二维混合目标散射问题的快速计算及其RCS减缩
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摘要
翼面是飞行器后向雷达散射截面(RCS)的重要来源之一,为了缩减其散射截面,需要对翼面的模型的散射问题进行有效的理论分析。针对这一问题,本论文从两个方面进行了系统、深入的研究。第一,寻求精确、高效的计算方法,能够对电大尺寸金属-介质混合目标的散射问题进行快速和准确的计算,为了能在微机上对翼面模型进行有效的理论计算,算法应具有较小的系统内存占用和较小的计算复杂度的特点。第二,进一步将计算方法用于飞行器翼面RCS的理论预估中。通过对不同翼面模型RCS的计算结果的比较和讨论,得到飞行器翼面可行的RCS减缩有效手段,并揭示散射机理。
第一,本文对整个研究的关键技术之一-数学模型建立方法进行了介绍,并根据翼面的散射机理,选择了三种普适性的翼面隐身方案进行研究。
针对不同构成的混合目标,本文采用不同的散射计算方法。首先,本文将吸波介质前缘翼面和介质涂覆翼面,简化为二维电大尺寸导体和吸波介质体组成的混合目标进行研究,针对介质相对于导体的空间位置,提出了基于矩量法(MM)和多极子方法(FMM)的混合算法、基于矩量法和场量迭代法并用快速多极子加速的混合算法,分别用于计算介质镶嵌和介质涂覆的问题。
然后,本文将全吸波介质翼面简化为二维电大尺寸介质(包括非均匀介质)目标进行散射计算,采用广义递推T矩阵的计算方法。为了使广义递推算法更有效的用于电大尺寸介质目标的计算,本文提出了在计算中动态改变(矩阵维数的方法。
最后,本文将全吸波介质中有金属支撑的翼面,简化为电大尺寸吸波介质和金属所组成的混合目标进行散射计算,在导体部分由矩量法和奇异值分解理论解出导体的T矩阵,对于介质包裹导体和介质相邻于导体的情况,分别采用广义递推算法和二体(多体)散射体的方法求出整个问题的解。
第二,在对翼面后向RCS减缩的讨论中,本文采用用编制的计算程序对机翼的不同模型进行了理论计算,针对不同电磁参数和截面形状的模型进行RCS的理论预估并进行讨论,最终得出在不影响翼面强度和气动外形的情况下降低其后向RCS的可行办法。在这部分中,本文讨论了吸波介质前缘翼面
在金属-介质界面和吸波介质前缘电磁参数对后向RCS的影响,重点讨论了界面为V字形时夹角与RCS的关系。然后讨论了吸波介质涂覆翼面的涂层厚度和涂层介质电磁参数对RCS的影响。最后讨论了全吸波介质翼面在较宽的频段缩减后向RCS能力,以及增加金属支撑后对RCS减缩的影响,并重点讨论了金属支撑的截面几何形状对后向RCS的影响。
本文研究作为二维混合散射目标电磁散射的基础研究为该类问题的精确建模和高效分析提供强有力的理论分析工具,对翼面RCS减缩及其散射机理的讨论可为飞行器翼面的目标隐身提供有效的理论指导。
Radar scattering characteristic of the aircraft is an important factor for its survivability. Wings are one of the important scattering source on the aircraft. In order to reduce their RCS, the intense and powerful electromagnetic analysis are needed. For reducing the complexity, the wings can be viewed as a two dimensional large electric objects consisting of both conductors and inhomogeneous dielectrics. In this dissertation, we aim at a precision and efficiency method for numerical computing of two dimension objects. Moded wings and the RCS of the wings can be calculated in turn. The RCS results of different wing are compared and examined, and the stealth technology of wing are found out. Scattering mechanism are explained, which can give strong predictive power for stealth technology of aircraft.
For reducing the RCS of metal wing, we choose three models those may have less backscatter RCS. Different electromagnetic analysis algorithms are applied. In order to compute on PC, all the algorithms have less computational complexity and resource occupy.
Both the lossy material front edge of metal wing and lossy material coated metal wing can simply be treated as a target consist the large electric size conduct part and the lossy inhomogeneous dielectric part. In the first case, Fast multipole algorithm(FMM) and methods of moment(MM) are used to work out the scattering fields. In the second case, FMM and iterative technique and conjugate gradient method(CGM) are used to work out the scattering fields.
Lossy material wing can simply treated as large electric size lossy inhomogeneous dielectric target. The generalize recursive aggregate T-matrix algorithm are used to solve this problem. In order to reduce the computing error when analyze the large electric size target, the dimensions of T-matrix are no longer invariable but turn bigger slowly during the recursive process.
Lossy material wing with metal support staff can be treated as large electric
lossy inhomogeneous dielectric target with conduct part. MM and Bi-orthogonal mode analysis are used to work out the T-matrix of conducting parts. when conduct part laid inside the dielectrics or in neighbour with the dielectrics, generalize recursive aggregate T-matrix algorithm or the method of divinding a large into parts are used to calculate the scattering field.
Computer codes are designed and used to simulate the scattering of different wing models. Models of different structure with different lossy material are analyzed and the results are carefully examined. Under the condition of keeping the configuration and mechanical strength, different stealth methods are tested. Computation result shows that the lossy material front edged metal wing with a V shaped interface have a better effect to reduce the backscatter RCS, and the interior angle of interface have a very important role in this stealth effect. On the coated wing case, when the thickness d of dielectric layer is small enough(f=10G, d<2mm), the coated material wing have a little ability to reduce the backscatter RCS. Add the thickness of dielectric layer or add the imaginary parts of dielectric ( can both reduce the backscatter RCS. The lossy dielectric wing have a better stealth effect(f=2~10G). But if with a inside metal support staff, the backscatter RCS of the wing turn bigger. The shape of the staff’s section affect the RCS strongly.
As a basic research work for electromagnetic scattering of 2D complex target, this disseration provides the powerful way in rigorous modeling and effective solution. The informations given in the disseration can help the stealth technology of aircraft.
第一,本文对整个研究的关键技术之一-数学模型建立方法进行了介绍,并根据翼面的散射机理,选择了三种普适性的翼面隐身方案进行研究。
针对不同构成的混合目标,本文采用不同的散射计算方法。首先,本文将吸波介质前缘翼面和介质涂覆翼面,简化为二维电大尺寸导体和吸波介质体组成的混合目标进行研究,针对介质相对于导体的空间位置,提出了基于矩量法(MM)和多极子方法(FMM)的混合算法、基于矩量法和场量迭代法并用快速多极子加速的混合算法,分别用于计算介质镶嵌和介质涂覆的问题。
然后,本文将全吸波介质翼面简化为二维电大尺寸介质(包括非均匀介质)目标进行散射计算,采用广义递推T矩阵的计算方法。为了使广义递推算法更有效的用于电大尺寸介质目标的计算,本文提出了在计算中动态改变(矩阵维数的方法。
最后,本文将全吸波介质中有金属支撑的翼面,简化为电大尺寸吸波介质和金属所组成的混合目标进行散射计算,在导体部分由矩量法和奇异值分解理论解出导体的T矩阵,对于介质包裹导体和介质相邻于导体的情况,分别采用广义递推算法和二体(多体)散射体的方法求出整个问题的解。
第二,在对翼面后向RCS减缩的讨论中,本文采用用编制的计算程序对机翼的不同模型进行了理论计算,针对不同电磁参数和截面形状的模型进行RCS的理论预估并进行讨论,最终得出在不影响翼面强度和气动外形的情况下降低其后向RCS的可行办法。在这部分中,本文讨论了吸波介质前缘翼面
在金属-介质界面和吸波介质前缘电磁参数对后向RCS的影响,重点讨论了界面为V字形时夹角与RCS的关系。然后讨论了吸波介质涂覆翼面的涂层厚度和涂层介质电磁参数对RCS的影响。最后讨论了全吸波介质翼面在较宽的频段缩减后向RCS能力,以及增加金属支撑后对RCS减缩的影响,并重点讨论了金属支撑的截面几何形状对后向RCS的影响。
本文研究作为二维混合散射目标电磁散射的基础研究为该类问题的精确建模和高效分析提供强有力的理论分析工具,对翼面RCS减缩及其散射机理的讨论可为飞行器翼面的目标隐身提供有效的理论指导。
Radar scattering characteristic of the aircraft is an important factor for its survivability. Wings are one of the important scattering source on the aircraft. In order to reduce their RCS, the intense and powerful electromagnetic analysis are needed. For reducing the complexity, the wings can be viewed as a two dimensional large electric objects consisting of both conductors and inhomogeneous dielectrics. In this dissertation, we aim at a precision and efficiency method for numerical computing of two dimension objects. Moded wings and the RCS of the wings can be calculated in turn. The RCS results of different wing are compared and examined, and the stealth technology of wing are found out. Scattering mechanism are explained, which can give strong predictive power for stealth technology of aircraft.
For reducing the RCS of metal wing, we choose three models those may have less backscatter RCS. Different electromagnetic analysis algorithms are applied. In order to compute on PC, all the algorithms have less computational complexity and resource occupy.
Both the lossy material front edge of metal wing and lossy material coated metal wing can simply be treated as a target consist the large electric size conduct part and the lossy inhomogeneous dielectric part. In the first case, Fast multipole algorithm(FMM) and methods of moment(MM) are used to work out the scattering fields. In the second case, FMM and iterative technique and conjugate gradient method(CGM) are used to work out the scattering fields.
Lossy material wing can simply treated as large electric size lossy inhomogeneous dielectric target. The generalize recursive aggregate T-matrix algorithm are used to solve this problem. In order to reduce the computing error when analyze the large electric size target, the dimensions of T-matrix are no longer invariable but turn bigger slowly during the recursive process.
Lossy material wing with metal support staff can be treated as large electric
lossy inhomogeneous dielectric target with conduct part. MM and Bi-orthogonal mode analysis are used to work out the T-matrix of conducting parts. when conduct part laid inside the dielectrics or in neighbour with the dielectrics, generalize recursive aggregate T-matrix algorithm or the method of divinding a large into parts are used to calculate the scattering field.
Computer codes are designed and used to simulate the scattering of different wing models. Models of different structure with different lossy material are analyzed and the results are carefully examined. Under the condition of keeping the configuration and mechanical strength, different stealth methods are tested. Computation result shows that the lossy material front edged metal wing with a V shaped interface have a better effect to reduce the backscatter RCS, and the interior angle of interface have a very important role in this stealth effect. On the coated wing case, when the thickness d of dielectric layer is small enough(f=10G, d<2mm), the coated material wing have a little ability to reduce the backscatter RCS. Add the thickness of dielectric layer or add the imaginary parts of dielectric ( can both reduce the backscatter RCS. The lossy dielectric wing have a better stealth effect(f=2~10G). But if with a inside metal support staff, the backscatter RCS of the wing turn bigger. The shape of the staff’s section affect the RCS strongly.
As a basic research work for electromagnetic scattering of 2D complex target, this disseration provides the powerful way in rigorous modeling and effective solution. The informations given in the disseration can help the stealth technology of aircraft.
引文
[1] Keller J.B. Determination of reflected and transmitted field by geometrical optics. Journal of the Optical Society of America, 1950, 40(1): 48～52
[2] R.G. Kouyoumjian and P.H. Pathak. A uniform theory of Diffraction for an Edge in a perfectly conducting surface. Proc IEEE, 1974,62(11): 1448～1461
[3] R.F. Harrington. Time-Harmonic Electromagnetic Field. New York: McGraw-Hill. 271～272
[4] Fock G.T. Electromagnetic diffraction and propagation problem. New York: Pergamon, 1961
[5] J.B. Keller. Geometrical theory of Diffraction. Journal of the Optical Society of America. 1962, 52: 116～130
[6] Sloan D. Robertson. Target for Microwave radar navigation. Bell Sys Tech. 1947, 26: 852～869
[7] Lubbers R.J. A heuristic UTD slope diffraction coefficient for rough lossy wedges. IEEE Trans on Antennas Propagate. 1989,37(2): 206～211
[8] S.W. Lee and G.A. Deschamps. A uniform asymptotic theory of electromagnetic diffraction by a curved wedge. IEEE Trans on Antennas Propagate. 1976, 24(1): 25～34
[9] G.A. Deschamps, J. Boersma. Three-Dimensional half-plane diffraction: Exact solution and testing of uniform theories. IEEE Trans on Antennas Propagate. 1984, 32(3): 264～271
[10] R.F. Millar. An approximate theory of the diffraction of an electromagnetic wave by an aperture in a plane screen. Proc. IEEE, 1956, 103(c):177～185
[11] A. Michaeli. Equivalent edge currents for arbitrary aspects of observation. IEEE Trans on Antennas Propagate. 1984, 23(3): 252～258
[12] A. Michaeli. A closed from physical theory of diffraction solution for electromagnetic scattering by strip and 90? dihedrals. Radio science,1984. 19(2): 609～616
[13] Keller J.B, Strefer W. Complex rays with an application to Gaussian beams. J. Opt. Soc, 1971, 61: 40～43
[14] Felsen L B. Complex rays. Philips Res., Special Issue in honor of C.J. Bouwkamp 30,1975: 169～184
[15] 阮颖铮等. 雷达截面与隐身技术. 北京. 国防工业出版社. 1998: 67～73
[16] R. F. Harrington. Matrix methods for fields problems. Proc. IEEE, 1967, 55(2): 136～149
[17] R. F. Harrington. Matrix methods for fields problems. Proc. IEEE, 1967, 55(2): 136～149
[18] Michel M. Ney. Method of Moment as Applied to Electromagnetic Problem. IEEE Trans on Antennas Propagate. 1985, 33(10): 972～980
[19] Raj Mittra and Varadarajan. A technique for solving 2d method-of-moment problems involving large scatterers. Microwave and Optical Tec. Let. 1995, 8(3):127～132
[20] Lee S W., Gee A W. How Good is the impedance boundary condution?. IEEE Trans. Antennas Propagat,1987,35(11): 1313-1315
[21] J. A.Potti, J.A.Motente. RCS of low observable targets with the TLM method. IEEE Trans., 1998, 46(5): 741～743
[22] K. Yashiro and S. Ohkawa. Boundary element method for electromagnetic scattering from cylinders. IEEE Antenna and Propagation, 1985, AP-33(4):383～389
[23]Umashankar K. R. and Taflove A. A Novel Method to Analyze Electromagnetic Scattering of Complex Objects. IEEE Trans. On Electromagnetic Compatibility, 1982,24(4):397～405
[24] A. Tallove,. Review of FDTD numerical modeling of EM wave scattering and radar cross section. IEEE Proceedings, 1989,17(5): 682～699
[25] T.K. Sarkar, E. Arvas, and S. M. Rao. Application of FFT and the conjugate gradient method for thesolution of electromagnetic radiation from electrically large and small conducting bodies. IEEE Trans.Antennas Propagation,1986, AP-34( 5) :635～ 640
[26] Qing Huo Liu, Zhong Qing Zhang, and Xue Min Xu. The Hybrid Extended Born Approximation and CG-FFT Method for Electromagnetic Induction Problems. IEEE Trans. on Geoscience and Remote Sensing, 2001,39(2):347～355
[27] V. Rokhlin. Rapid solution of integral equations of scattering theory in two dimension. Journal of computational physics, 1990 86: 414～439
[28] Engheta.N, Murphy.W.D, Rokhlin.V and Vassiliou.M.S. The fast multipole method (FMM) for electromagnetic scattering problems [J]. IEEE Trans. On Antennas and Propagation, 1992, 40 (6): 634-641
[29] Nader Engheta, Marius S., The Fast Multipole Method (FMM) for Electromagnetic Scattering Problems [J]. IEEE Trans On Antennas and Propagation, 1992, 40(6):634～641
[30] C.C. Lu, W.C.Chew. Fast algorithm for solving hybrid integral equations [J]. IEEE Trans. On Antennas and Propagation, 1993, 140(6): 445-460
[31] J.M. Song, W.C.Chew. Fast multipole method solution of three dimension integral equation [J]. IEEE Antennas and propagation Symposium,1995: 1528～1531
[32] C.C. Lu and W.C. Chew. A multilevel algorithm for solving boundary-value scattering. Micro. Opt. Tech. Lett., 1994, 7(10): 466～470
[33] C.C. Lu, W.C.Chew. A Multilevel algorithm for solving a boundary integral equation of wave scattering [J]. Microwave and Optical technology Letters, 1994, 7(10): 466～470
[34] C.C. Lu, W. C. Chew. A Coupled Surface-Volume Integral Equation Approach for the Calculation of Electromagnetic Scattering from Composite Metallic and Material Targets [J]. IEEE Trans. On Antennas and Propagation, 2000, 48(12): 1866～1868
[35] W.C.Chew. An N2algorithm for the multiple scattering solution of N scatters [J]. Microwave Opt. Tech. Lett, 1989,2: 380～383.
[36] Wang,Y.M. and W.C.Chew, An efficient algorithm for solution of a scattering problem [J], Microwave Opt. Tech.Lett. 1990,3: 102-106.
[39] Y.M. Wang, W.C.Chew. Application of the fast recursive algorithm to a large inhomogeneous scatterer for TM polarization. Micro. Opt. Tech. Lett., 1991,4(4): 155157
[38] Y.M.Wang, and W.C.Chew. A recursive T-matrix approach for the solution of electromagnetic scattering by many spheres [J], IEEE Trans Antennas Propag,1993 ,41(12): 1633-1639.
[39] 汤炜等. 广义递推T矩阵算法及其应用[J]. 电波科学学报, 1998, 13(13):245-249.
[41] N.N. Youssef. Radar cross section of complex target. IEEE Proc. 1989, 77(5): 722～734
[42] E.F. Knott. A progression of high-frequency RCS prediction technique. IEEE Proc. 1985,73(2): 252～264
[43] Burside W.D. A technology to combine the geometrical theory of diffraction and the moment method. IEEE Trans, 1975, 23(6): 551～558
[44] Wang D.S. Current-base hybrid analysis for surface wave effects on large scatterers. IEEEE Trans., 1991,39(7): 839～850
[45] Cui Suomin. A hybrid method for EM scattering from a finned cylinder. Chinese Journal of Electronics, 1995, 4(1): 81～84
[46] Cui Suomin. Hybrid method for EM scattering by large bodies with cracks and gaps. Microwave and Optical technology Let. 1996, 12(5): 295～298
[47] Louis N. Hybrid solutions for Large Impedance coated bodies of revolution. IEEE Trans. On Antennas and Propagation, 34(11): 1319～1386
[48] R.C. Hansen. Geometric theory of diffraction. New York IEEE Press, 1981.
[49] Thiele G.A. A hybrid technique for combining moment with a geometrical theory of diffraction. IEEE Trans. 1975, 23(1): 62～69
[50] Medgyeai Mitschang L.N, Wang D.S. Hybrid solution for scattering for scattering from perfectly conducting bodies of revolution. IEEE Trans. 1983, 31(4): 570～583
[51] Chia T.T., Burkhoder R.J. The application of FTTD in hybrid methods for cavity scattering analysis. IEEE Trans, 1995, 43(10): 1082～1090
[52] S.M. Rao, G K Cothard. Application of finite integral technique to electromagnetic scatting by two-dimensional cavity—backed aperture in a ground plane. IEEE Trans, 1998, 46(5): 679～685
[53] Jin J.M. Hybridization of SBR and FEM for scattering by large body with cracks and cavities. IEEE Trans., 1995,43(10): 1123～1139
[54] P.C.Waterman. Matrix Formulation of Electromagnetic scattering. Proc. IEEE, 1965, 53(8): 805～812
[55] P.C.Waterman. New formulation of acoustic scattering. J Acoust Soc Am. 1969, 45: 1417～1429
[56] P.C. Waterman. Symmetry, Unitarity, and geometry in electromagnetic scattering. Phys Rev D, 1971, 3: 825～835
[57] P.C. Waterman. Matrix methods in potential theory and electromagnetic scattering. J Appl Phys, 1979,50: 4550～4566
[58] 朱贤阳, 杨儒贵. 复杂目标雷达散射截面计算方法的新进展.电波科学学报,1998,13(3): 322～328
[59] Jernejcic R.O, Terzuoli, A.J. Electromagnetic backscatter predictions using XPATCH. IEEE Trans. On Antennas and Propagation, 1994, 1:602～605
[60] Sundararajan P., Niamat M.Y. FPGA implementation of the ray tracing algorithm used in the XPATCH software. Proc. IEEE 2001 1: 446～449
[61] Rius J.M., Ferrando, M. High-frequency RCS of complex radar targets in real-time. IEEE Trans. on Antennas and Propagation, 1993, 41(9): 1308～1319
[62] Rius J.M., Ferrando. GRECO: graphical electromagnetic computing for RCS prediction in real time. IEEE Antennas and Propagation, 1993, 35(2): 7～17
[63] J. Song, C. Lu, W. chew. Fast Illinois code. IEEE Antennas and Propagation. 1998,40: 27～34
[64] S. Velamparambil, J.Song. Scale Me: A portable ,scalable multipole engine for electromagnetic and acoustic integral equation solvers. IEEE Antennas Propagar,1998,3: 1774～1777
[65] 尹家贤,刘克成. 用FDTD和物理光学混合法分析毫米波抛物面天线. 电子学报, 2002, 30(06): 791～793
[66] 崔索民, 汪茂光. 单翼圆柱电磁散射的混合解. 电子学报, 1995, 23(06): 108～110
[67] 高火涛,柯亨玉.部件分解法/高频混合法在复杂目标散射近场预估中的应用. 微波学报, 2001, 17(02): 54～59
[68] 王浩刚,聂在平等. 对三维多层快速多极子方法中不变项计算的优化. 电子学报, 2000, 28(9): 105～107
[69]丁振宇,洪伟.快速多极子在任意截面均匀介质柱散射中的应用. 电波科学学报, 2001, 16(3): 283～286
[70] 聂在平,胡俊等. 用于复杂目标三维矢量散射分析的快速多极子方法. 电子学报, 1999, 27(6): 104～109
[71] 张跃江,龚中麟. 介质涂敷电大尺寸导体柱电磁散射特性的有限元-快速多极混合算法分析. 微波学报 2000, 16(3): 272～254
[72] 汤炜等. 广义递推T矩阵算法及其应用. 电波科学学报, 1998, 13(13):245-249.
[73] 朱峰,盛克敏,任朗. 用于大纵横比物体二维电磁散射问题的推广T矩阵方法. 电波科学学报. 1997, 12(2): 169～175
[74] 秦德华, 王宝发. 动目标双站 RCS预估的图形电磁计算 (GRECO)方法(英文). Chinese Journal of Aeronautics, 2002, 15(3): 161～165
[76] Weng Cho Chew.聂在平、柳清伙译.非均匀介质中的场与波,电子工业出版社,1992.391～392.
[77] 魏彦玉. 任意阶复宗量贝塞尔函数的数值计算.电子科技大学学报, 1998,27(2):171～176
[78] Cotnelis f.Du. The Numerical Computation of Bessel Function of the First and Second for Integer Order and Complex Arguments. IEEE trans. 1990, 38(9): 1341～1349
[79] David L. Heckmann. Numerical computation of Hankel function of integer order for complex-valued arguments. Radio Science, 2001 36(6): 1265～1270
[80] Michael S. Yeung. Single Integral Equation for Electromagnetic Scattering by Three-Dimensional Homogeneous Dielectric Objects. IEEE Trans on antennas and propagation, 1999, 47(10): 1615～1623
[81] Gang Kang. A Novel Grid-Robust Higher Order Vector Basis Function for the Method of Moments. IEEE Trans on antennas and propagation, 2001, 49(6):908～915
[82] David L. Heckmann. Numerical Computation of Hankel function of integer order for complex-valued arguments. Radio Science, 2001,36(6):1265～1270
[83] 颜锦奎, 徐长龙, 徐得名. 有耗介质覆盖金属圆柱体的散射. 应用科学学报, 1997, 15(4): 402～407
[84] 王锡良, 沈丽英.有耗介质覆盖导电圆柱的电磁散射. 电波科学学报, 1996, 11(4): 50～54
[85] Tapan K. Sarkar. The application of the conjugate gradient method for the solution of operator equation arising in electromagnetic scattering from wire antennas. Radio Science, 1984, 19(5): 1156～1172
[86] C. C. Lu and W. C. Chew. Fast algorithm for solving hybrid integral equations. IEE PROCEEDINGS-H, 1993, 140(6): 455～460
[87] Michael S. Yeung. Single Integral Equation for Electromagnetic Scattering by Three-Dimensional Homogeneous Dielectric Objects. IEEE Trans on antennas and propagation, 1999, 47(10): 1615～1623
[88] Gang Kang. A Novel Grid-Robust Higher Order Vector Basis Function for the Method of Moments. IEEE Trans on antennas and propagation, 2001, 49(6):908～915
[89] Eric Michielssen and Amir Boag. Multilevel evaluation of electromagnetic fields for the rapid solution of scattering problems. 1994.7(17):790～795
[90] JACK H. RICHMOND. Scattering by Dielectric Cylinder of Arbitrary Cross Section Shape. IEEE Trans on antennas and propagation, 1964 Nov: 334～341
[91] 孙玉发、徐善驾. 基于奇异值分解的方法求解目标内谐振时的散射截面. 电子学报,2001,29(7):959～960
[92] Y.M. Wang. Application of the fast recursive algorithm to large inhomogeneous scatter for TM polarization. Microwave and Optical Technology let. 1991,4(4): 155～157
[93] W.C.Chew and Yi-Min Wang. A General recursive Algorithm for Wave-Scattering Solutions in Two Dimension. IEEE Trans on Microwave theory and techniques. 1992 40(4) 716～723
[94] W.C.Chew,Y.M. Wang. Recursive Algorithm for Wave-Scattering Solutons Using Windowed Addition Theory. J.Electromagnetic Wave and Application. 1992,6(11): 1537~1560
[95] Levent Gurel, Weng Cho Chew. Recursive algorithms for calculating the scattering from N strips or patches. IEEE Trans on Microwave theory and techniques. 1990, 35(4): 507~515
[96] Levent Gurel, Weng Cho Chew. Scattering solution of three-dimensional array of patches using the recursive T-matrix algorithms. IEEE Trans on Microwave theory and techniques. 1990, 2(5): 182~185
[97] C,C, Lu , Weng Cho Chew. Electromagnetic scattering of finite strip array on a dielectric slab. IEEE Trans on Microwave theory and techniques. 1993, 41(1): 97~111
[98] Weng Cho Chew, Yi Min Wang. A recursive algorithm for reducing algorithmic complexity of scattering problems. IEEE Trans on Microwave theory and techniques 1990:52~56
[99] Zhang yaojiang, Gongzhonglin,Xu Chenhe. Relationship between MoM and T-matrix approach TM case in 2-D conducting scattering problems. IEEE,1998: 982~994
[100] Levent Gurel, Weng Cho Chew. the connection of T matrices and integral equations. IEEE. 1990:1624~1628
[2] R.G. Kouyoumjian and P.H. Pathak. A uniform theory of Diffraction for an Edge in a perfectly conducting surface. Proc IEEE, 1974,62(11): 1448～1461
[3] R.F. Harrington. Time-Harmonic Electromagnetic Field. New York: McGraw-Hill. 271～272
[4] Fock G.T. Electromagnetic diffraction and propagation problem. New York: Pergamon, 1961
[5] J.B. Keller. Geometrical theory of Diffraction. Journal of the Optical Society of America. 1962, 52: 116～130
[6] Sloan D. Robertson. Target for Microwave radar navigation. Bell Sys Tech. 1947, 26: 852～869
[7] Lubbers R.J. A heuristic UTD slope diffraction coefficient for rough lossy wedges. IEEE Trans on Antennas Propagate. 1989,37(2): 206～211
[8] S.W. Lee and G.A. Deschamps. A uniform asymptotic theory of electromagnetic diffraction by a curved wedge. IEEE Trans on Antennas Propagate. 1976, 24(1): 25～34
[9] G.A. Deschamps, J. Boersma. Three-Dimensional half-plane diffraction: Exact solution and testing of uniform theories. IEEE Trans on Antennas Propagate. 1984, 32(3): 264～271
[10] R.F. Millar. An approximate theory of the diffraction of an electromagnetic wave by an aperture in a plane screen. Proc. IEEE, 1956, 103(c):177～185
[11] A. Michaeli. Equivalent edge currents for arbitrary aspects of observation. IEEE Trans on Antennas Propagate. 1984, 23(3): 252～258
[12] A. Michaeli. A closed from physical theory of diffraction solution for electromagnetic scattering by strip and 90? dihedrals. Radio science,1984. 19(2): 609～616
[13] Keller J.B, Strefer W. Complex rays with an application to Gaussian beams. J. Opt. Soc, 1971, 61: 40～43
[14] Felsen L B. Complex rays. Philips Res., Special Issue in honor of C.J. Bouwkamp 30,1975: 169～184
[15] 阮颖铮等. 雷达截面与隐身技术. 北京. 国防工业出版社. 1998: 67～73
[16] R. F. Harrington. Matrix methods for fields problems. Proc. IEEE, 1967, 55(2): 136～149
[17] R. F. Harrington. Matrix methods for fields problems. Proc. IEEE, 1967, 55(2): 136～149
[18] Michel M. Ney. Method of Moment as Applied to Electromagnetic Problem. IEEE Trans on Antennas Propagate. 1985, 33(10): 972～980
[19] Raj Mittra and Varadarajan. A technique for solving 2d method-of-moment problems involving large scatterers. Microwave and Optical Tec. Let. 1995, 8(3):127～132
[20] Lee S W., Gee A W. How Good is the impedance boundary condution?. IEEE Trans. Antennas Propagat,1987,35(11): 1313-1315
[21] J. A.Potti, J.A.Motente. RCS of low observable targets with the TLM method. IEEE Trans., 1998, 46(5): 741～743
[22] K. Yashiro and S. Ohkawa. Boundary element method for electromagnetic scattering from cylinders. IEEE Antenna and Propagation, 1985, AP-33(4):383～389
[23]Umashankar K. R. and Taflove A. A Novel Method to Analyze Electromagnetic Scattering of Complex Objects. IEEE Trans. On Electromagnetic Compatibility, 1982,24(4):397～405
[24] A. Tallove,. Review of FDTD numerical modeling of EM wave scattering and radar cross section. IEEE Proceedings, 1989,17(5): 682～699
[25] T.K. Sarkar, E. Arvas, and S. M. Rao. Application of FFT and the conjugate gradient method for thesolution of electromagnetic radiation from electrically large and small conducting bodies. IEEE Trans.Antennas Propagation,1986, AP-34( 5) :635～ 640
[26] Qing Huo Liu, Zhong Qing Zhang, and Xue Min Xu. The Hybrid Extended Born Approximation and CG-FFT Method for Electromagnetic Induction Problems. IEEE Trans. on Geoscience and Remote Sensing, 2001,39(2):347～355
[27] V. Rokhlin. Rapid solution of integral equations of scattering theory in two dimension. Journal of computational physics, 1990 86: 414～439
[28] Engheta.N, Murphy.W.D, Rokhlin.V and Vassiliou.M.S. The fast multipole method (FMM) for electromagnetic scattering problems [J]. IEEE Trans. On Antennas and Propagation, 1992, 40 (6): 634-641
[29] Nader Engheta, Marius S., The Fast Multipole Method (FMM) for Electromagnetic Scattering Problems [J]. IEEE Trans On Antennas and Propagation, 1992, 40(6):634～641
[30] C.C. Lu, W.C.Chew. Fast algorithm for solving hybrid integral equations [J]. IEEE Trans. On Antennas and Propagation, 1993, 140(6): 445-460
[31] J.M. Song, W.C.Chew. Fast multipole method solution of three dimension integral equation [J]. IEEE Antennas and propagation Symposium,1995: 1528～1531
[32] C.C. Lu and W.C. Chew. A multilevel algorithm for solving boundary-value scattering. Micro. Opt. Tech. Lett., 1994, 7(10): 466～470
[33] C.C. Lu, W.C.Chew. A Multilevel algorithm for solving a boundary integral equation of wave scattering [J]. Microwave and Optical technology Letters, 1994, 7(10): 466～470
[34] C.C. Lu, W. C. Chew. A Coupled Surface-Volume Integral Equation Approach for the Calculation of Electromagnetic Scattering from Composite Metallic and Material Targets [J]. IEEE Trans. On Antennas and Propagation, 2000, 48(12): 1866～1868
[35] W.C.Chew. An N2algorithm for the multiple scattering solution of N scatters [J]. Microwave Opt. Tech. Lett, 1989,2: 380～383.
[36] Wang,Y.M. and W.C.Chew, An efficient algorithm for solution of a scattering problem [J], Microwave Opt. Tech.Lett. 1990,3: 102-106.
[39] Y.M. Wang, W.C.Chew. Application of the fast recursive algorithm to a large inhomogeneous scatterer for TM polarization. Micro. Opt. Tech. Lett., 1991,4(4): 155157
[38] Y.M.Wang, and W.C.Chew. A recursive T-matrix approach for the solution of electromagnetic scattering by many spheres [J], IEEE Trans Antennas Propag,1993 ,41(12): 1633-1639.
[39] 汤炜等. 广义递推T矩阵算法及其应用[J]. 电波科学学报, 1998, 13(13):245-249.
[41] N.N. Youssef. Radar cross section of complex target. IEEE Proc. 1989, 77(5): 722～734
[42] E.F. Knott. A progression of high-frequency RCS prediction technique. IEEE Proc. 1985,73(2): 252～264
[43] Burside W.D. A technology to combine the geometrical theory of diffraction and the moment method. IEEE Trans, 1975, 23(6): 551～558
[44] Wang D.S. Current-base hybrid analysis for surface wave effects on large scatterers. IEEEE Trans., 1991,39(7): 839～850
[45] Cui Suomin. A hybrid method for EM scattering from a finned cylinder. Chinese Journal of Electronics, 1995, 4(1): 81～84
[46] Cui Suomin. Hybrid method for EM scattering by large bodies with cracks and gaps. Microwave and Optical technology Let. 1996, 12(5): 295～298
[47] Louis N. Hybrid solutions for Large Impedance coated bodies of revolution. IEEE Trans. On Antennas and Propagation, 34(11): 1319～1386
[48] R.C. Hansen. Geometric theory of diffraction. New York IEEE Press, 1981.
[49] Thiele G.A. A hybrid technique for combining moment with a geometrical theory of diffraction. IEEE Trans. 1975, 23(1): 62～69
[50] Medgyeai Mitschang L.N, Wang D.S. Hybrid solution for scattering for scattering from perfectly conducting bodies of revolution. IEEE Trans. 1983, 31(4): 570～583
[51] Chia T.T., Burkhoder R.J. The application of FTTD in hybrid methods for cavity scattering analysis. IEEE Trans, 1995, 43(10): 1082～1090
[52] S.M. Rao, G K Cothard. Application of finite integral technique to electromagnetic scatting by two-dimensional cavity—backed aperture in a ground plane. IEEE Trans, 1998, 46(5): 679～685
[53] Jin J.M. Hybridization of SBR and FEM for scattering by large body with cracks and cavities. IEEE Trans., 1995,43(10): 1123～1139
[54] P.C.Waterman. Matrix Formulation of Electromagnetic scattering. Proc. IEEE, 1965, 53(8): 805～812
[55] P.C.Waterman. New formulation of acoustic scattering. J Acoust Soc Am. 1969, 45: 1417～1429
[56] P.C. Waterman. Symmetry, Unitarity, and geometry in electromagnetic scattering. Phys Rev D, 1971, 3: 825～835
[57] P.C. Waterman. Matrix methods in potential theory and electromagnetic scattering. J Appl Phys, 1979,50: 4550～4566
[58] 朱贤阳, 杨儒贵. 复杂目标雷达散射截面计算方法的新进展.电波科学学报,1998,13(3): 322～328
[59] Jernejcic R.O, Terzuoli, A.J. Electromagnetic backscatter predictions using XPATCH. IEEE Trans. On Antennas and Propagation, 1994, 1:602～605
[60] Sundararajan P., Niamat M.Y. FPGA implementation of the ray tracing algorithm used in the XPATCH software. Proc. IEEE 2001 1: 446～449
[61] Rius J.M., Ferrando, M. High-frequency RCS of complex radar targets in real-time. IEEE Trans. on Antennas and Propagation, 1993, 41(9): 1308～1319
[62] Rius J.M., Ferrando. GRECO: graphical electromagnetic computing for RCS prediction in real time. IEEE Antennas and Propagation, 1993, 35(2): 7～17
[63] J. Song, C. Lu, W. chew. Fast Illinois code. IEEE Antennas and Propagation. 1998,40: 27～34
[64] S. Velamparambil, J.Song. Scale Me: A portable ,scalable multipole engine for electromagnetic and acoustic integral equation solvers. IEEE Antennas Propagar,1998,3: 1774～1777
[65] 尹家贤,刘克成. 用FDTD和物理光学混合法分析毫米波抛物面天线. 电子学报, 2002, 30(06): 791～793
[66] 崔索民, 汪茂光. 单翼圆柱电磁散射的混合解. 电子学报, 1995, 23(06): 108～110
[67] 高火涛,柯亨玉.部件分解法/高频混合法在复杂目标散射近场预估中的应用. 微波学报, 2001, 17(02): 54～59
[68] 王浩刚,聂在平等. 对三维多层快速多极子方法中不变项计算的优化. 电子学报, 2000, 28(9): 105～107
[69]丁振宇,洪伟.快速多极子在任意截面均匀介质柱散射中的应用. 电波科学学报, 2001, 16(3): 283～286
[70] 聂在平,胡俊等. 用于复杂目标三维矢量散射分析的快速多极子方法. 电子学报, 1999, 27(6): 104～109
[71] 张跃江,龚中麟. 介质涂敷电大尺寸导体柱电磁散射特性的有限元-快速多极混合算法分析. 微波学报 2000, 16(3): 272～254
[72] 汤炜等. 广义递推T矩阵算法及其应用. 电波科学学报, 1998, 13(13):245-249.
[73] 朱峰,盛克敏,任朗. 用于大纵横比物体二维电磁散射问题的推广T矩阵方法. 电波科学学报. 1997, 12(2): 169～175
[74] 秦德华, 王宝发. 动目标双站 RCS预估的图形电磁计算 (GRECO)方法(英文). Chinese Journal of Aeronautics, 2002, 15(3): 161～165
[76] Weng Cho Chew.聂在平、柳清伙译.非均匀介质中的场与波,电子工业出版社,1992.391～392.
[77] 魏彦玉. 任意阶复宗量贝塞尔函数的数值计算.电子科技大学学报, 1998,27(2):171～176
[78] Cotnelis f.Du. The Numerical Computation of Bessel Function of the First and Second for Integer Order and Complex Arguments. IEEE trans. 1990, 38(9): 1341～1349
[79] David L. Heckmann. Numerical computation of Hankel function of integer order for complex-valued arguments. Radio Science, 2001 36(6): 1265～1270
[80] Michael S. Yeung. Single Integral Equation for Electromagnetic Scattering by Three-Dimensional Homogeneous Dielectric Objects. IEEE Trans on antennas and propagation, 1999, 47(10): 1615～1623
[81] Gang Kang. A Novel Grid-Robust Higher Order Vector Basis Function for the Method of Moments. IEEE Trans on antennas and propagation, 2001, 49(6):908～915
[82] David L. Heckmann. Numerical Computation of Hankel function of integer order for complex-valued arguments. Radio Science, 2001,36(6):1265～1270
[83] 颜锦奎, 徐长龙, 徐得名. 有耗介质覆盖金属圆柱体的散射. 应用科学学报, 1997, 15(4): 402～407
[84] 王锡良, 沈丽英.有耗介质覆盖导电圆柱的电磁散射. 电波科学学报, 1996, 11(4): 50～54
[85] Tapan K. Sarkar. The application of the conjugate gradient method for the solution of operator equation arising in electromagnetic scattering from wire antennas. Radio Science, 1984, 19(5): 1156～1172
[86] C. C. Lu and W. C. Chew. Fast algorithm for solving hybrid integral equations. IEE PROCEEDINGS-H, 1993, 140(6): 455～460
[87] Michael S. Yeung. Single Integral Equation for Electromagnetic Scattering by Three-Dimensional Homogeneous Dielectric Objects. IEEE Trans on antennas and propagation, 1999, 47(10): 1615～1623
[88] Gang Kang. A Novel Grid-Robust Higher Order Vector Basis Function for the Method of Moments. IEEE Trans on antennas and propagation, 2001, 49(6):908～915
[89] Eric Michielssen and Amir Boag. Multilevel evaluation of electromagnetic fields for the rapid solution of scattering problems. 1994.7(17):790～795
[90] JACK H. RICHMOND. Scattering by Dielectric Cylinder of Arbitrary Cross Section Shape. IEEE Trans on antennas and propagation, 1964 Nov: 334～341
[91] 孙玉发、徐善驾. 基于奇异值分解的方法求解目标内谐振时的散射截面. 电子学报,2001,29(7):959～960
[92] Y.M. Wang. Application of the fast recursive algorithm to large inhomogeneous scatter for TM polarization. Microwave and Optical Technology let. 1991,4(4): 155～157
[93] W.C.Chew and Yi-Min Wang. A General recursive Algorithm for Wave-Scattering Solutions in Two Dimension. IEEE Trans on Microwave theory and techniques. 1992 40(4) 716～723
[94] W.C.Chew,Y.M. Wang. Recursive Algorithm for Wave-Scattering Solutons Using Windowed Addition Theory. J.Electromagnetic Wave and Application. 1992,6(11): 1537~1560
[95] Levent Gurel, Weng Cho Chew. Recursive algorithms for calculating the scattering from N strips or patches. IEEE Trans on Microwave theory and techniques. 1990, 35(4): 507~515
[96] Levent Gurel, Weng Cho Chew. Scattering solution of three-dimensional array of patches using the recursive T-matrix algorithms. IEEE Trans on Microwave theory and techniques. 1990, 2(5): 182~185
[97] C,C, Lu , Weng Cho Chew. Electromagnetic scattering of finite strip array on a dielectric slab. IEEE Trans on Microwave theory and techniques. 1993, 41(1): 97~111
[98] Weng Cho Chew, Yi Min Wang. A recursive algorithm for reducing algorithmic complexity of scattering problems. IEEE Trans on Microwave theory and techniques 1990:52~56
[99] Zhang yaojiang, Gongzhonglin,Xu Chenhe. Relationship between MoM and T-matrix approach TM case in 2-D conducting scattering problems. IEEE,1998: 982~994
[100] Levent Gurel, Weng Cho Chew. the connection of T matrices and integral equations. IEEE. 1990:1624~1628