摘要
本论文研究介质体的时域散射和辐射问题。通过时域边界积分方程(BIE)和时间递推方法(MOT)求解这类问题,相对于时域有限差分法(FDTD),它在内存、计算时间、计算精度上都比较有优势,并且有新的快速算法发展空间。因此本文的研究都围绕这种方法展开。
本文首先从时变电磁场的对称形式的Maxwell方程组出发,基于等效原理和边界条件,推导了针对解决在无界自由空间中存在的均匀介质散射问题的基于等效电流源和等效磁流源的各种时域电磁场积分方程,包括时域电场积分方程(TD-EFIE)、时域磁场积分方程(TD-MFIE)和时域耦合积分方程(包含时域PMCHW耦合积分方程和时域Müller耦合积分方程)三种形式。这是本论文重要的理论基础。
论文研究了用时间递推方法求解时域Müller耦合积分方程。其过程涉及介质体的建模剖分和数据提取、算法实现过程中的一些数学推导、矩阵元素的求解、计算后参数的提取和处理等问题。论文推导了矩阵元素的求解计算公式,并用若干算例说明了所推导的公式的正确性,也说明了算法实现的正确性。在求解奇异积分时,提出了一种改进的求解MOT算法中奇异积分的方法。这种方法在原来对时间项参与计算的简化近似求解的基础上,提出了新的计算公式,提高了计算的精度。这种计算方法有利于分析电磁干扰等对精度敏感的问题。
论文研究了用Laguerre多项式作为时间基函数的MOT算法。推导了利用Laguerre多项式的伽略金求解过程,并提供了算例。对其中一些重要的计算步骤提供了优化算法。算法实现过程中在时间域做了伽略金内积,因而在计算过程中消除了MOT算法以前存在的晚时不稳定性。采用Laguerre多项式作为时间基函数时,计算过程中除了通常的对空间基函数的伽略金内积,还有对时间基函数的伽略金内积,这种方法将时间变量从计算过程中完全分离了出来。对于源的伽略金积分,对比各种方法,最后选用了Gauss-Laguerre求积方法。
采用MOT算法分析了终端渐变的圆柱形介质棒天线。给出了天线近区时域波形、天线方向图、以及天线结构参数变化时天线特性的变化。这比历来介质棒天线的近似分析要可靠的多。
论文最后研究了目前正在发展的时域平面波算法(PWTD),它是MOT算法的加速算法。本文推导了算法中的关键方程;完整地阐述了PWTD算法的思想和实现的聚集、转移和发散的三个过程;阐述了二层PWTD-MOT算法的实现思想,结合分析介质问题的时域耦合积分方程——Müller方程,从理论上分析了用PWTD加速MOT算法的实现。
The scattering and radiation of dielectric bodies in time domain are thoroughly studied in this paper. Compared with finite-difference time-domain (FDTD) method, when utilizing the boundary integral equation (BIE) and marching-on in-time (MOT) scheme to solve these questions, it has the advantage over computer memory, computer time and accuracy of results. Also, there is a new algorithm to enhance the speed of the marching-on in-time scheme. So the studies in this paper surround the MOT scheme.
Several integral equations of electromagnetic field in time domain, which express the scattering of homogeneous dielectric bodies in free space, are formulated in this paper using the equivalence electric currents and magnetic currents according to the symmetry Maxwell equations in time domain, the equivalence principle and boundary condition. These integral equations include the electric field integral equation in time domain, the magnetic field integral equation in time domain and the coupled integral equations in time domain ( the PMCHW equations and the Müller equations). These are the important bases in theory of this paper.
It’s researched how to resolve the Müller equations in time domain using the marching-on in-time scheme. The procedure includes the model building, data extraction, some mathematical formulations in realizing the algorithm, resolving the matrix elements, the parameter extraction and the post process after the simulation, etc. The formulations of the matrix elements are deduced in this paper. An improved method to resolving the singular integrals in the MOT scheme is presented, which gives the new formulations on the approximate resolving to the time parts in the normal method and can improve the accuracy of results. The new method is better to analyzing the sensitive questions on accuracy such as electromagnetic interference (EMI).
The MOT scheme is also studied based on the Laguerre polynomials as the temporal basis function in this paper. The procedure on Galerkin testing is deduced when using the Laguerre polynomials, and some examples are given. Some optimize method in the computation are supplied. When realizing the algorithm, the Galerkin testing is done in time domain, so the late-time instabilities existing previously are eliminated in the procedure. Based on the Laguerre polynomials as the temporal basis function, there has not only the Galerkin testing to the spatial basis function but also to the temporal basis function, therefore the time variable is separated from the space variable completely in this method. For the integral of Galerkin testing on the source, the Gauss-Laguerre method is chose after the comparing of several integral methods.
The dielectric rod antenna, which end changes gradually, is analyzed using the MOT scheme. The wave shapes in near space, radiation patterns and the antenna characteristic changed with the changeable structure parameter are given. The MOT method is more reliable than the approximate analytical method.
The plane-wave time-domain (PWTD) algorithm is researched, which can enhance the speed of the MOT method. We deduce the key formulation in PWTD algorithm, expatiate the idea and the three steps in the procedure of PWTD algorithm, formulate the idea of two-level PWTD enhanced MOT method and analyze how to resolve Müller coupled integral equation in time domain using PWTD enhanced MOT method in theory.
引文
[1] Rao S M. Time Domain Electromagnetics [M]. San Diego & San Francisco: Academic Press, 1999.
[2] Harrington R F. Time-Harmonic Electromagnetic Fields [M]. New York: John Wiley & Sons, 2001.
[3] Sengupta D L, Sarkar T K. Maxwell,Hertz,the Maxwellians,and the Early History of Electromagnetic Waves [J]. IEEE Antennas and Propagation Magazine, 2003, 45 (2): 14-19.
[4] 傅君眉, 冯恩信. 高等电磁理论 [M]. 西安: 西安交通大学出版社, 2000.
[5] 盛新庆. 计算电磁学要论 [M]. 北京: 科学出版社, 2004.
[6] 王秉中. 计算电磁学 [M]. 北京: 科学出版社, 2002.
[7] Akleman F, Sevgi L. A Novel Finite-Difference Time-Domain Wave Propagator [J]. IEEE Transactions on Antennas and Propagation, 2000, 48 (3): 839-841.
[8] Martin H C, Carey G F. Introduction to Finite Element Analysis: Theory and Application [M]. New York: McGraw Hill, 1973.
[9] Harrington R F. Filed Computation by Moment Method [M]. Marlabar: FL:Krieger, 1982.
[10] Rao S M, Sarkar T K. An Efficient Method to Evaluate the Time-Domain Scattering from Arbitrarily Shaped Conducting Bodies [J]. Microwave and Optical Technology Letters, 1998, 17 (5): 321-325.
[11] Harrington R F. Boundary Integral Formulations for Homogeneous Material Bodies [J]. Journal of Electromagnetic Waves and Application, 1989 (3): 1-15.
[12] 毛钧杰, 何建国. 电磁场理论 [M]. 长沙: 国防科技大学出版社, 1998.
[13] Zhao J-S, Chew W C. Integral Equation Solution of Maxwell's Equations from Zero Frequency to Microwave Frequencies [J]. IEEE Transactions on Antennas and Propagation, 2000, 48 (10): 1635-1645.
[14] Kangro U, Nicolaides R. Spurious Fields in Time-Domain Computations of Scattering Problems [J]. IEEE Trans. on Antennas and Propogation, 1997, 45 (2): 228-234.
[15] Bluck M J, Walker S P. Time-Domain BIE Analysis of Large Three Dimensional Electromagnetic Scattering Problems [J]. IEEE Transactions on Antennas and Propagation, 1997, 45: 894-901.
[16] Burghignoli P. Integral Representations of the Electromagnetic Field and Boundary Integral Equations [M]: "La Sapienza" University of Rome, 2003.
[17] Atle A. Numerical Approximations of Time Domain Boundary Integral Equation for Wave Propogation. Stockholm: Stochholm University, 2003.
[18] Jung B H, Sarkar T K, Ji Z, et al. A Stable of Time Domain Electric Field Integral Equation [A]. In: IEEE [C]: 2002. 178-181.
[19] Dodson S J, Walker S P, Bluck M J. Implicitness and Stability of Time Domain Integral Equation Scattering Analyses [M]: Imperial College of Science Technology and Medicine.
[20] Manara G, Monorchio A, Reggiannini R. A Space-Time Discretization Criterion for a Stable Time-Marching Solution of the Electric Field Integral Equation [J]. IEEE Transactions on Antennas and Propagation, 1997, 45 (3): 527-532.
[21] Antoine X, Bendali A, Darbas M. Analytic Preconditioners for the Electric Field Integral Equation [J]. International Journal for Numerical Methods in Engineering, 2004, 61: 1310-1331.
[22] Chen Q, Lu M, Michielssen E. Integral-Equation-Based Analysis of Transient Scattering from Surfaces with an Impedance Boundary Condition [J]. Microwave and Optical Technology Letters, 2004, 42 (3): 213-20.
[23] Zhao Y-W, Nie z-P, Xu J-H, et al. Stable and Accurate Solution of Time-Domain Electric Field Integral Equation [A]. In: The 3th International conference on computational electromagnetic and its applications proceedings [C]: 2004
[24] Weile D S, Shanker B, Michielssen E. An Accurate Scheme for the Numerical Solution of the Time Domain Electric Field Integral Equation, 2001.
[25] Kobidze G, Gao J, Shanker B. A Fast Time Domain Integral Equation Based Scheme for Analyzing Scattering from Dispersive Objects [J]. IEEE Transactions on Antennas and Propagation, 2005, 53 (3): 1215-26.
[26] Kobidze G, Shanker B, Michielssen E. A Fast Time Domain Integral Equation Based Scheme for Analyzing Scattering from Dispersive Objects [A]. In: IEEE Antennas and Propagation Society International Symposium (IEEE Cat. No.02CH37313) [C]: 2002. 164-7.
[27] Jung B H, Sarkar T K. Time-Domain CFIE for the Analysis of Transient Scattering from Arbitrarily Shaped 3D Conducting Objects [J]. Microwave and Optical Technology Letters, 2002, 34 (4): 289-296.
[28] Chen N-W, Shanker B, Michielssen E. Integral-Equation-Based Analysis of Transient Scattering from Periodic Perfectly Conducting Structures [M], 2003.
[29] Jung B H, Sarkar T K. Analysis of Scattering from Arbitrarily Shaped 3-D Conducting Dielectric Composite Objects Using a Combined Field Integral Equation [J]. Journal of Electromagnetic Wave and Applications, 2004, 18 (6): 729-743.
[30] Rao S M, Sarkar T K. Numerical Solution of Time Domain Integral Equations for Arbitrarily Shaped Conductor Dielectric Composite Bodies [J]. IEEE Transactions on Antennas and Propagation, 2002, 50 (12): 1831-1837.
[31] Nie X-C, Li L-W, Yuan N, et al. Precorrected-FFT Solution of the Volume Integral Equation for 3-D Inhomogeneous Dielectric Objects [J]. IEEE Transactions on Antennas and Propagation, 2005, 53 (1): 313-320.
[32] Wang J, Fan R. Two-Dimensional Time-Domain Volume Integral Equations for Scattering of Inhomogeneous Objects [J]. Radio Science, 2003, 38 (4): 9-1-12.
[33] Tsang L, Ong C J, H C C, et al. Evaluation of the Green's Function for the Mixed Potential Integral Equation (MPIE) Method in the Time Domain for Layered Media [J]. IEEE Transactions on Antennas and Propagation, 2003, 51 (7): 1559-1571.
[34] Jung B H, Sarkar T K, Chung Y-S, et al. An Accurate and Stable Implicit Solution for Transient Scattering and Radiation from Wire Structures [J]. Microwave and Optical Technology Letters, 2002, 34 (5): 354-359.
[35] Poljak D. Time Domain Integral Equation Method for Transient Scattering from Thin Wire Structures [J]. Engineering Analysis with Boundary Elements, 2003, 27 (4): 283-90.
[36] Aygun K, Fisher S E, Ergin A A, et al. Transient Analysis of Multielement Wire Antennas Mounted on Arbitrarily Shaped Perfectly Conducting Bodied [J]. Radio Science, 1999, 34 (4): 781-796.
[37] Shlivinski A, Heyman E, Kastner R. Antenna Characterization in the Time Domain [J]. IEEE Transactions on Antennas and Propagation, 1997, 45: 1140-1149.
[38] Lee K H, Venkatarayalu N V, Chen C C. Numerical Modeling Development for Characterizing Complex GPR Problems [A]. In: The 9th International Conference on Ground Penetrating Radar [C]: 2002. 652-656.
[39] Mieras H, Bennet C L. Space-Time Integral Equation Approach to Dielectric Targets [J]. IEEE Transactions on Antennas and Propagation, 1982 (AP-30): 2-9.
[40] Marx E. Integral Equation for Scattering by a Dielectric [J]. IEEE Transactions on Antennas and Propagation, 1984, 32 (2): 166-172.
[41] Jung B H, Sarkar T K, Chung Y-S. A Survey of Various Frequency Domain Integral Equations for the Analysis of Scattering from Three-Dimensional Dielectric Objects [J]. Progress In Electromagnetic Research, 2002, 36: 193-246.
[42] Rao S M, Wilton D R, Glisson A W. Electromagnetic Scattering by Surfaces of Arbitrary Shape [J]. IEEE Transactions on Antennas and Propagation, 1982, 30 (3): 409-418.
[43] Rao S M, Wilton D R. Transient Scattering by Conducting Surfaces of Arbitrary Shape [J]. IEEE Transactions on Antennas and Propagation, 1991, 39 (1): 56-61.
[44] Cha C C, Wilkers D, Lane M. Method of Moments Formulation for an Arbitrary Material Configuration, 1991: 1508-1511.
[45] Electromagnetic Scattering by Three-Dimensional Arbitrary Complex Material Conducting Bodies, 1990: 590-593.
[46] Moheb H, Shafai L. Numerical Solution of Scattering from Homogeneous Material Bodies of Arbitrary Cross-Section a New Approach [A]. In: IEEE [C]: 1990. 598-601.
[47] Gradshteyn I S, Ryzhik I M. Table of Integrals, Series, and Products [M]. New York: Academic, 1980.
[48] Taaghol A, Sarkar T K. Near-Field to near Far-Field Transformation for Arbitrary Near-Field Geometry Utilizing an Equivalent Magnetic Current [J]. IEEETransactions on Electromagnetic Compatibility, 1996, 38 (3): 536-542.
[49] Vechinski D A, Rao S M. A Stable Procedure to Calculate the Transient Scattering by Conducting Surfaces of Arbitrary Shape [J]. IEEE Transactions on Antennas and Propagation, 1992, 40: 661-665.
[50] Jung B H, Sarkar T K. Time-Domain Electric-Field Integral Equation with Central Finite Difference [J]. Microwave and Optical Technology Letters, 2001, 31 (6): 429-435.
[51] Jung B H, Sarkar T K. Corrections to "Time-Domain Electric-Field Integral Equation with Central Finite Difference" [J]. Microwave and Optical Technology Letters, 2002, 33 (2): 148.
[52] Rynne B P, Smith P D. Stability of Time Marching Algorithms for the Electric Field Integral Equations [J]. Journal of Electromagnetic Waves and Application, 1990, 12: 1181-1205.
[53] Caorsi S, Moreno D, Sidoti F. Theoretical and Numerical Treatment of Surface Integrals Involving the Free-Space Green's Function [J]. IEEE Transactions on Antennas and Propagation, 1993, 41 (9): 1296-1301.
[54] Caorsi S, Moreno D, Sidoti F. Theoretical and Numerical Treatment of Surface Integrals Involving the Free-Space Green's Function [J]. IEEE Trans. on Antennas and Propagation, 1993, 41 (9): 1296-1301.
[55] Davies P J. On the Stability of Time-Marching Schemes for the General Surface Electric-Field Integral Equation [J]. IEEE Transactions on Antennas and propagation, 1996, 44 (11): 1467-1473.
[56] Davies P J. A Stability Analysis of a Time Marching Scheme for the General Surface Electric Field Integral Equation [J]. Applied Numerical Mathematics, 1998, 27: 35-57.
[57] Hu J L, Chan C H. Improved Temporal Basis Function for Time Domain Electric Field Integral Equation Method [J]. Electronics Letters, 1999, 35 (11): 883-885.
[58] Hu J L, Chan C H, Xu Y. A New Temporal Basis Function for the Time-Domain Integral Equation Method [J]. IEEE Microwave and Wireless Components Letters, 2001, 11 (11): 465-466.
[59] Hu J L, Chan C H. Novel Approach to Construct Temporal Basis Functions for Time-Domain Integral Equation Method [A]. In: IEEE [C]: 2001. 172-175.
[60] Rius J M, Ubeda E, Parron J. On the Testing of the Magnetic Field Integral Equation with RWG Basis Functions in Method of Moments [J]. IEEE Transactions on Antennas and Propagation, 2001, 49 (11): 1550-1553.
[61] Cai W, Yu T J, Wang H, et al. High-Order Mixed RWG Basis Functions for Electromagnetic Applications [J]. IEEE Transactions on Antennas and Propagation, 2001, 49 (7): 1295-1303.
[62] Peterson A F, Kempel L C. Solution of the MFIE Using Curl-Conforming Basis Functions [J]. IEEE, 2002: 70-73.
[63] Ergul O, Gurel L. Improving the Accuracy of the MFIE with the Choice of Basis Functions [A]. In: IEEE [C]: 2004. 3389-3392.
[64] Jung B H, Sarkar T K. Transient Scattering from Three-Dimensional Conducting Bodied by Using Magnetic Field Integral Field Integral Equation [J]. Journal of Electromagnetic Waves and Application, 2002, 16 (1): 111-128.
[65] Ergul O, Gurel L. Investigation of the Inaccuracy of the MFIE Discretized with the RWG Basis Functions [A]. In: IEEE [C]: 2004. 3393-3396.
[66] Hodges R E, Rahmat-Samii Y. The Evaluation of MFIE Integrals with the Use of Vector Triangle Basis Functions [J]. Microwave and Optical Technology Letters, 1997, 14 (1): 9-14.
[67] Yl?-Oijala P, Taskinen M. Calculation of CFIE Impedance Matrix Elements with RWG and n×RWG Functions [J]. IEEE Transactions on Antennas and Propagation, 2003, 51: 1183-1846.
[68] Shanker B, Ergin A A, Aygün K, et al. Analysis of Transient Electromagnetic Scattering from Closed Surfaces Using a Combined Field Integral Equation [J]. IEEE Transactions on Antennas and Propagation, 2000, 48 (7): 1064-1074.
[69] Mautz J R. A Stable Integral Equation for Electromagnetic Scattering from Homogeneous Dielectric Bodies [J]. IEEE Transactions on Antennas and Propagation, 1989, 37 (8): 1070-1071.
[70] Vechinski D A, Rao S M. Transient Scattering from Dielectric Cylinders: E-Field, H-Field, and Combined Field Solutions [J]. Radio Science, 1992, 27 (5): 611-622.
[71] Vechinski D A, Rao S M. Transient Scattering from Two-Dimensional Dielectric Cylinders of Arbitrary Shape [J]. IEEE Transactions on Antennas and Propagation, 1992, 40 (9): 1054-1060.
[72] Schlemmer E, Rucker W M, Richter K R. A Marching-on-in-Time Method for 2-D Transient Electromagnetic Scattering from Homogeneous, Lossy Dielectric Cylinders Using Boundary Elements [J]. IEEE Transactions on Magnetic, 1991, 27 (5): 3856-3859.
[73] Jakobus U, Landstorfer F M. Novel Basis Function for the Equivalent Magnetic Current in the Method of Moments Solution of Dielectric Scattering Problems [J]. Electronics Letters, 1993, 29 (14): 1272-1273.
[74] Vechinski D A, Rao S M, Sarker T K. Transient Scattering from Three-Dimensional Arbitrarily Shaped Dielectric Bodies [J]. Journal of the Optical Society of America A, 1994 (11): 1458-1470.
[75] Rynne B P. Time Domain Scattering from Dielectric Bodies [J]. Electromagnetics, 1994, 14: 181-193.
[76] Pocock M D, Bluck M J, Walker S P. Electromagnetic Scattering from 3-D Curved Dielectric Bodies Using Time-Domain Integral Equations [J]. IEEE Transactions on Antennas and Propagation, 1998, 46 (8): 1212-1219.
[77] Bagci H, Yilmaz A E, Lomakin V. Fast and Accurate Solution of Time DomainElectric Field Integral Equation for Dielectric Half-Space [A]. In: IEEE Antennas and Propagation Society International Symposium. Digest. [C]: 2003. 583-6.
[78] Nie X C, Li L W, Yuan N, et al. A Fast Analysis of Electromagnetic Scattering by Arbitrarily Shaped Homogeneous Dielectric Objects [J]. Microwave and Optical Technology Letters, 2003, 38 (1): 30-35.
[79] Rao S M, Sarkar T K. Implicit Solution of Time-Domain Integral Equations for Arbitrarily Shaped Dielectric Bodies [J]. Microwave and Optical Technology Letters, 1999, 21 (3): 201-205.
[80] Jung B H, Sarkar T K, Chung Y-S. Solution of Time Domain PMCHW Formulation for Transient Electromagnetic Scattering from Arbitrarily Shaped 3-D Dielectric Objects [J]. Progress In Electromagnetics Research, 2004, PIER 45: 291-312.
[81] Jung B H, Sarkar T K, Salazar-Palma M. Time Domain EFIE and MFIE Formulations for Analysis of Transient Electromagnetic Scattering from 3-D Dielectric Objects [J]. Progress In Electromagnetics Research, 2004, 49: 113-142.
[82] Chung Y-S, Sarkar T K, Jung B H. Solution of Time Domain Electric Field Integral Equation for Arbitrarily Shaped Dielectric Bodies Using an Unconditionally Stable Methodology [J]. Radio Science, 2003, 38 (3).
[83] Coves A, Gimeno B, Blas A A S, et al. Three-Dimensional Scattering of Dielectric Gratings under Plane-Wave Excitation [J]. IEEE Antennas and Wireless Propagation Letters, 2003, 2: 215-218.
[84] Chung Y-S, Sarkar T K, Jung B H. Solution of a Time-Domain Magnetic-Field Integral Equation for Arbitrarily Closed Conducting Bodies Using an Unconditionally Stable Methodology [J]. Microwave and Optical Technology Letters, 2002, 35 (6): 493-499.
[85] Shin J, Glisson A W, Kishk A A. Analysis of Combined Conducting and Dielectric Structures of Arbitrary Shapes Using an E-PMCHW Integral Equation Formulation [M]: University of Mississippi, 2000.
[86] Li J-Y, Li L-W. Electromagnetic Scattering by a Mixture of Conducting and Dielectric Objects Analysis Using Method of Moments [J]. IEEE Transactions on Antennas and Propagation, 2004, 53 (2): 514-520.
[87] Nikoskinen K I. Time-Domain Study of Half-Space Transmission Problem with Vertical and Horizontal Dipoles [J]. IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, 1993, 41 (10): 1399-1407.
[88] R.W.Freund. A Transpose-Free Quasi-Minimal Residual Algorithm for Non-Hermitian Linear Systems [J]. SIAM (Soc.Ind.Appl.Math.) Journal of Scientific Computing, 1993, 14: 470-482.
[89] Umashankar K, Taflove A, Rao S M. Electromagnetic Scattering by Arbitrary Shaped Three-Dimensional Homogeneous Lossy Dielectric Objects [J]. IEEE Transactions on Antennas and Propagation, 1986, AP-34 (6): 758-766.
[90] Shanker B, Aygun K, Michielssen E. Fast Analysis of Transient Scattering from Lossy Inhomogeneous Dielectric Bodies [J]. Radio Science, 2004, 39 (2).
[91] Panteleev A A, Roerich V K, Starostin A N. Transient Scattering of Resonance Radiation in a Two-Level System [J]. Journal of Experimental and Theoretical Physics, 2003 (2): 222-40255-75.
[92] Yilmaz A E, Weile D S, Shanker B. Fast Analysis of Transient Scattering in Lossy Media [J]. IEEE Antennas and Wireless Propagation Letters, 2002, 1 (1): 14-17.
[93] Graglla R D. The Use of Parametric Elements in the Moment Method Solution of Static and Dynamic Volume Integral Equations [J]. IEEE Transaction on Antennas and Propagation, 1988, 36 (5): 636-646.
[94] Schaubert D H, Wilton D R, Glisson A W. A Tetrahedral Modeling Method for Electromagnetic Scattering by Arbitrarily Shaped Inhomogeneous Dielectric Bodies [J]. IEEE Transactions on Antennas and Propagation, 1984, 32 (1): 77-85.
[95] Shanker B, Aygün K, Gres N, et al. Fast Integral Equation Based Analysis of Transient Electromagnetic Scattering from Three-Dimensional Inhomogeneous Lossy Dielectric Objects, 2001: 532-535.
[96] Gres N T, Ergin A A, Michielssen E. Volume-Integral-Equation-Based Analysis of Transient Electromagnetic Scattering from Three-Dimensional Inhomogeneous Dielectric Objects [J]. Radio Science, 2001, 36 (3): 379-386.
[97] Wang J, Lu M, Michielssen E. Volume Integral Equation Based Method for Transient Scattering from Nonlinear Penetrable Objects-TM Case [A]. In: IEEE Antennas and Propagation Society International Symposium (Cat. No.00CH37118) [C]: 2000. 729-32.
[98] Gres N T, Shanker B, Ergin A A, et al. Fast Transient Analysis of Electromagnetic Scattering from Three Dimensional Dielectric Inhomogeneities Using a Volume Integral Equation [M], 2000.
[99] Rubin B J. General Solution for Propagation, Radiation and Scattering in Arbitrary 3D Inhomogeneous Structures [J]. IEEE Antennas and Propagation Magazine, 1992, 34 (1): 17-25.
[100] Schaubert D H, Meaney P M. Efficient Computation of Scattering by Inhomogeneous Dielectric Bodies [J]. IEEE Transactions on Antennas and Propagation, 1986, AP-43 (4): 587-592.
[101] Damaskos N J, Brown R T, Jameson J R, et al. Transient Scattering by Resistive Cylinders [J]. IEEE Transactions on Antennas and Propagation, 1985, AP-33 (1): 21-25.
[102] Kishk A A, Shafai L. Different Formulations for Numerical Solution of Single or Multibodies of Revolution with Mixed Boundary Conditions [J]. IEEE Transactions on Antennas and Propagation, 1986, 34 (5): 666-673.
[103] Alleon G, Benzi M, Giraud L. Sparse Approximate Inverse Preconditioning for Dense Linear Systems Arising in Computational Electromagnetics [J]. Numerical Algorithm, 1997, 16: 1-15.
[104] Wilton D R, Rao S M, Glisson A W, et al. Potential Integrals for Uniform and Linear Source Distributions on Polygonal and Polyhedral Domains [J]. IEEE Transactionson Antennas and Propagation, 1984, AP-32 (3): 276-281.
[105] Sunder K S, Cookson R A. Integration Points for Triangles and Tetrahedrons Obtained from the Gaussian Quadrature Points for a Line [J]. Comput.Struct., 1985, 21 (5): 881-885.
[106] Eibert T F, Hansen V. On the Calculation of Potential Integrals for Linear Source Distributions on Triangular Domains [J]. IEEE Transactions on Antennas and Propagation, 1995, 43 (12): 1499-1502.
[107] Doncker P D. A Potential Integral Equations Method for Electromagnetic Scattering by Penetrable Bodies [J]. IEEE Transactions on Antennas and Propagation, 2001, 49 (7): 1037-1042.
[108] Nevels R D, Miller J A, Miller R E. A Path Integral Time-Domain Method for Electromagnetic Scattering [J]. IEEE Transactions on Antennas and Propagation, 2000, 48 (4): 565-573.
[109] Yeung M S. Single Integral Equation for Electromagnetic Scattering by Three-Dimensional Homogeneous Dielectric Objects [J]. IEEE Transactions on Antennas and Propagation, 1999, 47 (10): 1615-1622.
[110] 徐利明. 分层介质中三维目标电磁散射的积分方程方法及其关键技术 [D].博士学位论文. 成都: 电子科技大学, 2005.
[111] 魏丹丹, 徐晓文. 任意形体金属目标电磁散射计算中奇异积分处理的新方法 [J]. 北京理工大学学报, 2002, 22 (6): 739-742.
[112] Graglia R D. Static and Dynamic Potential Integrals for Linearly Varying Source Distributions in Two- and Three-Dimensional Problems [J]. IEEE Transaction on Antennas and Propagation, 1987, AP-35 (6): 662-669.
[113] Marx E. Alternative Single Integral Equation for Scattering by a Dielectric [M].
[114] Rynne B P. Stability and Convergence of Time Marching Methods in Scattering Problems [J]. Int. J. Appl. Math, 1985, 35: 297-310.
[115] Bluck M J, Pocock M D, Walker S P. An Accurate Method for the Calculation of Singular Integrals Arising in Time-Domain Integral Equation Analysis of Electromagnetic Scattering [J]. IEEE Transactions on Antennas and Propagation, 1997, 45 (12): 1793-1798.
[116] Graglia R D. On the Numerical Integration of the Linear Shape Functions Times the 3-D Green's Function or Its Gradient on a Plane Triangle [J]. IEEE Transactions on Antennas and Propagation, 1993, 41 (10): 1448-1455.
[117] Cai W, Yu Y, Yuan X C. Singularity Treatment and High-Order RWG Basis Functions for Integral Equations of Electromagnetic Scattering [J]. International Journal for Numerical Methods in Engineering, 2002, 53: 31-47.
[118] Yeung M S. Solution of Electromagnetic Scattering Problems Involving Three-Dimensional Homogeneous Dielectric Objects by the Single Integral Equation Method [J]. Journal of Scientific Computing, 2002, 15 (1): 1-17.
[119] Gürel L, Ergül ?. Singularity of the Magnetic-Field Integral Equation and ItsExtraction [J]. IEEE Antennas Wireless Propagation Letters, 2005, 4: 229-232.
[120] 数学手册编写组. 数学手册 [M]. 北京: 高等教育出版社, 1979.
[121] 郭大钧主编. 大学数学手册 [M]. 济南: 山东科学技术出版社, 1985.
[122] 清华大学应用数学系《现代应用数学手册》编委会. 现代应用数学手册计算方法分册 [M]. 北京: 北京出版社, 1990.
[123] 米特拉. 计算机技术在电磁学中的应用 [M]: 人民邮电出版社, 1983.
[124] Sarkar T K, Koh J. Generation of Wideband Electromagnetic Response through a Laguerre Expansion Using Early Time and Low Frequency Data [A]. In: IEEE MTT-S Digest [C]: 2002. 1989-1992.
[125] Sarkar T K, Koh J. Generation of a Wide-Band Electromagnetic Response through a Laguerre Expansion Using Early-Time and Low-Frequency Data [J]. IEEE Transactions on Microwave Theory and Techniques, 2002, 50 (5): 1408-1416.
[126] Chung Y-S, Sarkar T K, Llorento-Romano S, et al. Finite Element Time Domain Method Using Laguerre Polynomials [A]. In: IEEE MTT-S Digest [C]: 2003. 981-984.
[127] Jung B H, Chung Y-S, Sarkar T K. Time-Domain EFIE, MFIE, and CFIE Formulations Using Laguerre Polynomials as Temporal Basis Functions for the Analysis of Transient Scattering from Arbitrary Shaped Conducting Structures [J]. Progress In Electromagnetics Research, 2003, 39: 1-45.
[128] Jung B H, Chung Y-S, Yuan M. Analysis of Transient Scattering from Conductors Using Laguerre Polynomials as Temporal Basis Functions [J]. Applied Computational Electromagnetics Society Journal, 2004, 19 (2): 84-92.
[129] Chung Y-S, Sarkar T K, Jung B H, et al. Solution of Time Domain Electric Field Integral Equation Using the Laguerre Polynomials [J]. IEEE Transactions on Antennas and Propagation, 2004, 52 (9): 2319-2328.
[130] Ji Z, Sarkar T K, Jung B H, et al. A Stable Solution of Time Domain Electric Field Integral Equation for Thin-Wire Antennas Using the Laguerre Polynomials [J]. IEEE Transactions on Antennas and Propagation, 2004, 52 (10): 2641-2649.
[131] Jung B H, Sarkar T K, Chung Y-S, et al. Transient Electromagnetic Scattering from Dielectric Objects Using the Electric Field Integral Equation with Laguerre Polynomials as Temporal Basis Functions [J]. IEEE Transactions on Antennas and Propagation, 2004, 52 (9): 2329-2340.
[132] Yuan M, Sarkar T K, Jung B H, et al. Use of Discrete Laguerre Sequences to Extrapolate Wide-Band Response from Early-Time and Low-Frequency Data [J]. IEEE Transactions on Microwave Theory and Techniques, 2004, 52 (7): 1740-1750.
[133] 黎滨洪. 表面电磁波和介质波导 [M]. 上海: 上海交通大学出版社, 1990.
[134] 刘克成, 宋学诚. 天线原理 [M]. 长沙: 国防科技大学出版社, 1989.
[135] [苏]F.3.爱金堡, 汪茂光译. 超高频天线(上) [M]. 北京: 人民邮电出版社, 1981.
[136] [苏]F.3.爱金堡, 汪茂光译. 超高频天线(下) [M]. 北京: 人民邮电出版社, 1981.
[137] 周蔚红. 时域天线在无载波脉冲探地雷达中的理论及应用研究 [D].博士. 长沙:国防科学技术大学, 2006.
[138] 叶红霞. 超宽带介质天线设计和机载雷达信号模拟 [D].硕士学位论文. 西安: 西安交通大学, 2003.
[139] 姚海英. 介质以及涂敷介质结构电磁散射特性的基础研究-积分方程法及其快速求解 [D].博士学位论文. 成都: 电子科技大学, 2002.
[140] 叶红霞, 蒋延生, 汪文秉, et al. 介质杆天线的时域特性分析 [J]. 电波科学学报, 2003, 18 (4): 413-417.
[141] 尹家贤. 时域有限差分法在天线计算中的理论和应用 [D].博士. 长沙: 国防科学技术大学, 2003.
[142] 王长清, 祝西里. 电磁场计算中的时域有限差分法 [M]. 北京: 北京大学出版社, 1994.
[143] Chen C C, Rao K R, Lee R. A New Ultrawide-Bandwidth Dielectric-Rod Antenna for Ground-Penetrating Radar Applications [J]. IEEE Transactions on Antennas and Propagation, 2003, 51 (3): 371-377.
[144] Devaney A J, Sherman G C. Plane-Wave Representations for Scalar Wave Fields [J]. SIAM Review, 1973, 15 (4): 765-786.
[145] Devaney A J, Wolf E. Multipole Expansions and Plane Wave Representations of the Electromagnetic Field [J]. Journal of Mathematical Physics, 1974, 15 (2): 234-244.
[146] Heyman E. Time-Dependent Plane-Wave Spectrum Representations for Radiation from Volume Source Distributions [J]. Journal of Mathematical Physics, 1996, 37 (2): 658-681.
[147] Marengo E A, Devaney A J. Time-Dependent Plane Wave and Multipole Expansions of the Electromagnetic Field [M]. 1998.
[148] Marengo E A, Devaney A J. Time-Dependent Plane Wave and Multipole Expansions of the Electromagnetic Field [J]. Journal of Mathematical Physics, 1998, 39 (7): 3643-3660.
[149] Hansen T B, Yaghjian A D. Plane-Wave Theory of Time-Domain Fields Near-Field Scattering Applications [M]. New York: IEEE Press, 1999.
[150] Ergin A A, Shanker B, Michielssen E. The Plane-Wave Time-Domain Algorithm for the Fast Analysis of Transient Wave Phenomena [J]. IEEE Antennas and Propagation Magazine, 1999, 41 (4): 39-52.
[151] Shanker B, Ergin A A, Aygün K, et al. Analysis of Transient Electromagnetic Scattering Phenomena Using a Two-Level Plane Wave Time-Domain Algorithm [J]. IEEE Transactions on Antennas and Propagation, 2000, 48 (4): 510-523.
[152] Aygün K, Shanker B, Ergin A A, et al. A Two-Level Plane Wave Time-Domain Algorithm for Fast Analysis of EMC/EMI Problems [J]. IEEE Transactions on Antennas and Propagation, 2002, 44 (1): 152-154.
[153] Shanker B, Ergin A A, Michielssen E. Plane-Wave-Time-Domain-Enhanced Marching-on-in-Time Scheme for Analyzing Scattering from Homogeneous Dielectric Structures [J]. Journal of Optical Society of America A, 2002, 19 (4):716-726.
[154] Shanker B, Ergin A A, Michielssen E. The Multilevel Plane Wave Time Domain Algorithm for the Fast Analysis of Transient Scattering Phenomena [M]: IEEE, 1999.
[155] Shanker B, Ergin A A, Lu M Y, et al. Fast Analysis of Transient Electromagnetic Scattering Phenomena Using the Multilevel Plane Wave Time Domain Algorithm [J]. IEEE Transactions on Antennas and Propagation, 2003, 51 (3): 628-641.
[156] Lu M, Wang J, Ergin A A, et al. A Diagonal Translation Operator for the Fast Evaluation of Two-Dimensional Transient Wave Fields [A]. In: IEEE [C]: 1999. 1338-1341.
[157] Michielssen E, Ergin A A, Shanker B. Diagonal Translation Operators for Transient Wave Fields [M]: IEEE, 1998.
[158] Ergin A A, Shanker B, Michielssen E. Fast Evaluation of Three-Dimensional Transient Wave Fields Using Diagonal Translation Operators [J]. Journal of Computational Physics, 1998, 146: 157-180.
[159] Lu M, Sarvas J, Michielssen E. A Simplified 3D Plane Wave Time Domain (PWTD) Algorithm [A]. In: Proc. IEEE Antennas Propagat. Soc. International Symposium [C]: 2001. 188-191.
[160] Lu M, Wang J, Ergin A A, et al. Fast Evaluation of Two-Dimensional Transient Wave Fields [J]. Journal of Computational Physics, 2000, 158: 161-185.
[161] Lu M, Shanker B, Ergin A A, et al. Novel 2D Transient EFIE, MFIE, and CFIE Solvers Based on the Multilevel Plane Wave Time Domain Algorithm, 2000: 737-740.
[162] Lu M, Wang J, Ergin A A, et al. A Diagonal Translating Operator for the Fast Evaluation of Two-Dimensional Transient Wave Fields [M].
[163] Lu M, Yegin K, Michielssen E. Fast Time Domain Integral Equation Solvers for Analyzing Two-Dimensional Scattering Phenomena; Part I Temporal Acceleration [J]. Electromagnetics, 2004, 24 (6): 425-449.
[164] Lu M, Michielssen E. Fast Time Domain Integral Equation Solvers for Analyzing Two-Dimensional Scattering Phenomena; Part Ii Full PWTD Acceleration [J]. Electromagnetics, 2004, 24 (6): 451-470.
[165] Ergin A A, Shanker B, Aygün K, et al. Computational Complexity and Implementation of Two-Level Plane Wave Time Domain Algorithm for Scalar Wave Equation [M].
[166] Knab J J. Interpolation of Band-Limited Functions Using the Approximate Prolate Series [J]. IEEE Transactions on Information Theory, 1979, 25: 717-720.
[167] Bucci O M, Franceschetti G. On the Spatial Bandwidth of Scattering Fields [J]. IEEE Transactions on Antennas and Propagation, 1987, 35 (12): 1445-1455.
[168] Bucci O M, Gennarelli C, Savarese C. Optimal Interpolation of Radiated Fields over a Sphere [J]. IEEE Transactions on Antennas and Propagation, 1991, 39: 1633-1643.
[169] Fast Numerical Techniques for Electromagnetic Problems in Frequency Domain.
[170] R.Coifman V R a S W. The Fast Multipole Method for the Wave Equation: A Pedestrian Prescription [J]. IEEE Antennas Propagation Magazine, 1993, 35 (3): 7-12.
[171] Darve E. The Fast Multipole Method: Numerical Implementation [J]. Journal of Computational Physics, 2000, 160: 195-240.
[172] Nilsson M. Fast Numerical Techniques for Electromagnetic Problems in Frequency Domain [M]. 2003.
[173] Li J-Y, Li L-W. Characterizing Scattering by 3-D Arbitrarily Shaped Homogeneous Dielectric Objects Using Fast Multipole Method [J]. IEEE Antennas and Wireless Propagation Letters, 2004, 3: 1-4.
[174] Hariharan B, Alurn S, Shanker B. A Scalable Parallel Fast Multipole Method for Analysis of Scattering from Perfect Electrically Conducting Surfaces, 2002.
[175] 董健. 边界积分方程及快速算法在分析复杂电磁问题中的研究与应用 [D].博士学位论文. 长沙: 国防科学技术大学, 2005.
[176] Li J-Y, Oo Z-Z, Li L-W. Solution of Scattering from Homogeneous Dielectric Object Using Fast Multipole Method [A]. In: The 3th International Conference on Microwave and Millimeter Wave Technology Proceedings [C]: 2002. 424-427.
[177] Michielssen E, Chew W C, Jin J M, et al. Fast Time Domain Integral Equation Solvers for Large-Scale Electromagnetic Analysis [M]. 2005.
[178] Shanker B, Ergin A A, Aygün K, et al. Computation of Transient Scattering from Electrically Large Structures Using the Plane Wave Time Domain Algorithm [M]: IEEE, 1998.
[179] Liu N, Lu M, Shanker B. The Parallel Plane Wave Time Domain Algorithm-Accelerated Marching on in Time Solvers for Large-Scale Electromagnetic Scattering Problems [A]. In: IEEE Antennas and Propagation Society Symposium (IEEE Cat. No.04CH37529) [C]: 2004. 4212-15.
[180] Ergin A A, Shanker B, Michielssen E. Accuracy and Efficiency of PWTD Enhanced Exact Radiation Boundary Conditions in FDTD Simulations [A]. In: IEEE [C]: 2000. 1354-1357.
[181] Kobidze G, Shanker B, Michielssen E. Hybrid PO-PWTD Scheme for Analysis of Scattering from Electrically Large PEC Objects [A]. In: IEEE [C]: 2003.
[182] Aygun K, Lu M, Shanker B, et al. Analysis of PCB Level EMI Phenomena Using an Adaptive Low_Frequency Plane Wave Time Domain Algorithm [A]. In: IEEE [C]: 2000. 295-300.
[183] Edelvik F, Ledfelt G. A Comparison of Time-Domain Hybrid Solvers for Complex Scattering Problems [J]. International Journal OF Numerical Modelling: Electronic Networks, Devices And Fields, 2002: 475-487.
[184] Rao S M. Electromagnetic Scattering and Radiation of Arbitrarily-Shaped Surface by Triangle Patch Modeling[D]. PH.D. Dissertation Univ. Mississippi, 1980.
[185] Eleftheriades G V, Mosig J R. On the Network Characterization of Planar PassiveCircuits Using the Method of Moments [J]. IEEE Transactions on Microwave Theory and Techniques, 1996, 44(3): 438-445.
[186] Abdulla M N, Steer M B. Extraction of Network Parameters in the Electromagnetic Analysis of Planar Structures Using the Method of Moments [J]. IEEE Transactions on Microwave Theory and Techniques, 2001, 49(1): 94-103.
[187] Debnath L. Integral Transforms and Their Applications [M]. Boca Raton, FL:CRC,1995.
[188] Mueller G E, Tyrrel W A. Polyrod Antennas [J]. Bell System Technical Journal, 1947, 26:837-851.
[189] Watson R B, Horton C W. The Radiation Patterns of Dielectric Rods-Experiment and Theory [J]. Journal of Application Physics, 1948, 19: 661-670.
[190] Brown J, Spector J O. The Radiating Properties of End-Fire Aerials. Proc.Inst.Elec.Eng, London, 1957,104: 27-34.
[191] Yaghjian A D, Kornhauser E T. A Model Analysis of the Dielectric Rod Antenna Excited by the HE11 Mode [J]. IEEE Transactions on Antennas and Propagation, 1972, 20: 122-128.
[192] Blakey J R. A Scattering Theory Approach to the Prediction of Dielectric Rod Antenna Radiation Patterns: The TM01 Mode [J]. IEEE Transactions on Antennas and Propagation, 1975, 23: 577-579.
[193] Ergin A A. Plane-Wave Time-Domain Algorithms for Efficient Analysis of Three-Dimensional Transient Wave Phenomena [D]. PH.D. Dissertation Univ. Illinois, 2000.
[194] Friedman M B, Shaw R. Diffraction of Pulses by Cylindrical Obstacles of Arbitrary Cross Section [J]. J.Appl.Mech, 1962, 29: 40-46.
[195] Müller C. Foundations of the Mathematical Theory of Electromagnetic Waves [M]. Springer-Verlag, Berlin, 1969.