Z变换直接应用于色散介质FDTD方法将导致高的数值误差。在对脉冲响应不变法改进的基础上,从极化矢量P和电场E的关系入手,重新推导了Z变换FDTD更新公式,解决了原Z变换FDTD方法内存占用大的问题。同时,对于极化率函数时域表达式χ( t)在t = 0时刻不连续的色散介质,还使FDTD计算的精度得到提高。
提出一种基于DSP的色散介质改进SO-FDTD方法。借鉴IIR数字滤波器转置直接Ⅱ型结构和级联实现思想,并对其状态变量方程进行改进,将其引入色散介质SO-FDTD方法中,得到改进SO-FDTD更新公式。减少了高阶色散介质SO方法内存占用、简化了SO方法在处理高阶有理分式形式色散介质时更新公式系数计算。使内存减少量不低于33%,达到与RC方法相同,更新公式系数计算不超过二阶。
提出一种适用于高阶Debye、Lorentz和Drude模型的SO-FDTD方法。借鉴IIR数字滤波器并联思想,从极化矢量P与电场E的关系入手,利用SO方法推导了适用于三种常用色散模型的SO-FDTD更新公式,避免原SO方法在对三种常用色散介质处理时需将低阶有理分式转化为高阶有理分式,简化了公式推导,且三种常用模型对应的更新公式具有统一的形式,适于处理高阶色散介质以及混合模型色散介质,并便于编制通用的计算程序。同时,极大地减少了SO-FDTD方法的内存占用和计算时间。
研究并实现了基于改进SO-FDTD方法和SARC-FDTD方法的UPML吸收边界和CFS-PML吸收边界,可有效地实现色散介质FDTD计算时的计算区域截断。结合所提出的SO-FDTD方法或SARC-FDTD方法,新的PML吸收边界不仅独立于被截断介质,而且PML区域的FDTD更新公式具有不随所截断介质变化的统一形式。
提出一种同时适用于SARC、ADE、改进Z变换及改进SO方法的色散介质FDTD更新公式的统一形式,解决了不同方法因FDTD更新公式不同而带来的使用不便问题。在该统一更新公式中,使用者可以根据所熟悉的FDTD方法和要处理的色散介质,通过给出色散介质模型参数,由独立的建模程序给出建模数据和更新公式所需系数即可进行计算。
The transient electromagnetic problems with dispersive medium play an important role in stealth technology, bio-electromagnetics, and many other areas. Combination of digital signal processing (DSP) theory and technology, the Finite-Difference Time-Domain (FDTD) algorithms for dispersive medium and related problems are studied and a number of practical issues are analyzed using the proposed new methods.
Combining with the Semi-Analytical Recursive Convolution (SARC) algorithm in DSP techniques, a novel FDTD update formulas for the analysis of electromagnetic characteristic of dispersive objects is proposed, namely as SARC-FDTD algorithm in here. In this scheme, the absolute stability, high accuracy, less storage and high effectiveness are retained, and a unified update formulation for general dispersive media, i.e., Debye, Drude, Lorentz and hybrid model is possessed. The SARC FDTD can therefore be applied to the analysis of general dispersive media provided that the poles and corresponding residues in dispersive medium model of interest are given. The complex derivation of coefficients in update formulas for the specified dispersive model is not requested and the separate treatment for a variety of dispersion media model in the existing RC-FDTD method is avoided.
A novel SARC-FDTD algorithm for the dispersive medium described with high order rational fraction model based on the cascade implementation of Infinite Impulse Response (IIR) filter in DSP techniques is presented. The rational fraction is one of the dispersive models that can accurately and efficiently approximate to the complicated variation of the parameters of dispersive medium with the frequency. In this method, the high-order rational fraction model in frequency domain is firstly expressed as the product of a series low-order rational fraction and is further transformed into the convolution of a series complex exponential function responding to the each low-order rational fractions in time domain. Finally, the convolution is solved by the SARC-FDTD. The FDTD analysis of transient electromagnetic problems for dispersive medium with high-order rational fraction and asymptotic stability model is solved. It is applied to the analysis of dielectric described with wide-band Lorentz model, narrow-band Lorentz model and border-line case.
An improved Z transformation is presented and improved FDTD method is implemented. The classical impulse invariance method in Z-transform theory is found to be incorrect and inaccurate when the impulse response is discontinuous at initial time t=0. Such inaccuracy results in higher numerical errors if it is used to develop the update equations for frequency-dependent FDTD. Thorough discussion of corrected impulse invariance method in the realm of Z-transform, a novel ZT-FDTD update formulas for dispersive media is discussed by the relation of polarization P with electric field E. Compared with the commonly used ZT-FDTD, the storage variables in the improved ZT-FDTD are reduced and high accuracy is achieved for dispersive media which exhibit discontinuity at t=0 in the time domain susceptibility function.
An improved shifted operator (SO) FDTD method for general dispersive medium based on the implementation of IIR filter in DSP techniques is presented. Combining with the improved state-space equation of transposed direct-Ⅱstructure of IIR filter and cascade implementation, the update formulas of improved SO-FDTD are obtained. Compared with the commonly used SO-FDTD, the storage variables in the improved SO-FDTD are reduced by 33% and computational efficiency is also increased. The simple coefficients for high-order rational fraction model can be obtained in the novel scheme.
A novel SO-FDTD scheme for high-order Debye, Lorentz and Drude dispersion model is presented as well. The transformation of low-order rational fraction into high-order form in commonly used SO-FDTD is avoided and derivation of the update formulas is simplified. A unified update formula is possessed for three typical kinds of dispersive model i.e. Debye, Lorentz and Drude medium and is suitable for dealing with high-order dispersive media as well as the hybrid model media. The general computational program can be conveniently developed.
The novel Uniaxial Perfectly matched layers (UPML) absorbing boundary and Complex Frequency-Shifted PML (CFS-PML) absorbing boundary based on improved SO-FDTD and SARC-FDTD are presented and is suitable for truncating the FDTD computational domain for calculation of dispersive medium. Combined with the proposed SO-FDTD and SARC-FDTD, the implementation of PML is not only independent for the truncated medium, and the FDTD update formula in PML region is a unified form for the different dispersive medium.
A unified FDTD update formulas simultaneously applied to SARC, Auxiliary Differential Equation (ADE), improved Z transform and improved SO algorithm is proposed. The inconvenience bringing with the different FDTD formulas for the above several algorithm is avoided. In this scheme, the coefficients in the unified update formulas are obtained providing the dispersion model parameters are specified. Then, FDTD calculation using the user-familiar FDTD algorithm can be conveniently carried out.
结合DSP理论中的半解析递归卷积(SARC)算法提出了一种用于色散介质的半解析递归卷积时域有限差分(SARC-FDTD)方法。SARC算法是建立在数值逼近理论基础上的一种卷积递归计算方法,具有绝对稳定、高精度、低内存、高效率等优点。将SARC引入色散介质FDTD,在保留RC方法优点的基础上,提高了算法的通用性,使得在应用时只需给出色散介质模型的极点及其留数,即可进行计算,无需再针对色散模型计算更新公式的系数。解决了现有色散介质RC-FDTD方法对于各种色散介质模型需要单独处理,公式推导复杂、不具有通用性的问题。
结合DSP技术中的IIR数字滤波器级联思想,研究了一种高阶有理分式模型色散介质的级联SARC FDTD算法。有理分式是描述介质色散特性的精确、高效的模型之一,常用于复杂介质的色散特性描述。在该方法中,通过先将高阶有理分式频域模型表示为一系列低阶有理分式之积,再将各低阶有理分式表示为时域复指数函数形式,使得高阶色散模型转化为一系列时域复指数函数的卷积,然后通过SARC-FDTD得到求解。解决了现有RC方法处理高阶有理分式模型和渐进稳定色散介质电磁问题时的困难,并将所提算法应用于宽带Lorentz介质、窄带Lorentz介质及其临界情况的分析,表明了算法的有效性。
研究并实现了一种改进的Z变换方法。DSP理论中的脉冲响应不变法当脉冲响应h ( t )在t = 0时刻不连续时是不精确的。如果将传统Z变换直接应用于色散介质FDTD方法将导致高的数值误差。在对脉冲响应不变法改进的基础上,从极化矢量P和电场E的关系入手,重新推导了Z变换FDTD更新公式,解决了原Z变换FDTD方法内存占用大的问题。同时,对于极化率函数时域表达式χ( t)在t = 0时刻不连续的色散介质,还使FDTD计算的精度得到提高。
提出一种基于DSP的色散介质改进SO-FDTD方法。借鉴IIR数字滤波器转置直接Ⅱ型结构和级联实现思想,并对其状态变量方程进行改进,将其引入色散介质SO-FDTD方法中,得到改进SO-FDTD更新公式。减少了高阶色散介质SO方法内存占用、简化了SO方法在处理高阶有理分式形式色散介质时更新公式系数计算。使内存减少量不低于33%,达到与RC方法相同,更新公式系数计算不超过二阶。
提出一种适用于高阶Debye、Lorentz和Drude模型的SO-FDTD方法。借鉴IIR数字滤波器并联思想,从极化矢量P与电场E的关系入手,利用SO方法推导了适用于三种常用色散模型的SO-FDTD更新公式,避免原SO方法在对三种常用色散介质处理时需将低阶有理分式转化为高阶有理分式,简化了公式推导,且三种常用模型对应的更新公式具有统一的形式,适于处理高阶色散介质以及混合模型色散介质,并便于编制通用的计算程序。同时,极大地减少了SO-FDTD方法的内存占用和计算时间。
研究并实现了基于改进SO-FDTD方法和SARC-FDTD方法的UPML吸收边界和CFS-PML吸收边界,可有效地实现色散介质FDTD计算时的计算区域截断。结合所提出的SO-FDTD方法或SARC-FDTD方法,新的PML吸收边界不仅独立于被截断介质,而且PML区域的FDTD更新公式具有不随所截断介质变化的统一形式。
提出一种同时适用于SARC、ADE、改进Z变换及改进SO方法的色散介质FDTD更新公式的统一形式,解决了不同方法因FDTD更新公式不同而带来的使用不便问题。在该统一更新公式中,使用者可以根据所熟悉的FDTD方法和要处理的色散介质,通过给出色散介质模型参数,由独立的建模程序给出建模数据和更新公式所需系数即可进行计算。
The transient electromagnetic problems with dispersive medium play an important role in stealth technology, bio-electromagnetics, and many other areas. Combination of digital signal processing (DSP) theory and technology, the Finite-Difference Time-Domain (FDTD) algorithms for dispersive medium and related problems are studied and a number of practical issues are analyzed using the proposed new methods.
Combining with the Semi-Analytical Recursive Convolution (SARC) algorithm in DSP techniques, a novel FDTD update formulas for the analysis of electromagnetic characteristic of dispersive objects is proposed, namely as SARC-FDTD algorithm in here. In this scheme, the absolute stability, high accuracy, less storage and high effectiveness are retained, and a unified update formulation for general dispersive media, i.e., Debye, Drude, Lorentz and hybrid model is possessed. The SARC FDTD can therefore be applied to the analysis of general dispersive media provided that the poles and corresponding residues in dispersive medium model of interest are given. The complex derivation of coefficients in update formulas for the specified dispersive model is not requested and the separate treatment for a variety of dispersion media model in the existing RC-FDTD method is avoided.
A novel SARC-FDTD algorithm for the dispersive medium described with high order rational fraction model based on the cascade implementation of Infinite Impulse Response (IIR) filter in DSP techniques is presented. The rational fraction is one of the dispersive models that can accurately and efficiently approximate to the complicated variation of the parameters of dispersive medium with the frequency. In this method, the high-order rational fraction model in frequency domain is firstly expressed as the product of a series low-order rational fraction and is further transformed into the convolution of a series complex exponential function responding to the each low-order rational fractions in time domain. Finally, the convolution is solved by the SARC-FDTD. The FDTD analysis of transient electromagnetic problems for dispersive medium with high-order rational fraction and asymptotic stability model is solved. It is applied to the analysis of dielectric described with wide-band Lorentz model, narrow-band Lorentz model and border-line case.
An improved Z transformation is presented and improved FDTD method is implemented. The classical impulse invariance method in Z-transform theory is found to be incorrect and inaccurate when the impulse response is discontinuous at initial time t=0. Such inaccuracy results in higher numerical errors if it is used to develop the update equations for frequency-dependent FDTD. Thorough discussion of corrected impulse invariance method in the realm of Z-transform, a novel ZT-FDTD update formulas for dispersive media is discussed by the relation of polarization P with electric field E. Compared with the commonly used ZT-FDTD, the storage variables in the improved ZT-FDTD are reduced and high accuracy is achieved for dispersive media which exhibit discontinuity at t=0 in the time domain susceptibility function.
An improved shifted operator (SO) FDTD method for general dispersive medium based on the implementation of IIR filter in DSP techniques is presented. Combining with the improved state-space equation of transposed direct-Ⅱstructure of IIR filter and cascade implementation, the update formulas of improved SO-FDTD are obtained. Compared with the commonly used SO-FDTD, the storage variables in the improved SO-FDTD are reduced by 33% and computational efficiency is also increased. The simple coefficients for high-order rational fraction model can be obtained in the novel scheme.
A novel SO-FDTD scheme for high-order Debye, Lorentz and Drude dispersion model is presented as well. The transformation of low-order rational fraction into high-order form in commonly used SO-FDTD is avoided and derivation of the update formulas is simplified. A unified update formula is possessed for three typical kinds of dispersive model i.e. Debye, Lorentz and Drude medium and is suitable for dealing with high-order dispersive media as well as the hybrid model media. The general computational program can be conveniently developed.
The novel Uniaxial Perfectly matched layers (UPML) absorbing boundary and Complex Frequency-Shifted PML (CFS-PML) absorbing boundary based on improved SO-FDTD and SARC-FDTD are presented and is suitable for truncating the FDTD computational domain for calculation of dispersive medium. Combined with the proposed SO-FDTD and SARC-FDTD, the implementation of PML is not only independent for the truncated medium, and the FDTD update formula in PML region is a unified form for the different dispersive medium.
A unified FDTD update formulas simultaneously applied to SARC, Auxiliary Differential Equation (ADE), improved Z transform and improved SO algorithm is proposed. The inconvenience bringing with the different FDTD formulas for the above several algorithm is avoided. In this scheme, the coefficients in the unified update formulas are obtained providing the dispersion model parameters are specified. Then, FDTD calculation using the user-familiar FDTD algorithm can be conveniently carried out.
引文
[1]王秉中.计算电磁学[M].北京:科学出版社,2003.
[2] Peterson A F, Ray S, Mittra R. Computational method for electromagnetic [M]. New York: IEEE Press, 1998.
[3]盛新庆.计算电磁学要论[M].北京:科学出版社,2004.
[4]王长清.现代计算电磁学基础[M].北京:北京大学出版社,2005.
[5]葛德彪,闫玉波.电磁波时域有限差分法[M]。西安:西安电子科技大学出版社,2005,第二版.
[6] Taflove A, Hagness S C. Computational electrodynamics the finite-difference time-domain method (3rd edition) [M]. Artech House Boston London, 2005.
[7] Harrington R F. Field computation by moment method (2nd edition) [M]. New York: IEEE Press, 1993.
[8] Jin J M. The finite element method in electromagnetics [M]. New York: John Wiley & Sons, 1993.
[9] Yee K S. Numerical solution of initial boundary value problems involving Maxwell equations in isotropic media [J]. IEEE Trans. Antennas Propagat., 1966, AP-14(3): 302-307.
[10] Yee K S and Chen J S. The finite-difference time-domain (FDTD) and finite-volume time-domain (FVTD) method in solving Maxwell’s equations [J]. IEEE Trans. Microwave Theory and Tech., 1997, 45(3): 354-363.
[11] Chen Z and Xu J. The generalized TLM based FDTD summary of recent progress [J]. IEEE Microwave and Guided Wave Letters, 1997, 7(11): 12-14.
[12] Auckenthaler A M and Bennett C L. Computer solution of transient and time domain thin-wire antenna problems[J]. IEEE Trans. Microwave Theory Tech., 1971, 19(11): 892-893.
[13] Lynch D R and Paulsen K D. Time-domain integration of the Maxwell equations of finite elements [J]. IEEE Trans. Antennas Propagat., 1990, 38(12): 1933-1942
[14] Komisarek K S, Wang N N and Dominek A K, et al. An investigation of new FETD/ABC methods of computation of scattering from three-dimensional material objects [J]. IEEE Trans. Antennas Propagat., 1999, 47(10): 1579-1585
[15] Krumpholz M and Katechi L P B. MRTD: New time-domain schemes based onmultiresolution analysis[J]. IEEE Trans. Microwave Theory Tech., 1996, 44(4): 555-571
[16] Fujii M and Hoefer W J R. A three-dimensional Haar-wavelet-based multiresolution analysis similar to the FDTD method-derivation and application [J]. IEEE Trans. Microwave Theory Tech., 1998, 46(12): 2463-2475
[17] Tentzeris E M, Harvey J F and Katechi L P B. Stability and dispersion analysis of Battle-Lemarie-based MRTD schemes [J]. IEEE Trans. Microwave Theory Tech., 1997, 47(7): 1004-1013
[18] Dogaru T and Carin L. Multiresolution time-domain using CDF biorthogonal wavelets [J]. IEEE Trans. Microwave Theory Tech., 2001, 49(7): 902-912
[19] Liu Q H. The PSTD algorithm: A time-domain method requiring only two cells per wavelength [J]. Microwave and Optical Technology Letters, 1997, 15(3): 159-165
[20] Liu Q H. A frequency-dependent PSTD algorithm for general dispersive media [J]. IEEE Microwave and Guided Wave Letters, 1999, 9(2): 51-53
[21] Veruttipong T W. Time-domain version of the uniform GTD [J]. IEEE Trans. Antennas Propagat., 1990, 38(11): 1757-1764
[22] Rousseau P R and Pathak P H. Time-domain uniform GTD for a curved wedge [J]. IEEE Trans. Antennas Propagat., 1995, 43(12): 1375-1382
[23] Sun E Y and Rusch W V T. Time-domain physical-optics [J]. IEEE Trans. Antennas Propagat., 1994, 42(1): 9-15
[24] Johansen P M. Time-domain version of the physical theory of diffraction [J]. IEEE Trans. Antennas Propagat., 1999, 47(2): 261-270
[25] Altintas A and Russer P. Time-domain equivalent edge currents for transient scattering [J]. IEEE Trans. Antennas Propagat., 2001, 49(4): 602-606
[26] Kunz K S, Lee K M. A 3-D finite difference solution of the external response of an aircraft to a complex transient EM environment: I-The method and its implementation [J]. IEEE Trans. Electromagn. Compat., 1978, EMC-20(2): 328-333.
[27] Umashankar K R, Taflove A. A novel method of analyzing electromagnetic scattering of complex objects [J]. IEEE Trans. Electromagn. Compat., 1982, EMC-24(4): 397-405.
[28] Choi D H, Hoefer W J R. The finite difference time domain method and its application to eigenvalue problem [J]. IEEE Trans. Microwave Theory Tech., 1986, MTT-34(12): 1464-1470.
[29] Liang G C, Liu Y W, and Mei K K. Full-wave analysis of coplanar waveguide and slotline using the TDFD method [J]. IEEE Trans. Microwave Theory and Techniques, 1989, 37(12): 1949-1957.
[30] Wang J G, Chen Y S, Fan R Y, et al. Numerical studies on nonlinear coupling of high power microwave pulses into a cylindrical cavity [J]. IEEE Trans. Plasma Science, Feb. 1996, 24(1): 193-197.
[31] Maloney J G, Smith G S and R. Scott. Accurate computation of the radiation from simple antennas using the FDTD method [J]. IEEE Trans. Antennas Propagat., 1990, AP-38(7): 1059-1068.
[32] Zhang X L, Fang J Y, Mei K K, and Liu Y W. Calculation of the dispersive characteristics of microstrip by the time-domain finite-difference method [J]. IEEE Trans. Microwave Theory and Techniques, 1988, 36(2): 263-267.
[33] Tsay W J, Pozar D M. Application of the FDTD technique to periodic problems in the scattering and radiation [J]. IEEE Microwave Guided Wave Lett., 1993, 3(8): 250-252.
[34] Harms P, Mittra R, Ko W. Implementation of the periodic boundary condition in the finite difference time domain algorithm for FSS structures [J]. IEEE Trans. Antennas Propagat., 1994, AP-42(9): 1317-1324.
[35] Roden J A, Gedney S D, Kesler M P, Maloney J G, Harms P H. Time-Domain Analysis of periodic structures at oblique incidence: orthogonal and nonorthogonal FDTD implementations [J]. IEEE Transactions on Microwave Theory and Techniques, 1998, 46(4): 420-427.
[36] Turner G M, Christodoulou C. FDTD analysis of phased array antennas [J]. IEEE Trans. Antennas Propagat., 1999, AP-47(4): 861-867.
[37] Holter H, Steyskai H. Infinite phased-array analysis using FDTD periodic boundary conditions pulse scanning in oblique directions [J]. IEEE Trans. Antennas Propagat., 1999, AP-47(10): 1508-1514.
[38] Sui W, Cristensen D A, Durney C H. Extending the two dimensional FDTD method to hybrid electromagnetic systems with active and passive lumped elements [J]. IEEE Trans. Microwave Theory Tech., 1992, MTT-40(4): 724-730.
[39]周璧华,陈彬,高成.现代战争面临的高功率电磁环境分析[J].微波学报,2002,18(1):88-92.
[40] Prather D W, Shi S Y. Formulation and application of the finite difference time domain method for the analysis of axially symmetric diffractive optical elements [J]. J. Opt. Soc. Am. A, 1999, 16(5): 1131-1142.
[41] Sullivan D. 3-D computer simulation in deep regional hyperthermia using the FDTD method [J]. IEEE Trans. Microwave Theory Tech., 1990, MTT-38(2): 204-211.
[42] Sheen D M,.ALI S M, et al. Application of the three-dimensional finite-differencetime-domain method to the analysis of planar microstrip circuits [J]. IEEE Trans., 1990, MTT-38(7): 849-856.
[43] Veselago V G. The electrodynamics of substance with simultaneously negative values ofεandμ[J]. Sov. Phys. Usp. 1968, 10(4): 509-514.
[44] Yin H C, Chao Z M, Xu Y P. A new free-space method for measurement of electromagnetic parameters of biaxial materials at microwave frequencies [J]. Microwave and Optical Technology Letters, 2005, 46(1): 72-78.
[45]匡磊,金亚秋.三维随机粗糙面与目标复合电磁散射的FDTD方法[J].计算物理,2007,24(5):154~955+065.
[46] Lampe B, Holliger K, green A G. A finite-difference time-domain simulation tool for ground-penetrating radar antennas [J]. Geophysics, 2003, 68: 971-987.
[47]汪彤.色散媒质的瞬态电磁特性研究[D].上海大学博士研究生论文,2001年。
[48] R. J. Luebbers, F. P. Huusberger, K. S. Kunz, et al. A frequency-dependent finite-difference time-domain formulation for dispersive materials[J]. IEEE Trans. Electromagn. Compat., 1990, 32(8): 222-227.
[49] R. J. Luebbers, F. P. Huusberger, K. S. Kunz. A frequency-dependent finite-difference time-domain formulation for transient propagation in plasma[J]. IEEE Trans. AP, 1991, 39(1):29-34.
[50] Forrest Hunsberger, Raymond Luebbers, and Karl Kuru. Finite-Difference Time-Domain Analysis of Gyrotropic Media-I: Magnetized Plasma[J]. IEEE Trans. AP, 1992, 40(12):1489-1495.
[51] R. J. Luebbers and F. P. Hunsberger, FDTD for Nth-order dispersive media[J]. IEEE Trans. AP., 1992, 40(11):1297-1301.
[52] Raymond Luebbers, David Steich, and Karl Kunz. FDTD Calculation of Scattering from Frequency-Dependent Materials[J]. IEEE Trans. Antennas Propagat. 1993, 41(9): 1249-1257.
[53] Riaz Siushansian and Joe LoVetri. An Efficient Higher Order Numerical Convolution for Modellirig Nth-Order Loreiitz Dispersion[C]. IEEE, 1995.
[54] D. F. Kelley, R. J. Luebbers. Piecewise linear recursive convolution for dispersive media using FDTD[J]. IEEE Trans. AP, 1996, 44(6):792-797.
[55] S. Joe Yakura and Jeff MacGillivray. Finte-Difference Time-Domain Calcualations Based on Recursive Convolution Approach For Propagation of Electromagnetic Waves in Nonlinear Dispersive Media[]. 1997.10.
[56] Guo-Xin Fan, Qing Huo Liu. An FDTD algorithm with perfectly matched layersfor general dispersive media[J]. IEEE Trans. AP, 2000,48(5):637-646.
[57] S. B. Liu, N. C. Yuan, and J. J. Mo. A novel FDTD formulation for dispersive media[J]. IEEE Microw. Wireless Compon. Lett., 2003, 13(5): 187–189.
[58]张玉强,葛德彪.基于半解析递归卷积的通用色散介质FDTD方法[J].物理学报, 2009, 58(7): 4573-4578.
[59] Joseph, R. M., S. C. Hagness, and A. Taflove. Direct time integration of Maxwell’s equation in linear dispersive media with absorption for scattering and propagation of femtosecond electromagnetic pulses[J]. Optics Lett.. 1991,16:1412-1414.
[60] Om P. Gandhi, Ben-Qing Gao, and Jin-Yuan Chen. A Frequency-Dependent Finite-Difference Time-Domain Formulation for General Dispersive Media[J]. IEEE Trans. Microwave Theory and Techniques, 1993,41(4): 657-665.
[61] Cynthia M. Furse, Jin-Yuan Chen, et al. The Use of the Frequency-Dependent Finite-Difference Time-Domain Method for Induced Current and SAR Calculations for a Heterogeneous Model of the Human Body[J]. IEEE Trans. Electromagnetic Compatibility, 1994, 36(2): 128-133.
[62] Jeffrey L. Young. Propagation in Linear Dispersive Media: Finite Difference Time-Domain Methodologies[J]. IEEE Trans. Antennas and Propagation, 1995, 43(4):422-426.
[63] M. Okoniewski, M. Mrozowski, and M. A. Stuchly. Simple treatment of multi-term dispersion in FDTD[J]. IEEE Microwave and Guided Wave Letters, 1997, 7(5): 121-123.
[64] Yoshihisa Takayama and Werner Klaus. Reinterpretation of the Auxiliary Differential Equation Method for FDTD[J]. IEEE Microwave and Wireless Componens Letters, 2002, 12(3):102-104.
[65] M. Okoniewski and E. Okoniewska. Drude dispersion in ADE FDTD revisited[J]. Electronics Letters, 2006, 42(9).
[66] M. Han, R. Dutton, and S. Fan. Model dispersive media in finite-difference time-domain method with complex-conjugate pole-residue pairs[J]. IEEE Microw. Wireless Compon. Lett., 2006, 16(3):119–121.
[67] Mohammad A. Alsunaidi and Ahmad A.AJabr. A General ADE-FDTD Algorithm for the Simulation of Dispersive Structures[J]. IEEE Photonics Technology Letters, 2009, 21(12): 817-819.
[68] D. M. Sullivan. A frequency dependent FDTD method for biological applications[J]. IEEE Trans. Microwave Theory Tech., 1992, 40(3): 532-539.
[69] D. M. Sullivan. Frequency-Dependent FDTD Methods Using Z Transforms[J].IEEE Trans. AP, 1992, 40(10):1223-1230.
[70] Dennis M. Sullivan. Nonlinear FDTD Formulations Using Z Transforms[J]. lEEE Trans. Microwave Theory and Techniques, 1995, 43(3):676-682.
[71] D. M. Sullivan. Z-Transform Theory and the FDTD Method[J]. IEEE Trans. AP, 1996, 44(1):28-34.
[72] Kakhkhor Abdijalilov, and Haim Grebel. Z-Transform Theory and FDTD Stability[J]. IEEE Trans. AP, 2004, 52(11):2950-2954.
[73]葛德彪,吴跃丽,朱湘琴.等离子体散射FDTD分析的移位算子方法[J].电波科学学报, 2003, 18(4):359~362.
[74]杨宏伟,陈如山,张云.等离子体的SO-FDTD算法和对电磁波反射系数的计算分析[J].物理学报,2006,55(7): 3464-3469.
[75]杨利霞,葛德彪.磁各向异性色散介质散射的Padé时域有限差分方法分析[J].物理学报,2006,55(4): 1751-1758.
[76]杨宏伟,陈如山,张云.等离子体的SO-FDTD算法和对电磁波反射系数的计算分析[J].物理学报,2006, 55(7): 3464-3469.
[77]杨宏伟,袁洪,陈如山等.各向异性磁化等离子体的SO-FDTD算法[J]. 2007, 56(3):1443-1446.
[78]王茂琰,徐军,魏兵等.基于移位算子法高斯波束与双负介质板相互作用的FDTD分析[J].微波学报,2008年,24(1):10-14.
[79]王飞,葛德彪,魏兵.磁化铁氧体电磁散射的移位算子FDTD分析[J]. 2009, 58(9): 6357-6362.
[80]魏兵,葛德彪,王飞.一种处理色散介质问题的通用FDTD方法[J].物理学报, 2008, 57(10): 6290~6297.
[81]张玉强,葛德彪.一种基于数字信号处理技术的改进通用色散介质移位算子时域有限差分方法[J].物理学报,2009, 58(12):143-148.
[82] William H. Weedon, and Carey M. Rappaport. A General Method for FDTD Modeling of Wave Propagation in Arbitrary Frequency-Dispersive Media[J]. IEEE Trans. Antennas and Propagation, 1997, 45(3): 401-410.
[83] JoséA. Pereda,ángel Vegas, and Andrés Prieto. FDTD Modeling of Wave Propagation in Dispersive Media by Using the Mobius Transformation Technique[J]. IEEE Trans. Microwave Theory and Techniques, 2002, 50(7): 1689-1695.
[84] B. Engquist and A. Majda. Absorbing boundary conditions for the numerical simulation of waves [J]. Mathematics of computation, 1977, 31: 629-651.
[85] Mur G., Absorbing boundary conditions for the finite-difference approximation of the time-domain electromagnetic-field equations [J]. IEEE Trans. Electromagn. Compat.1981, EMC-23(4): 377–382.
[86] K. Mei and J. Fang, Superabsorption-a method to improve absorbing boundary conditions[J]. IEEE Trans. On AP. 1992, 40(9): 1001-1010.
[87] Z. Liao, H. Wong, Y. Baipo and Y. Yifan, A transmitting boundary for transient wave analyszes[J]. Scientiz Sinica, (Series A), 1984, 27(10): 1062-1076.
[88] Berenger J P. A perfectly matched layer medium for the absorption of electromagnetic waves [J], J. Comput. Phys., 1994, 114: 185-200.
[89] Berenger J P. Perfectly matched layer for the FDTD solution of wave-structure interaction problem [J]. IEEE Trans. Antennas Propagat, Jan., 1996, AP-44 (1): 110-117.
[90] J. P. Berenger, Improved PML for the FDTD solution of wave-structure interaction problems[J]. IEEE Transactions on Antennas and Propagation. 1997, 45: 466-473.
[91] Sacks Z S, Kingsland D M, Lee D M and Lee J F. A perfectly matched anisotropic absorber for use as an absorbing boundary condition [J]. IEEE Trans. Antennas Propagat., Dec. 1995, AP-43(12): 1460~1463
[92] Gedney S D. An anisotropic perfectly matched layer absorbing media for the truncation of FDTD lattices [J]. IEEE Trans. Antennas Propagat., 1996, 44(12): 1630-1639
[93] Gedney S D. An anisotropic PML absorbing media for the FDTD simulation for fields in lossy and dispersive media [J]. Electromagnetics, 1996, 16(4): 399-415.
[94] J. Y. Fang, Z. H. Wu. Generalized perfectly matched layer for the absorption of propagating and evanescent waves in lossless and lossy media [J]. IEEE Trans. Microwave Theory Tech., 1996, 44(12): 2216-2222.
[95] Weng Cho Chew and William H. Weedon. A 3D Perfectly Matched Medium from Modifyed Maxwells Equations with Stretched Coordinates[J]. Microwave and Optical Technology Letters, 1994, 7(13): 599-604.
[96] M. Kuzuoglu and R. Mittra, Frequency dependence of the constitutive parameters of causal perfectly matched anisotropic absorbers[J]. IEEE Microwave and Guided Wave Letters. 1996, 6: 447-449.
[97] Jianxiong Li, Chunjiao Miao. An Efficient FDTD Implementation of the CFS-PML Based on the ADE Method and its Validation along with the PLRC method in Dispersive Media[C]. ICMMT 2008 Proceedings.
[98] Roden J.A., Gedney S.D. Convolutional PML (CPML): an efficient FDTD implementation of CFS-PML for arbitrary media [J]. Microwave Opt. Tech. Lett., 2000, 27(12): 334~339.
[99] O. Ramadan and A. Y. Oztoprak. Z-transform implementation of the perfectly matched layer for truncating FDTD domains[J]. IEEE Microwave and Wireless Components Letters. 2003, 13(9): 402–404.
[100] Jianxiong Li and Jufeng Dai, Z-Transform Implementations of the CFS-PML[J]. IEEE Antennas and Wireless Propagation Letters. 2006(5): 410-413.
[101] Jianxiong Li and Jufeng Dai. Z-Transform Implementation of the CFS-PML for Arbitrary Media[J]. IEEE Microwave and Wireless Components Letters. 2006, 16(8):437-439.
[102] Xiaoting Dong, Wen-Yan Yin, and Yeow-Beng Gan. Perfectly Matched Layer Implementation Using Bilinear Transform for Microwave Device Applications[J]. IEEE Trans. Microwave Theory and Techniques, 2005, 53(10):3098-3015.
[103]张玉强,葛德彪.用于通用介质的CFS-PML移位算子方法实现[C]. 2008全国电磁散射与逆散射学术交流会论文集: 163~166.
[104]魏兵,李小勇,王飞,葛德彪.一种色散介质FDTD通用吸收边界[J].物理学报,2009,58(9):6184-6178.
[105] William D. Hurt. Multiterm Debye Dispersion Relations for Permittivity of Muscle[J]. IEEE Trans. Biomedical Engineering, 1985, 32(1): 60-64.
[106] Mariya Lazebnik, Michal Okoniewski, John H. Booske, et al. Highly Accurate Debye Models for Normal and Malignant Breast Tissue Dielectric Properties at Microwave Frequencies[J]. IEEE Microwave and Wireless Componets Letters, 2007, 17(12): 822-824.
[107] Tuya Wuren, Toshio Takai, Masafumi Fujii. Effective 2-Debye-Pole FDTD Model of Electromagnetic Interaction Between Whole Human Body and UWB Radiation[J]. IEEE Microwave and Wireless Components Letters, 2007, 17(7): 483-485.
[108] M. Mrozowski and M. A. Stuchly. Parameterization of media dispersive properties for FDTD[J]. IEEE Trans. Antennas Propag., 1997, 45(9): 1438–1439.
[109] D. F. Kelley and R. J. Luebbers. Debye function expansions of empirical models of complex permittivity for use in FDTD solutions[J]. IEEE Antennas Propag. Soc. Int. Symp., 2003, 4:372–375.
[110] P.Kosmas, C. M. Rappaport, and E. Bishop. Modeling with the FDTD method for microwave breast cancer detection[J]. IEEE Trans. Microw. Theory Tech., 2004, 52( 8): 1890–1897.
[111] Riaz Siushansian and Joe LoVetri. An Efficient Higher Order Numerical Convolution for Modellirig Nth-Order Lorentz Dispersion[C]. IEEE, 1995, 632-635.
[112] Zhili Lin, Pan Ou, Yudong Jia, and Chunxi Zhang. A Highly Accurate FDTDModel for Simulating Lorentz Dielectric Dispersion[J]. IEEE Photonics Technology Letters, 2009, 21(22): 1692-1694.
[113] Marina Y. Koledintseva, James L. Drewniak, David J. Pommerenke, et al. Wide-Band Lorentzian Media in the FDTD Algorithm[J]. IEEE Transactions on Elecromagnetic Compatibility, 2005, 47(2):392-399
[114] Ana Grande, JoséA. Pereda, Oscar González, et al. Stability and Accuracy of a Finite-Difference Time-Domain Scheme for Modeling Double-Negative Media With High-Order Rational Constitutive Parameters[J]. IEEE Trans. Microwave Theory and Techniques, 2008, 56(1): 94-104.
[115] S. Gabriel, R. W. Lau, and C. Gabriel. The dielectric properties of biological tissues: III. Parametric models for the dielectric spectrum of tissues[J]. Phys. Med. Biol., 1996, 41(11): 2271–2293.
[116] J. M. Schuster and R. J. Luebbers. An FDTD algorithm for transient propagation in biological tissue with a Cole–Cole dispersion relation[J]. IEEE Antennas Propag. Soc. Int. Symp., 1998, 4(7):1988–1991.
[117] Bin Guo, Jian Li, and Henry Zmuda. A New FDTD Formulation for Wave Propagation in Biological Media With Cole–Cole Model[J]. IEEE Microwave and Wireless Components Letters, 2006, 16(12): 633-635.
[118] C. Gabriel. Compilation of the dielectric properties of body tissues at RF and microwave frequencies[R]. Tech. Rep., Brooks Air Force Technical Report AL/OE-TR-1996-0037, 1996.
[119] Carey M. Rappaport, Shuang Wu and Scott C. Winton. FDTD Wave Propagation in Dispersive Soil Using a Single Pole Conductivity Model[J]. IEEE TRANS. ON MAGNETICS, 1999, 35(3): 1542-1545.
[120] Wolfram H. P. Pernice, Frank P. Payne, and Dominic F. G. Gallagher. A General Framework for the Finite-Difference Time-Domain Simulation of Real Metals[J]. IEEE Trans. On Antennas and Propagation, 2007, 55(3): 916-923.
[121] Jun Shibayama, Ryoji Ando, Akifumi Nomura, et al. Simple Trapezoidal Recursive Convolution Technique for the Frequency-Dependent FDTD Analysis of a Drude–Lorentz Model[J]. IEEE Photonics Technology Letters, 2009, 21(2): 100-102.
[122]汪彤,张文俊,刘维亮. N阶色散媒质的FDTD法与数字信号处理技术[J].电波科学学报,2000.12
[123]丁玉美,高西全.数字信号处理(第二版)[M],西安:西安电子科技大学出版社,2001.
[124] Emmanuel C. Ifeachor, Barrie W. Jervis.数字信号处理实践方法(第二版)[M],北京:电子工业出版社,2004.
[125] W. Janke, G. Blakiewicz. Semi-analytical recursive algorithms for convolution calculations[J]. IEE Proc. Circuits Devices Syst. 1995, 142(2):125-130.
[126] M. Ramme, E. Griese, M. Kurten. Fast simulation method for a transient analysis of lossy coupled transmission lines using a semi-analytical recursive convolution procedure[C]. Electromagnetic Compatibility, 1997.
[127] Lin, S., and Kuh, E.S Transient simulation of lossy interconnects based on the recursive convolution formulation[J]. IEEE Trans, 1992, CAS-39, (ll), pp. 879-892
[128] Tuyen V., Nguyen, Recursive convolution and discrete time domain simulation of lossy coupled transmission lines[J]. IEEE Trans. 1994,13(10):1301-1305
[129] Wac?aw Pietrenko, W?odzimierz Janke, and Marian K. Kazimierczuk. Application of Semianalytical Recursive Convolution Algorithms for Large-Signal Time-Domain Simulation of Switch-Mode Power Converters[J]. IEEE Transactions ON Circuits and Systems, 2001, 48(10):1246-1252.
[130] Y.-Q. Zhang and D.-B. Ge. A Unified FDTD Approch for Electromagnetic Analysis of Dispersive Obejects[J]. Progress in Electromagnetics Research, 2009, PIER 96: 155-172.
[131]苏金明,阮沈勇等. MATLAB实用指南(上,下册)[M].北京:电子工业出版社,2002.
[132] Serkan Aksoy. An Alternative Algorithm for Both Narrowband and Wideband Lorentzian Dispersive Materials Modeling in the Finite-Difference Time-Domain Method[J]. IEEE Trans. ON Microwave Theory and Techniques, 2007, 55( 4):703-708
[133] L. B. Jackson. A correction to impulse invariance[J]. IEEE Signal Processing Lett., 2000, 7(10): 273–275.
[134] W. F. G. Mecklenbrauker. Remarks on and correction to the impulse invariant method for the design of IIR digital filters[J]. Signal Process., 2000, 80(10): 1687–1690.
[135] Ding Yu Heh, and Eng Leong Tan. Corrected Impulse Invariance Method in Z-Transform Theory for Frequency-Dependent FDTD Methods[J]. IEEE Trans. ON Antennas and Propagation, 2009, 57(9): 2683-2690.
[136] Eng Leong Tan and Ding Yu Heh. Corrected Impulse Invariance Method for Dispersive Media Using FDTD[C]. 2008 Asia-Pacific Sympsoium on Electromagnetic Compatibility & 56 19th International Zurich Symposium on Electromagnetic Compatibility, 19–22 May 2008, Singapore
[137] Jose A. Pereda, Luis A. Vielva, Angel Vegas, et al. State-Space Approach to theFDTD Formulation for Dispersive Media[J]. IEEE Trans. Magnetics. 1995, 31(3): 1602-1605.
[138] O. Ramadan. State-space FDTD implementation of anisotropic perfectly matched layer[J]. Electronics Letters. 2003, 39(13):969-970.
[139] Peter G. Petropoulos. On the Time-Domain Response of Cole–Cole Dielectrics[J]. IEEE Trans. Antennas and Propagation, 2005, 53(11): 3741-3746.
[140] W. H. P. Pernice, F. P. Payne and D. F. G. Gallagher.An FDTD method for the simulation of dispersive metallic structures[J]. Optical and Quantum Electronics,2006, 38:843-856.
[141] Antonios Giannopoulos. An improved new implementation of complex frequency shifted PML for the FDTD method [J]. IEEE Trans. Antennas and Propagation, 2008, 56(9): 2995-3000.
[142] Omar Ramadan, Digital Filtering Technique for the FDTD Implementation of the Anisotropic Perfectly Matched Layer[J]. IEEE Microwave and Wireless Components Letters, 2003,13(8):340-342.
[143] Jiayuan Fang, Zhonghua Wu. Closed-Form Expression of Numerical Reflection Coefficient at PML Interfaces and Optimization of PML Performance[J]. IEEE Microwave and Guided Wave Letters, 1996, 6(9): 332-334.
[144] B. Chatry, M. Aubourg and P. Guillon. Perfectly matched layer: Variable discretisation against variable conductivity[J]. Electronics Letters. 1997, 33(4):277-278.
[145] Scott C. Winton and Carey M. Rappaport. Specifying PML Conductivities by Considering Numerical Reflection Dependencies[J]. IEEE Trans. Antennas and Propagation, 2000, 48(7): 1055-1063.
[146] Jaakko S. Juntunen, Nikolaos V. Kantartzis, Theodoros D. Tsiboukis. Zero Reflection Coefficient in Discretized PML[J]. IEEE Microwave and Wireless Components Letters, 2001, 11(4): 155-157.
[147] Sherwood W. Samn. Modeling Dispersive Dielectric Media in FDTD: A Systematic Approach[J]. IEEE Trans. Antennas and Propagation, 2005, 53(10): 3367-3373.
[148]邓巍巍,王越男. Visual Fortran编程指南[M].北京:人民邮电出版社,2000.
[149] Fernando L. Teixeira. Time-Domain Finite-Difference and Finite-Element Methods for Maxwell Equations in Complex Media[J]. IEEE Trans. Antennas and Propagation, 2008, 56(8): 2150-2166.
[150] Riaz Siushansian and Joe LoVetri. A Comparison of Numerical Techniques for Modeling Electromagnetic Dispersive Media[J]. IEEE Microwave and Guided WaveLetters , 1995, 5(12): 426-428.
[151]詹毅.复杂有耗色散地层FDTD方法及在冲击探地雷达中的应用[D].西安电子科技大学,2000.12
[152]姜彦南. FDTD并行算法及层状半空间散射问题研究[D].西安电子科技大学博士学位论文. 2009.
[153]闫玉波. FDTD在工程瞬态电磁学中的应用[D].西安电子科技大学博士学位论文. 2001年.
[154]魏兵.各向异性介质电磁散射及参数反演研究[D].西安电子科技大学博士学位论文. 2004年.
[155]朱湘琴. FDTD在半空间及周期结构问题中的应用[D].西安电子科技大学博士学位论文. 2005年.
[156]郑奎松. FDTD网络并行计算及ADI-FDTD方法研究[D].西安电子科技大学博士学位论文. 2006年.
[157]杨利霞.复杂介质电磁散射的FDTD算法及其相关技术研究[D].西安电子科技大学博士学位论文. 2007年.
[158]胡晓娟.复杂目标电磁散射的FDTD及FDFD算法研究[D].西安电子科技大学博士学位论文. 2008年.
[2] Peterson A F, Ray S, Mittra R. Computational method for electromagnetic [M]. New York: IEEE Press, 1998.
[3]盛新庆.计算电磁学要论[M].北京:科学出版社,2004.
[4]王长清.现代计算电磁学基础[M].北京:北京大学出版社,2005.
[5]葛德彪,闫玉波.电磁波时域有限差分法[M]。西安:西安电子科技大学出版社,2005,第二版.
[6] Taflove A, Hagness S C. Computational electrodynamics the finite-difference time-domain method (3rd edition) [M]. Artech House Boston London, 2005.
[7] Harrington R F. Field computation by moment method (2nd edition) [M]. New York: IEEE Press, 1993.
[8] Jin J M. The finite element method in electromagnetics [M]. New York: John Wiley & Sons, 1993.
[9] Yee K S. Numerical solution of initial boundary value problems involving Maxwell equations in isotropic media [J]. IEEE Trans. Antennas Propagat., 1966, AP-14(3): 302-307.
[10] Yee K S and Chen J S. The finite-difference time-domain (FDTD) and finite-volume time-domain (FVTD) method in solving Maxwell’s equations [J]. IEEE Trans. Microwave Theory and Tech., 1997, 45(3): 354-363.
[11] Chen Z and Xu J. The generalized TLM based FDTD summary of recent progress [J]. IEEE Microwave and Guided Wave Letters, 1997, 7(11): 12-14.
[12] Auckenthaler A M and Bennett C L. Computer solution of transient and time domain thin-wire antenna problems[J]. IEEE Trans. Microwave Theory Tech., 1971, 19(11): 892-893.
[13] Lynch D R and Paulsen K D. Time-domain integration of the Maxwell equations of finite elements [J]. IEEE Trans. Antennas Propagat., 1990, 38(12): 1933-1942
[14] Komisarek K S, Wang N N and Dominek A K, et al. An investigation of new FETD/ABC methods of computation of scattering from three-dimensional material objects [J]. IEEE Trans. Antennas Propagat., 1999, 47(10): 1579-1585
[15] Krumpholz M and Katechi L P B. MRTD: New time-domain schemes based onmultiresolution analysis[J]. IEEE Trans. Microwave Theory Tech., 1996, 44(4): 555-571
[16] Fujii M and Hoefer W J R. A three-dimensional Haar-wavelet-based multiresolution analysis similar to the FDTD method-derivation and application [J]. IEEE Trans. Microwave Theory Tech., 1998, 46(12): 2463-2475
[17] Tentzeris E M, Harvey J F and Katechi L P B. Stability and dispersion analysis of Battle-Lemarie-based MRTD schemes [J]. IEEE Trans. Microwave Theory Tech., 1997, 47(7): 1004-1013
[18] Dogaru T and Carin L. Multiresolution time-domain using CDF biorthogonal wavelets [J]. IEEE Trans. Microwave Theory Tech., 2001, 49(7): 902-912
[19] Liu Q H. The PSTD algorithm: A time-domain method requiring only two cells per wavelength [J]. Microwave and Optical Technology Letters, 1997, 15(3): 159-165
[20] Liu Q H. A frequency-dependent PSTD algorithm for general dispersive media [J]. IEEE Microwave and Guided Wave Letters, 1999, 9(2): 51-53
[21] Veruttipong T W. Time-domain version of the uniform GTD [J]. IEEE Trans. Antennas Propagat., 1990, 38(11): 1757-1764
[22] Rousseau P R and Pathak P H. Time-domain uniform GTD for a curved wedge [J]. IEEE Trans. Antennas Propagat., 1995, 43(12): 1375-1382
[23] Sun E Y and Rusch W V T. Time-domain physical-optics [J]. IEEE Trans. Antennas Propagat., 1994, 42(1): 9-15
[24] Johansen P M. Time-domain version of the physical theory of diffraction [J]. IEEE Trans. Antennas Propagat., 1999, 47(2): 261-270
[25] Altintas A and Russer P. Time-domain equivalent edge currents for transient scattering [J]. IEEE Trans. Antennas Propagat., 2001, 49(4): 602-606
[26] Kunz K S, Lee K M. A 3-D finite difference solution of the external response of an aircraft to a complex transient EM environment: I-The method and its implementation [J]. IEEE Trans. Electromagn. Compat., 1978, EMC-20(2): 328-333.
[27] Umashankar K R, Taflove A. A novel method of analyzing electromagnetic scattering of complex objects [J]. IEEE Trans. Electromagn. Compat., 1982, EMC-24(4): 397-405.
[28] Choi D H, Hoefer W J R. The finite difference time domain method and its application to eigenvalue problem [J]. IEEE Trans. Microwave Theory Tech., 1986, MTT-34(12): 1464-1470.
[29] Liang G C, Liu Y W, and Mei K K. Full-wave analysis of coplanar waveguide and slotline using the TDFD method [J]. IEEE Trans. Microwave Theory and Techniques, 1989, 37(12): 1949-1957.
[30] Wang J G, Chen Y S, Fan R Y, et al. Numerical studies on nonlinear coupling of high power microwave pulses into a cylindrical cavity [J]. IEEE Trans. Plasma Science, Feb. 1996, 24(1): 193-197.
[31] Maloney J G, Smith G S and R. Scott. Accurate computation of the radiation from simple antennas using the FDTD method [J]. IEEE Trans. Antennas Propagat., 1990, AP-38(7): 1059-1068.
[32] Zhang X L, Fang J Y, Mei K K, and Liu Y W. Calculation of the dispersive characteristics of microstrip by the time-domain finite-difference method [J]. IEEE Trans. Microwave Theory and Techniques, 1988, 36(2): 263-267.
[33] Tsay W J, Pozar D M. Application of the FDTD technique to periodic problems in the scattering and radiation [J]. IEEE Microwave Guided Wave Lett., 1993, 3(8): 250-252.
[34] Harms P, Mittra R, Ko W. Implementation of the periodic boundary condition in the finite difference time domain algorithm for FSS structures [J]. IEEE Trans. Antennas Propagat., 1994, AP-42(9): 1317-1324.
[35] Roden J A, Gedney S D, Kesler M P, Maloney J G, Harms P H. Time-Domain Analysis of periodic structures at oblique incidence: orthogonal and nonorthogonal FDTD implementations [J]. IEEE Transactions on Microwave Theory and Techniques, 1998, 46(4): 420-427.
[36] Turner G M, Christodoulou C. FDTD analysis of phased array antennas [J]. IEEE Trans. Antennas Propagat., 1999, AP-47(4): 861-867.
[37] Holter H, Steyskai H. Infinite phased-array analysis using FDTD periodic boundary conditions pulse scanning in oblique directions [J]. IEEE Trans. Antennas Propagat., 1999, AP-47(10): 1508-1514.
[38] Sui W, Cristensen D A, Durney C H. Extending the two dimensional FDTD method to hybrid electromagnetic systems with active and passive lumped elements [J]. IEEE Trans. Microwave Theory Tech., 1992, MTT-40(4): 724-730.
[39]周璧华,陈彬,高成.现代战争面临的高功率电磁环境分析[J].微波学报,2002,18(1):88-92.
[40] Prather D W, Shi S Y. Formulation and application of the finite difference time domain method for the analysis of axially symmetric diffractive optical elements [J]. J. Opt. Soc. Am. A, 1999, 16(5): 1131-1142.
[41] Sullivan D. 3-D computer simulation in deep regional hyperthermia using the FDTD method [J]. IEEE Trans. Microwave Theory Tech., 1990, MTT-38(2): 204-211.
[42] Sheen D M,.ALI S M, et al. Application of the three-dimensional finite-differencetime-domain method to the analysis of planar microstrip circuits [J]. IEEE Trans., 1990, MTT-38(7): 849-856.
[43] Veselago V G. The electrodynamics of substance with simultaneously negative values ofεandμ[J]. Sov. Phys. Usp. 1968, 10(4): 509-514.
[44] Yin H C, Chao Z M, Xu Y P. A new free-space method for measurement of electromagnetic parameters of biaxial materials at microwave frequencies [J]. Microwave and Optical Technology Letters, 2005, 46(1): 72-78.
[45]匡磊,金亚秋.三维随机粗糙面与目标复合电磁散射的FDTD方法[J].计算物理,2007,24(5):154~955+065.
[46] Lampe B, Holliger K, green A G. A finite-difference time-domain simulation tool for ground-penetrating radar antennas [J]. Geophysics, 2003, 68: 971-987.
[47]汪彤.色散媒质的瞬态电磁特性研究[D].上海大学博士研究生论文,2001年。
[48] R. J. Luebbers, F. P. Huusberger, K. S. Kunz, et al. A frequency-dependent finite-difference time-domain formulation for dispersive materials[J]. IEEE Trans. Electromagn. Compat., 1990, 32(8): 222-227.
[49] R. J. Luebbers, F. P. Huusberger, K. S. Kunz. A frequency-dependent finite-difference time-domain formulation for transient propagation in plasma[J]. IEEE Trans. AP, 1991, 39(1):29-34.
[50] Forrest Hunsberger, Raymond Luebbers, and Karl Kuru. Finite-Difference Time-Domain Analysis of Gyrotropic Media-I: Magnetized Plasma[J]. IEEE Trans. AP, 1992, 40(12):1489-1495.
[51] R. J. Luebbers and F. P. Hunsberger, FDTD for Nth-order dispersive media[J]. IEEE Trans. AP., 1992, 40(11):1297-1301.
[52] Raymond Luebbers, David Steich, and Karl Kunz. FDTD Calculation of Scattering from Frequency-Dependent Materials[J]. IEEE Trans. Antennas Propagat. 1993, 41(9): 1249-1257.
[53] Riaz Siushansian and Joe LoVetri. An Efficient Higher Order Numerical Convolution for Modellirig Nth-Order Loreiitz Dispersion[C]. IEEE, 1995.
[54] D. F. Kelley, R. J. Luebbers. Piecewise linear recursive convolution for dispersive media using FDTD[J]. IEEE Trans. AP, 1996, 44(6):792-797.
[55] S. Joe Yakura and Jeff MacGillivray. Finte-Difference Time-Domain Calcualations Based on Recursive Convolution Approach For Propagation of Electromagnetic Waves in Nonlinear Dispersive Media[]. 1997.10.
[56] Guo-Xin Fan, Qing Huo Liu. An FDTD algorithm with perfectly matched layersfor general dispersive media[J]. IEEE Trans. AP, 2000,48(5):637-646.
[57] S. B. Liu, N. C. Yuan, and J. J. Mo. A novel FDTD formulation for dispersive media[J]. IEEE Microw. Wireless Compon. Lett., 2003, 13(5): 187–189.
[58]张玉强,葛德彪.基于半解析递归卷积的通用色散介质FDTD方法[J].物理学报, 2009, 58(7): 4573-4578.
[59] Joseph, R. M., S. C. Hagness, and A. Taflove. Direct time integration of Maxwell’s equation in linear dispersive media with absorption for scattering and propagation of femtosecond electromagnetic pulses[J]. Optics Lett.. 1991,16:1412-1414.
[60] Om P. Gandhi, Ben-Qing Gao, and Jin-Yuan Chen. A Frequency-Dependent Finite-Difference Time-Domain Formulation for General Dispersive Media[J]. IEEE Trans. Microwave Theory and Techniques, 1993,41(4): 657-665.
[61] Cynthia M. Furse, Jin-Yuan Chen, et al. The Use of the Frequency-Dependent Finite-Difference Time-Domain Method for Induced Current and SAR Calculations for a Heterogeneous Model of the Human Body[J]. IEEE Trans. Electromagnetic Compatibility, 1994, 36(2): 128-133.
[62] Jeffrey L. Young. Propagation in Linear Dispersive Media: Finite Difference Time-Domain Methodologies[J]. IEEE Trans. Antennas and Propagation, 1995, 43(4):422-426.
[63] M. Okoniewski, M. Mrozowski, and M. A. Stuchly. Simple treatment of multi-term dispersion in FDTD[J]. IEEE Microwave and Guided Wave Letters, 1997, 7(5): 121-123.
[64] Yoshihisa Takayama and Werner Klaus. Reinterpretation of the Auxiliary Differential Equation Method for FDTD[J]. IEEE Microwave and Wireless Componens Letters, 2002, 12(3):102-104.
[65] M. Okoniewski and E. Okoniewska. Drude dispersion in ADE FDTD revisited[J]. Electronics Letters, 2006, 42(9).
[66] M. Han, R. Dutton, and S. Fan. Model dispersive media in finite-difference time-domain method with complex-conjugate pole-residue pairs[J]. IEEE Microw. Wireless Compon. Lett., 2006, 16(3):119–121.
[67] Mohammad A. Alsunaidi and Ahmad A.AJabr. A General ADE-FDTD Algorithm for the Simulation of Dispersive Structures[J]. IEEE Photonics Technology Letters, 2009, 21(12): 817-819.
[68] D. M. Sullivan. A frequency dependent FDTD method for biological applications[J]. IEEE Trans. Microwave Theory Tech., 1992, 40(3): 532-539.
[69] D. M. Sullivan. Frequency-Dependent FDTD Methods Using Z Transforms[J].IEEE Trans. AP, 1992, 40(10):1223-1230.
[70] Dennis M. Sullivan. Nonlinear FDTD Formulations Using Z Transforms[J]. lEEE Trans. Microwave Theory and Techniques, 1995, 43(3):676-682.
[71] D. M. Sullivan. Z-Transform Theory and the FDTD Method[J]. IEEE Trans. AP, 1996, 44(1):28-34.
[72] Kakhkhor Abdijalilov, and Haim Grebel. Z-Transform Theory and FDTD Stability[J]. IEEE Trans. AP, 2004, 52(11):2950-2954.
[73]葛德彪,吴跃丽,朱湘琴.等离子体散射FDTD分析的移位算子方法[J].电波科学学报, 2003, 18(4):359~362.
[74]杨宏伟,陈如山,张云.等离子体的SO-FDTD算法和对电磁波反射系数的计算分析[J].物理学报,2006,55(7): 3464-3469.
[75]杨利霞,葛德彪.磁各向异性色散介质散射的Padé时域有限差分方法分析[J].物理学报,2006,55(4): 1751-1758.
[76]杨宏伟,陈如山,张云.等离子体的SO-FDTD算法和对电磁波反射系数的计算分析[J].物理学报,2006, 55(7): 3464-3469.
[77]杨宏伟,袁洪,陈如山等.各向异性磁化等离子体的SO-FDTD算法[J]. 2007, 56(3):1443-1446.
[78]王茂琰,徐军,魏兵等.基于移位算子法高斯波束与双负介质板相互作用的FDTD分析[J].微波学报,2008年,24(1):10-14.
[79]王飞,葛德彪,魏兵.磁化铁氧体电磁散射的移位算子FDTD分析[J]. 2009, 58(9): 6357-6362.
[80]魏兵,葛德彪,王飞.一种处理色散介质问题的通用FDTD方法[J].物理学报, 2008, 57(10): 6290~6297.
[81]张玉强,葛德彪.一种基于数字信号处理技术的改进通用色散介质移位算子时域有限差分方法[J].物理学报,2009, 58(12):143-148.
[82] William H. Weedon, and Carey M. Rappaport. A General Method for FDTD Modeling of Wave Propagation in Arbitrary Frequency-Dispersive Media[J]. IEEE Trans. Antennas and Propagation, 1997, 45(3): 401-410.
[83] JoséA. Pereda,ángel Vegas, and Andrés Prieto. FDTD Modeling of Wave Propagation in Dispersive Media by Using the Mobius Transformation Technique[J]. IEEE Trans. Microwave Theory and Techniques, 2002, 50(7): 1689-1695.
[84] B. Engquist and A. Majda. Absorbing boundary conditions for the numerical simulation of waves [J]. Mathematics of computation, 1977, 31: 629-651.
[85] Mur G., Absorbing boundary conditions for the finite-difference approximation of the time-domain electromagnetic-field equations [J]. IEEE Trans. Electromagn. Compat.1981, EMC-23(4): 377–382.
[86] K. Mei and J. Fang, Superabsorption-a method to improve absorbing boundary conditions[J]. IEEE Trans. On AP. 1992, 40(9): 1001-1010.
[87] Z. Liao, H. Wong, Y. Baipo and Y. Yifan, A transmitting boundary for transient wave analyszes[J]. Scientiz Sinica, (Series A), 1984, 27(10): 1062-1076.
[88] Berenger J P. A perfectly matched layer medium for the absorption of electromagnetic waves [J], J. Comput. Phys., 1994, 114: 185-200.
[89] Berenger J P. Perfectly matched layer for the FDTD solution of wave-structure interaction problem [J]. IEEE Trans. Antennas Propagat, Jan., 1996, AP-44 (1): 110-117.
[90] J. P. Berenger, Improved PML for the FDTD solution of wave-structure interaction problems[J]. IEEE Transactions on Antennas and Propagation. 1997, 45: 466-473.
[91] Sacks Z S, Kingsland D M, Lee D M and Lee J F. A perfectly matched anisotropic absorber for use as an absorbing boundary condition [J]. IEEE Trans. Antennas Propagat., Dec. 1995, AP-43(12): 1460~1463
[92] Gedney S D. An anisotropic perfectly matched layer absorbing media for the truncation of FDTD lattices [J]. IEEE Trans. Antennas Propagat., 1996, 44(12): 1630-1639
[93] Gedney S D. An anisotropic PML absorbing media for the FDTD simulation for fields in lossy and dispersive media [J]. Electromagnetics, 1996, 16(4): 399-415.
[94] J. Y. Fang, Z. H. Wu. Generalized perfectly matched layer for the absorption of propagating and evanescent waves in lossless and lossy media [J]. IEEE Trans. Microwave Theory Tech., 1996, 44(12): 2216-2222.
[95] Weng Cho Chew and William H. Weedon. A 3D Perfectly Matched Medium from Modifyed Maxwells Equations with Stretched Coordinates[J]. Microwave and Optical Technology Letters, 1994, 7(13): 599-604.
[96] M. Kuzuoglu and R. Mittra, Frequency dependence of the constitutive parameters of causal perfectly matched anisotropic absorbers[J]. IEEE Microwave and Guided Wave Letters. 1996, 6: 447-449.
[97] Jianxiong Li, Chunjiao Miao. An Efficient FDTD Implementation of the CFS-PML Based on the ADE Method and its Validation along with the PLRC method in Dispersive Media[C]. ICMMT 2008 Proceedings.
[98] Roden J.A., Gedney S.D. Convolutional PML (CPML): an efficient FDTD implementation of CFS-PML for arbitrary media [J]. Microwave Opt. Tech. Lett., 2000, 27(12): 334~339.
[99] O. Ramadan and A. Y. Oztoprak. Z-transform implementation of the perfectly matched layer for truncating FDTD domains[J]. IEEE Microwave and Wireless Components Letters. 2003, 13(9): 402–404.
[100] Jianxiong Li and Jufeng Dai, Z-Transform Implementations of the CFS-PML[J]. IEEE Antennas and Wireless Propagation Letters. 2006(5): 410-413.
[101] Jianxiong Li and Jufeng Dai. Z-Transform Implementation of the CFS-PML for Arbitrary Media[J]. IEEE Microwave and Wireless Components Letters. 2006, 16(8):437-439.
[102] Xiaoting Dong, Wen-Yan Yin, and Yeow-Beng Gan. Perfectly Matched Layer Implementation Using Bilinear Transform for Microwave Device Applications[J]. IEEE Trans. Microwave Theory and Techniques, 2005, 53(10):3098-3015.
[103]张玉强,葛德彪.用于通用介质的CFS-PML移位算子方法实现[C]. 2008全国电磁散射与逆散射学术交流会论文集: 163~166.
[104]魏兵,李小勇,王飞,葛德彪.一种色散介质FDTD通用吸收边界[J].物理学报,2009,58(9):6184-6178.
[105] William D. Hurt. Multiterm Debye Dispersion Relations for Permittivity of Muscle[J]. IEEE Trans. Biomedical Engineering, 1985, 32(1): 60-64.
[106] Mariya Lazebnik, Michal Okoniewski, John H. Booske, et al. Highly Accurate Debye Models for Normal and Malignant Breast Tissue Dielectric Properties at Microwave Frequencies[J]. IEEE Microwave and Wireless Componets Letters, 2007, 17(12): 822-824.
[107] Tuya Wuren, Toshio Takai, Masafumi Fujii. Effective 2-Debye-Pole FDTD Model of Electromagnetic Interaction Between Whole Human Body and UWB Radiation[J]. IEEE Microwave and Wireless Components Letters, 2007, 17(7): 483-485.
[108] M. Mrozowski and M. A. Stuchly. Parameterization of media dispersive properties for FDTD[J]. IEEE Trans. Antennas Propag., 1997, 45(9): 1438–1439.
[109] D. F. Kelley and R. J. Luebbers. Debye function expansions of empirical models of complex permittivity for use in FDTD solutions[J]. IEEE Antennas Propag. Soc. Int. Symp., 2003, 4:372–375.
[110] P.Kosmas, C. M. Rappaport, and E. Bishop. Modeling with the FDTD method for microwave breast cancer detection[J]. IEEE Trans. Microw. Theory Tech., 2004, 52( 8): 1890–1897.
[111] Riaz Siushansian and Joe LoVetri. An Efficient Higher Order Numerical Convolution for Modellirig Nth-Order Lorentz Dispersion[C]. IEEE, 1995, 632-635.
[112] Zhili Lin, Pan Ou, Yudong Jia, and Chunxi Zhang. A Highly Accurate FDTDModel for Simulating Lorentz Dielectric Dispersion[J]. IEEE Photonics Technology Letters, 2009, 21(22): 1692-1694.
[113] Marina Y. Koledintseva, James L. Drewniak, David J. Pommerenke, et al. Wide-Band Lorentzian Media in the FDTD Algorithm[J]. IEEE Transactions on Elecromagnetic Compatibility, 2005, 47(2):392-399
[114] Ana Grande, JoséA. Pereda, Oscar González, et al. Stability and Accuracy of a Finite-Difference Time-Domain Scheme for Modeling Double-Negative Media With High-Order Rational Constitutive Parameters[J]. IEEE Trans. Microwave Theory and Techniques, 2008, 56(1): 94-104.
[115] S. Gabriel, R. W. Lau, and C. Gabriel. The dielectric properties of biological tissues: III. Parametric models for the dielectric spectrum of tissues[J]. Phys. Med. Biol., 1996, 41(11): 2271–2293.
[116] J. M. Schuster and R. J. Luebbers. An FDTD algorithm for transient propagation in biological tissue with a Cole–Cole dispersion relation[J]. IEEE Antennas Propag. Soc. Int. Symp., 1998, 4(7):1988–1991.
[117] Bin Guo, Jian Li, and Henry Zmuda. A New FDTD Formulation for Wave Propagation in Biological Media With Cole–Cole Model[J]. IEEE Microwave and Wireless Components Letters, 2006, 16(12): 633-635.
[118] C. Gabriel. Compilation of the dielectric properties of body tissues at RF and microwave frequencies[R]. Tech. Rep., Brooks Air Force Technical Report AL/OE-TR-1996-0037, 1996.
[119] Carey M. Rappaport, Shuang Wu and Scott C. Winton. FDTD Wave Propagation in Dispersive Soil Using a Single Pole Conductivity Model[J]. IEEE TRANS. ON MAGNETICS, 1999, 35(3): 1542-1545.
[120] Wolfram H. P. Pernice, Frank P. Payne, and Dominic F. G. Gallagher. A General Framework for the Finite-Difference Time-Domain Simulation of Real Metals[J]. IEEE Trans. On Antennas and Propagation, 2007, 55(3): 916-923.
[121] Jun Shibayama, Ryoji Ando, Akifumi Nomura, et al. Simple Trapezoidal Recursive Convolution Technique for the Frequency-Dependent FDTD Analysis of a Drude–Lorentz Model[J]. IEEE Photonics Technology Letters, 2009, 21(2): 100-102.
[122]汪彤,张文俊,刘维亮. N阶色散媒质的FDTD法与数字信号处理技术[J].电波科学学报,2000.12
[123]丁玉美,高西全.数字信号处理(第二版)[M],西安:西安电子科技大学出版社,2001.
[124] Emmanuel C. Ifeachor, Barrie W. Jervis.数字信号处理实践方法(第二版)[M],北京:电子工业出版社,2004.
[125] W. Janke, G. Blakiewicz. Semi-analytical recursive algorithms for convolution calculations[J]. IEE Proc. Circuits Devices Syst. 1995, 142(2):125-130.
[126] M. Ramme, E. Griese, M. Kurten. Fast simulation method for a transient analysis of lossy coupled transmission lines using a semi-analytical recursive convolution procedure[C]. Electromagnetic Compatibility, 1997.
[127] Lin, S., and Kuh, E.S Transient simulation of lossy interconnects based on the recursive convolution formulation[J]. IEEE Trans, 1992, CAS-39, (ll), pp. 879-892
[128] Tuyen V., Nguyen, Recursive convolution and discrete time domain simulation of lossy coupled transmission lines[J]. IEEE Trans. 1994,13(10):1301-1305
[129] Wac?aw Pietrenko, W?odzimierz Janke, and Marian K. Kazimierczuk. Application of Semianalytical Recursive Convolution Algorithms for Large-Signal Time-Domain Simulation of Switch-Mode Power Converters[J]. IEEE Transactions ON Circuits and Systems, 2001, 48(10):1246-1252.
[130] Y.-Q. Zhang and D.-B. Ge. A Unified FDTD Approch for Electromagnetic Analysis of Dispersive Obejects[J]. Progress in Electromagnetics Research, 2009, PIER 96: 155-172.
[131]苏金明,阮沈勇等. MATLAB实用指南(上,下册)[M].北京:电子工业出版社,2002.
[132] Serkan Aksoy. An Alternative Algorithm for Both Narrowband and Wideband Lorentzian Dispersive Materials Modeling in the Finite-Difference Time-Domain Method[J]. IEEE Trans. ON Microwave Theory and Techniques, 2007, 55( 4):703-708
[133] L. B. Jackson. A correction to impulse invariance[J]. IEEE Signal Processing Lett., 2000, 7(10): 273–275.
[134] W. F. G. Mecklenbrauker. Remarks on and correction to the impulse invariant method for the design of IIR digital filters[J]. Signal Process., 2000, 80(10): 1687–1690.
[135] Ding Yu Heh, and Eng Leong Tan. Corrected Impulse Invariance Method in Z-Transform Theory for Frequency-Dependent FDTD Methods[J]. IEEE Trans. ON Antennas and Propagation, 2009, 57(9): 2683-2690.
[136] Eng Leong Tan and Ding Yu Heh. Corrected Impulse Invariance Method for Dispersive Media Using FDTD[C]. 2008 Asia-Pacific Sympsoium on Electromagnetic Compatibility & 56 19th International Zurich Symposium on Electromagnetic Compatibility, 19–22 May 2008, Singapore
[137] Jose A. Pereda, Luis A. Vielva, Angel Vegas, et al. State-Space Approach to theFDTD Formulation for Dispersive Media[J]. IEEE Trans. Magnetics. 1995, 31(3): 1602-1605.
[138] O. Ramadan. State-space FDTD implementation of anisotropic perfectly matched layer[J]. Electronics Letters. 2003, 39(13):969-970.
[139] Peter G. Petropoulos. On the Time-Domain Response of Cole–Cole Dielectrics[J]. IEEE Trans. Antennas and Propagation, 2005, 53(11): 3741-3746.
[140] W. H. P. Pernice, F. P. Payne and D. F. G. Gallagher.An FDTD method for the simulation of dispersive metallic structures[J]. Optical and Quantum Electronics,2006, 38:843-856.
[141] Antonios Giannopoulos. An improved new implementation of complex frequency shifted PML for the FDTD method [J]. IEEE Trans. Antennas and Propagation, 2008, 56(9): 2995-3000.
[142] Omar Ramadan, Digital Filtering Technique for the FDTD Implementation of the Anisotropic Perfectly Matched Layer[J]. IEEE Microwave and Wireless Components Letters, 2003,13(8):340-342.
[143] Jiayuan Fang, Zhonghua Wu. Closed-Form Expression of Numerical Reflection Coefficient at PML Interfaces and Optimization of PML Performance[J]. IEEE Microwave and Guided Wave Letters, 1996, 6(9): 332-334.
[144] B. Chatry, M. Aubourg and P. Guillon. Perfectly matched layer: Variable discretisation against variable conductivity[J]. Electronics Letters. 1997, 33(4):277-278.
[145] Scott C. Winton and Carey M. Rappaport. Specifying PML Conductivities by Considering Numerical Reflection Dependencies[J]. IEEE Trans. Antennas and Propagation, 2000, 48(7): 1055-1063.
[146] Jaakko S. Juntunen, Nikolaos V. Kantartzis, Theodoros D. Tsiboukis. Zero Reflection Coefficient in Discretized PML[J]. IEEE Microwave and Wireless Components Letters, 2001, 11(4): 155-157.
[147] Sherwood W. Samn. Modeling Dispersive Dielectric Media in FDTD: A Systematic Approach[J]. IEEE Trans. Antennas and Propagation, 2005, 53(10): 3367-3373.
[148]邓巍巍,王越男. Visual Fortran编程指南[M].北京:人民邮电出版社,2000.
[149] Fernando L. Teixeira. Time-Domain Finite-Difference and Finite-Element Methods for Maxwell Equations in Complex Media[J]. IEEE Trans. Antennas and Propagation, 2008, 56(8): 2150-2166.
[150] Riaz Siushansian and Joe LoVetri. A Comparison of Numerical Techniques for Modeling Electromagnetic Dispersive Media[J]. IEEE Microwave and Guided WaveLetters , 1995, 5(12): 426-428.
[151]詹毅.复杂有耗色散地层FDTD方法及在冲击探地雷达中的应用[D].西安电子科技大学,2000.12
[152]姜彦南. FDTD并行算法及层状半空间散射问题研究[D].西安电子科技大学博士学位论文. 2009.
[153]闫玉波. FDTD在工程瞬态电磁学中的应用[D].西安电子科技大学博士学位论文. 2001年.
[154]魏兵.各向异性介质电磁散射及参数反演研究[D].西安电子科技大学博士学位论文. 2004年.
[155]朱湘琴. FDTD在半空间及周期结构问题中的应用[D].西安电子科技大学博士学位论文. 2005年.
[156]郑奎松. FDTD网络并行计算及ADI-FDTD方法研究[D].西安电子科技大学博士学位论文. 2006年.
[157]杨利霞.复杂介质电磁散射的FDTD算法及其相关技术研究[D].西安电子科技大学博士学位论文. 2007年.
[158]胡晓娟.复杂目标电磁散射的FDTD及FDFD算法研究[D].西安电子科技大学博士学位论文. 2008年.
© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号 地址：北京市海淀区学院路29号 邮编：100083 电话：办公室：(+86 10)66554848；文献借阅、咨询服务、科技查新：66554700 |