导体介质组合目标电磁问题的精确建模和快速算法研究
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摘要
本文主要研究了具有电大尺寸和复杂材料组分的目标三维矢量电磁辐射与散射的精确建模和高效数值求解问题。针对这一问题,本文分别研究了复杂目标的精确几何建模和电磁建模方法、复杂导体介质组合目标快速求解算法,以及复杂不规则几何结构目标的快速算法。
首先,本文系统地阐述了矩量法的基本原理和关键步骤。采用曲面三角形单元和曲RWG基函数模拟曲面目标的几何形状以及曲面上的电流分布,运用Duffy变换方法处理积分方程的奇异性问题,采用广义最小残差算法(GMRES)对线性方程组进行迭代求解。数值算例验证了代码的可靠性。
接着本文着重讨论了用于任意导体介质组合目标电磁特性分析的表面积分方程方法。根据等效原理,推导得到多种形式的表面积分方程,提出了CFIE-JMCFIE组合形式的混合场积分方程,与其他组合形式的方程在迭代求解收敛性以及实用性方面进行了系统、全面地比较。证明该方程构造的阻抗矩阵形式对角线元素占优,条件数好,迭代求解具有良好的收敛性。CFIE-JMCFIE方程的提出为准确、高效地运用积分方程求解组合目标的散射问题打下基础。本文还研究了多个导体、介质材料的组合结构,分析了积分方程和基函数在多个分界面连接处的定义以及积分方程的组合形式。另外还研究了一类简化多区域分界面处理的电磁建模方法—连接域方法(CRM)。
为实现电大尺寸目标的高效求解,本文提出了基于CFIE-JMCFIE的多层快速多极子算法(MLFMA)。在全面阐述MLFMA的基本原理和数值实现过程的基础上,重点研究了介质域内MLFMA的参数选取和预条件技术。数值算例表明,利用CFIE-JMCFIE阻抗矩阵对角元素占优的特点,采用块对角预条件技术的MLFMA能实现对电大尺寸导体介质组合目标电磁特性分析的快速计算。在此基础上,进一步研究了基于MLFMA的稀疏近似逆(SAI)预条件技术。提出一类改进分组策略的SAI预条件方法,降低了构造预条件器的计算复杂度,提高了积分方程求解的收敛速度。
然后提出了基于高阶叠层矢量基函数的高阶MLFMA用于组合目标电磁散射分析。采用基于修正勒让德多项式的最大正交化高阶叠层矢量基函数减少未知量数目,降低阻抗矩阵条件数。针对大贴片剖分单元,详细分析了高阶MLFMA的分组策略,提出了参数最优化选取原则。数值算例表明在合理选择基函数阶数和剖分单元大小的情况下,高阶MLFMA具有较高的计算精度和计算效率。
针对含开放结构的导体介质组合目标问题,我们提出了一类新的混合场积分方程形式IEFIE-IPMCHW。通过引入积分方程的主值项,有效地改善了原积分方程算子的条件数。该方程利用内外两层迭代逼近真解,对分析开放、不规则目标的电磁问题具有较高的计算效率。
最后,本文研究具有线面连接结构的载体上天线问题。研究了线面连接结构的面面等效方法,对天线加载或者移动时仅对加载点附近剖分单元进行重新划分,准确地得到天线阻抗和辐射特性。进一步研究了Costa连接基函数,分别采用迭代矩量法-物理光学法(MoM-PO)以及结合预条件技术的MLFMA实现了复杂平台上天线问题的高效求解。
本文的研究工作为具有复杂形状和结构、复杂材料组分的目标电磁辐射与散射问题的精确建模和快速求解提供了有效的方法途径,也为该课题的进一步深入开展打下了坚实的基础。
The rigorous modeling and high efficient calculation of electromagnetic radiation and scattering from complex electrically-large targets is studied in this dissertation. It is discussed from three points. First, accurate geometrical and electromagnetic modeling for complex targets; secondly, the details of effectively solving the integral equations by fast numerical methods; thirdly, analyzing the fast algorithms for complex irregular objects.
Firstly, the crux techniques of the basic method for solving the integral equations-method of moment (MoM) have been studied. Curvilinear triangular patches and curvilinear RWG basis function are used to model the shape of the curved surface and the current distribution on the curved surface, respectively. A Duffy's transformation method is used to solve the singularity of integral equation and the general minimum residual method (GMRES) is used to solve linear equations. Numerical examples validate our codes.
Then, the surface integral equations (SIEs) for composite conducting and dielectric objects are presented. Some formulations of SIEs are derived from equivalent principle. A new CFIE-JMCFIE formulation is proposed and compared with other equations from iterative characteristics and the applicability. CFIE-JMCFIE requires fewer iterations than other formulations because its impedance matrix is diagonally dominant and has low condition number. A treatment for SIEs and basis functions on the junctions of composite objects with multiple metallic and dielectric regions is discussed. A new contact region method (CRM) is proposed to simplify the treatment for complex composite objects.
As key techniques for solving the scattering by electrically-large object efficiently, extensive study of the multilevel fast multipole algorithm (MLFMA) based on CFIE-JMCFIE has been carried out. The principles and the numerical realization in dielectric regions of MLFMA have been described. The numerical examples show that MLFMA with block-diagonal preconditioner can solve electrically-large problems accurately and efficiently. Where after, some other preconditioners based on MLFMA have been studied. A new grouped sparse approximate inverse (SAI) preconditioner is proposed to save the construction cost significantly and reduce the iteration number.
For the sake of reducing unknowns, a higher order MLFMA, using the maximally orthogonalized higher order hierarchical vector basis functions based on modified Legendre polynomials, is proposed. To improve the efficiency of higher order MLFMA with large patches, a detailed discussion for grouping and parameters and the referenced principle are given. Through reasonably chousing the order of basis function and the size of the patches, higher order MLFMA can solve scattering problem for composite objects efficiently and accurately.
Aimed at resolving the scattering by composite object with open metallic structure with high efficient solution, a new IEFIE-IPMCHW formulation has been proposed. By adding the principal value term into EFIE-PMCHW operator, a well-conditioned IEFIE-IPMCHW operator is constructed. To achieve a reasonable accuracy, several update steps for the current vector are required. This method attains much faster convergence of iterations than conventional methods, particularly for 3-D structures with open or sharp surface.
Finally, detailed work has been done for the problems of complicated objects attached with wires, such as wire monopoles on platform. A surface/surface junction mode has been used to model the wire/surface junction. When the monopole is added or moved on the surface, accurate results of impedance and radiation properties have been achieved and only a few triangular patches need to be resegmented near the attachment point. Then, a Costa's junction basis function is described. An iterative MoM-PO method and a preconditioned MLFMA are employed to solve the electrically-large problems, respectively.
As a basic research work for electromagnetic radiation and scattering characteristics of the 3-D electrically-large objects with arbitrary shape and materials, this research work presented in the dissertation provides the powerful way in rigorous modeling and effective solution, as well as a solid foundation for the further development in this subject.
首先,本文系统地阐述了矩量法的基本原理和关键步骤。采用曲面三角形单元和曲RWG基函数模拟曲面目标的几何形状以及曲面上的电流分布,运用Duffy变换方法处理积分方程的奇异性问题,采用广义最小残差算法(GMRES)对线性方程组进行迭代求解。数值算例验证了代码的可靠性。
接着本文着重讨论了用于任意导体介质组合目标电磁特性分析的表面积分方程方法。根据等效原理,推导得到多种形式的表面积分方程,提出了CFIE-JMCFIE组合形式的混合场积分方程,与其他组合形式的方程在迭代求解收敛性以及实用性方面进行了系统、全面地比较。证明该方程构造的阻抗矩阵形式对角线元素占优,条件数好,迭代求解具有良好的收敛性。CFIE-JMCFIE方程的提出为准确、高效地运用积分方程求解组合目标的散射问题打下基础。本文还研究了多个导体、介质材料的组合结构,分析了积分方程和基函数在多个分界面连接处的定义以及积分方程的组合形式。另外还研究了一类简化多区域分界面处理的电磁建模方法—连接域方法(CRM)。
为实现电大尺寸目标的高效求解,本文提出了基于CFIE-JMCFIE的多层快速多极子算法(MLFMA)。在全面阐述MLFMA的基本原理和数值实现过程的基础上,重点研究了介质域内MLFMA的参数选取和预条件技术。数值算例表明,利用CFIE-JMCFIE阻抗矩阵对角元素占优的特点,采用块对角预条件技术的MLFMA能实现对电大尺寸导体介质组合目标电磁特性分析的快速计算。在此基础上,进一步研究了基于MLFMA的稀疏近似逆(SAI)预条件技术。提出一类改进分组策略的SAI预条件方法,降低了构造预条件器的计算复杂度,提高了积分方程求解的收敛速度。
然后提出了基于高阶叠层矢量基函数的高阶MLFMA用于组合目标电磁散射分析。采用基于修正勒让德多项式的最大正交化高阶叠层矢量基函数减少未知量数目,降低阻抗矩阵条件数。针对大贴片剖分单元,详细分析了高阶MLFMA的分组策略,提出了参数最优化选取原则。数值算例表明在合理选择基函数阶数和剖分单元大小的情况下,高阶MLFMA具有较高的计算精度和计算效率。
针对含开放结构的导体介质组合目标问题,我们提出了一类新的混合场积分方程形式IEFIE-IPMCHW。通过引入积分方程的主值项,有效地改善了原积分方程算子的条件数。该方程利用内外两层迭代逼近真解,对分析开放、不规则目标的电磁问题具有较高的计算效率。
最后,本文研究具有线面连接结构的载体上天线问题。研究了线面连接结构的面面等效方法,对天线加载或者移动时仅对加载点附近剖分单元进行重新划分,准确地得到天线阻抗和辐射特性。进一步研究了Costa连接基函数,分别采用迭代矩量法-物理光学法(MoM-PO)以及结合预条件技术的MLFMA实现了复杂平台上天线问题的高效求解。
本文的研究工作为具有复杂形状和结构、复杂材料组分的目标电磁辐射与散射问题的精确建模和快速求解提供了有效的方法途径,也为该课题的进一步深入开展打下了坚实的基础。
The rigorous modeling and high efficient calculation of electromagnetic radiation and scattering from complex electrically-large targets is studied in this dissertation. It is discussed from three points. First, accurate geometrical and electromagnetic modeling for complex targets; secondly, the details of effectively solving the integral equations by fast numerical methods; thirdly, analyzing the fast algorithms for complex irregular objects.
Firstly, the crux techniques of the basic method for solving the integral equations-method of moment (MoM) have been studied. Curvilinear triangular patches and curvilinear RWG basis function are used to model the shape of the curved surface and the current distribution on the curved surface, respectively. A Duffy's transformation method is used to solve the singularity of integral equation and the general minimum residual method (GMRES) is used to solve linear equations. Numerical examples validate our codes.
Then, the surface integral equations (SIEs) for composite conducting and dielectric objects are presented. Some formulations of SIEs are derived from equivalent principle. A new CFIE-JMCFIE formulation is proposed and compared with other equations from iterative characteristics and the applicability. CFIE-JMCFIE requires fewer iterations than other formulations because its impedance matrix is diagonally dominant and has low condition number. A treatment for SIEs and basis functions on the junctions of composite objects with multiple metallic and dielectric regions is discussed. A new contact region method (CRM) is proposed to simplify the treatment for complex composite objects.
As key techniques for solving the scattering by electrically-large object efficiently, extensive study of the multilevel fast multipole algorithm (MLFMA) based on CFIE-JMCFIE has been carried out. The principles and the numerical realization in dielectric regions of MLFMA have been described. The numerical examples show that MLFMA with block-diagonal preconditioner can solve electrically-large problems accurately and efficiently. Where after, some other preconditioners based on MLFMA have been studied. A new grouped sparse approximate inverse (SAI) preconditioner is proposed to save the construction cost significantly and reduce the iteration number.
For the sake of reducing unknowns, a higher order MLFMA, using the maximally orthogonalized higher order hierarchical vector basis functions based on modified Legendre polynomials, is proposed. To improve the efficiency of higher order MLFMA with large patches, a detailed discussion for grouping and parameters and the referenced principle are given. Through reasonably chousing the order of basis function and the size of the patches, higher order MLFMA can solve scattering problem for composite objects efficiently and accurately.
Aimed at resolving the scattering by composite object with open metallic structure with high efficient solution, a new IEFIE-IPMCHW formulation has been proposed. By adding the principal value term into EFIE-PMCHW operator, a well-conditioned IEFIE-IPMCHW operator is constructed. To achieve a reasonable accuracy, several update steps for the current vector are required. This method attains much faster convergence of iterations than conventional methods, particularly for 3-D structures with open or sharp surface.
Finally, detailed work has been done for the problems of complicated objects attached with wires, such as wire monopoles on platform. A surface/surface junction mode has been used to model the wire/surface junction. When the monopole is added or moved on the surface, accurate results of impedance and radiation properties have been achieved and only a few triangular patches need to be resegmented near the attachment point. Then, a Costa's junction basis function is described. An iterative MoM-PO method and a preconditioned MLFMA are employed to solve the electrically-large problems, respectively.
As a basic research work for electromagnetic radiation and scattering characteristics of the 3-D electrically-large objects with arbitrary shape and materials, this research work presented in the dissertation provides the powerful way in rigorous modeling and effective solution, as well as a solid foundation for the further development in this subject.
引文
[1]楼仁海,符果行,袁敬闳.《电磁理论》.成都:电子科技大学出版社,1996.
[2]K.S.Yee,J.S.Chen,and A.H.Chang.Conformal finite-difference time-domain(FDTD) with overlapping grids.IEEE Trans.Antennas Propagat.,1992,40(2):1068-1075.
[3]A.Taflve.Computational electrodynamics:the finite-difference time-domain Method.Norwood,MA:Artech House,1995.
[4]金建铭.电磁场有限元方法.西安电子科技大学出版社,1998.
[5]R.F.Harrington.Time-harmonic electromagnetic fields.McGraw-Hill Book Company,New York,1961.
[6]R.F.Harrington.Field computation by moment methods.McMillan,New York,1968.
[7]李世智.电磁散射与辐射问题的矩量法.电子工业出版社,1985.
[8]A.W.Glisson and D.R.Wilton.Simple and efficient numerical methods for problems of electromagnetic radiation and scattering from surfaces.IEEE Trans.Antennas Propagat.,1980,28(5):593-603.
[9]S.M.Rao,D.R.Wilton and A.W.Glisson.Electromagnetic scattering by surfaces of arbitrary shape.IEEE Trans.Antennas Propagat.,1982,30(5):409-418.
[10]J.J.H.Wang.Generalized moment methods in electromagnetics:formulation and computer solution of integral equations.John Wiley & Sons,Inc.,1991.
[11]H.Schaubert,D.R.Wilton and A.W.Glisson.A tetrahedral modeling method for electromagnetic scattering by arbitrary shaped inhomogeneous dielectric bodies.IEEE Trans.Antennas Propagat.,1984,32(1):77-85.
[12]M.F.Catedra,E.Gago and L.Nulo.A numerical scheme to obtain the RCS of three dimensional bodies of resonant size using the conjugate gradient method and the fast fourier transform.IEEE Trans.Antennas Propagat.,1989,37(5):528-537.
[13]H.Gan and W.C.Chew.A discrete BCG-FFT algorithm for solving 3D inhomogeneous scatter problems.J.Electromag.Waves Appl.,1995,9(10):1339-1357.
[14]C.C.Lu,J.M.Song and W.C.Chew.Multilevel fast multipole algorithm for solving 3D volume integral equations of electromagnetic scattering.AP-S,2000(4):1864-1867.
[15]J.L.Guo,J.Y.Li and Q.Z.Liu.Analysis of arbitrarily shaped dielectric radomes using adaptive integral method based on volume integral equation.IEEE Trans.Antennas Propagat.,2006,54(7):1910-1916.
[16]H.Y.Yao,X.Q.Sheng,K.N.Yung and Z.P.Nie.Analysis of scattering by finite periodic dielectric structures using TFQMR-FFT.Microwave and Optical Technology Letters,2001,10(1):221-224.
[17]C.Muller.Foundations of the Mathematical Theory of Electromagnetic Waves.New York:Spinger,1969.
[18]J.R.Mautz and R.F.Harrington.Electromagnetic scattering from a homogeneous materical body of revolution.AEU,1979,33(2):71-80.
[19]A.J.Poggio and E.K.Miller.Integral equation solutions of three-dimensional scattering problems.In Computer Techniques for Electromagnetics,R.Mittra,Ed.Oxford:Pergamon Press,1973,Chap.4.
[20]T.K.Wu and L.L.Tsai.Scattering from arbitrarily-shaped lossy dielectric bodies of revolution.Radio Sci.,1997,vol.12,709-718.
[21]R.F.Harrington.Boundary integral formulations for homogeneous material bodies.J.Electromagn.Waves Applicat.,1989,3(1):1-15.
[22]Y.Chung and R.F.Harrington.A surface formulation for characteristic modes of material bodies.IEEE Trans.Antennas Propagat.,1977,25(11):789-795.
[23]S.M.Rao and D.R.Wilton.E-field,H-field,and combined field solution for arbitrarily shaped three-dimensional dielectric bodies.Electromagn.,1990,10(4):407-421.
[24]X.Q.Sheng,J.M.Jin,J.M.Song,W.C.Chew and C.C.Lu.Solution of combined-field integral equation using multilevel fast multipole algorithm for scattering by homogeneous bodies.IEEE Trans.Antennas Propagat.,1998,46(11):1718-1726.
[25]P.Yla-Oijala.Application of a novel CFIE for electromagnetic scattering by dielectric objects.Microwave and Optical Technology Letters,2002,35(10):3-5.
[26]P.Yla-Oijala and T Matti.Applieatinn of combined field integral equation for electromagnetic scattering by dielectric and composite objects.IEEE Trans.Antennas Propagat.,2003,53(3):1168-1173.
[27]P.Yla-Oijala and T Matti.Improving conditioning of electromagnetic surface integral equations using normalized field quantifies.IEEE Trans.Antennas Propagat.,2007,55(1):178-185.
[28]P.Yla-Oijala,M Taskinen and J Sarvas.Surface integral equation method for general composite metallic and dielectric structures with junctions.Progress in Electromagnetic Research,2005,52:81-108.
[29]P.Yla-Oijala and M.Taskinen.Well-conditioned Muller formulation for electromagnetic scattering by dielectric objects.IEEE Trans.Antennas Propagat.,2005.53(10):3316-3323.
[30]A.W.Glisson.An integral equation for electromagnetic scattering from homogeneous dielectric bodies.IEEE Trans.Antennas Propagat.,1984,32(2):172-175.
[31]M.S.Yeung.Single integral equation for electromagnetic scattering by three-dimensional homogeneous dielectric objects.IEEE Trans.Antennas Propagat.,1999,47(10):1615-1622.
[32]阙肖峰,聂在平,胡俊.基于混合场积分方程MLFMA分析导体介质复合目标电磁散射问题.电子学报,2007,35(11):2062-2066.
[33]J.M.Putman and L.N.Medgyesi-Mitschang.Combined field integral equation for inhomogeneous two- and three-dimensional bodies:The junction problem.IEEE Trans.Antennas Propagat.,1991,39(5):667-672.
[34]M.Carr,E.Topsakal and J.L.Volakis.A procedure for modeling material junctions in 3-D surface integral equation approaches.IEEE Trans.Antennas Propagat.,2004,52(5):1374-1379.
[35]B.M.Kolundzija.Electromagnetic modeling of composite metallic and dielectric structures.IEEE Trans.Microwave Theory and Techniques,1999,47(7):1021-1032.
[36]S.Y.Chen,J.S.Zhao and W.C.Chew.Analyzing low-frequency electromagnetic scattering from a composite object.IEEE Trans.Geoscience and Remot Sensing,2002,40(2):426-433.
[37]W.C.Chew,J.M.Jin,E.Miehielssen and J.M.Song.Fast and efficient algorithms in computational electromagnetics.Artech House,Boston,2001.
[38]J.Hu and Z.P.Nie.Improved electric field integral equation for analysis of scattering from 3-D conducting structures.IEEE Trans Electromagnetic Compatibility,2007,49(3):644-648.
[39]E.H.Newman and D.M.Pozar,Electromagnetic modeling of composite wire and surface geometries.IEEE Trans.Antennas Propagat.,1978,26(6):784-789.
[40]E.H.Newman and D.M.Pozar.Considerations for efficient wire/surface modeling.IEEE Trans.Antennas Propagat.,1980,28(1):121-125.
[41]D.M.Pozar and E.H.Newman.Analysis ofa monopole mounted near an edge or a vertex.IEEE Trans.Antennas Propagat.,1982,30(5):401-408.
[42]M.E Costa,R.F.Harrington,Minimization of radiation from computer systems.Int.Elect.Electron.Conference and Exposition Proc.,1983:660-665.
[43]S.U.Hwu,D.R.Wilton and S.M.Rao.Electromagnetic scattering and radiation by arbitrary conducting wire/surface configurations.IEEE AP-S,1988.
[44]逯贵祯,刘永俊,毛志及.位于任意形状导体上的天线输入阻抗分析.电波科学学报,1995,10(1):128-130.
[45]V.Rokhlin.Rapid solution of integral equations of scattering theory in two dimensions.Journal of Computational physics,1990,86:414-437.
[46]B.Dembart and E.Yip.A 3-D fast multipole method for electromagnetics with multipole levels.11~(th) Annu.Rev.progress Appl.Computat.Electromagn.,Monterery,CA,1995:621-628.
[47]N.Engheta,W.D.Murphy,V.Rokhlin,etc.The fast multipole method(FMM) for electromagnetic scattering problems.IEEE Trans.Antennas Propagat.,1992,40(6):634-641.
[48]R.Coifman,V.Rokhlin,S.Wandzura.The fast multipole method for the wave equation:a pedestrian prescription.IEEE AP magazine.1993,25(3):7-12.
[49]Sunil S.Bindiganavale and J.L.Volakis.Guidelines for using the fast multipole method to calculate the RCS of large objects.Microwave and Optical Technology Letters,1996,11(4):190-194.
[50]C.C.Lu,W.C.Chew.Fast algorithm for solving hybrid integral equations.IEEE proceedings-H,1993,140(6):455-460.
[51]J.M.Song and W.C.Chew.Fast multipole method solution using parametric geometry.Microwave and Optical Technology Letters,1994,7(16):760-765.
[52]J.M.Song,C.C.Lu and W.C.Chew.Multilevel fast multipole algorithm for electromagnetic scattering by large complex objects.IEEE Trans.Antennas Propagat.,1997,45(10):1488-1498.
[53]J.M.Song and W.C.Chew.Multilevel fast-multipole algorithm for solving combined field integral equations of electromagnetic scattering.Microwave and Optical Technology Letters,1995,8(1):14-19.
[54]J.M.Song and W.C.Chew.A multilevel algorithm for solving a boundary integral equation of wave scattering.Microwave and Optical Technology Letters,1994,7(10):466-470.
[55]J.M.Song,C.C.Lu and W.C.Chew.Fast Illinois Solver Code(FISC).IEEE Trans.Antennas Propagat.,1998,40(3):27-34.
[56]E.Bleszynski.AIM:adaptive integral method for solving large-scale electromagnetic scattering and radiation problems.Radio Science,1996,31(5):1225-1251.
[57]胡俊.复杂目标矢量电磁散射的高效方法-快速多极子方法及其应用.博士学位论文.成都:电子科技大学,2000.
[58]王浩刚.电大尺寸含腔复杂目标矢量电磁散射一体化精确建模与高效算法研究.博士学位论文,成都:电子科技大学,2001.
[59]胡俊,聂在平,王军.三维电大目标散射求解的多层快速多极子方法.电波科学学报,2004,19(5):509-514.
[60]聂在平,胡俊,姚海英,王浩刚.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.
[61]陆卫兵.复杂电磁问题的快速算法研究和软件实现.博士学位论文.南京:东南大学,2005.
[62]盛新庆.计算电磁学要论.科学出版社,2004.
[63]W.C.Chew,T.J.Cui,J.M.Song.A FAFFA-MLFMA algorithm for electromagnetic scattering.IEEE Tram Antennas and Propagat.,2002,50(11):1641-1649.
[64]T.J.Cui,W.C.Chew,G.Chen and J.J.Song.Efficient MLFMA,RPFMA,and FAFFA algorithm for EM scattering by very large:structures.IEEE Trans.Antennas Propagat.,2004,52(3):759-770.
[65]胡俊,聂在平,雷霖,王军.三维局部快速多极子算法.系统工程与电子技术,2006,28(3):329-330.
[66]J.H.Richmond.A wire-grid for scattering by conducting bodies.IEEE Trans.Antennas Propagat.,1966,14(6):782-786.
[67]Y.T.Lin and J.H.Richmond.EM modeling of aircraft at low frequencies.IEEE Trans.Antennas Propagat.,1975,23(1):53-56.
[68]J.H.Richmonda dn D.M.Pozar.Rigorous near-zone field expressions for rectangular sinusoidal surface monopole.IEEE Trans.Antennas Propagat.,1978,26(3):509-510.
[69]J.Hu,Z.P.Nie and X.D.Gong.Sovling electromagnetic scattering and radiation by FMM with curvilinear RWG basis.Chinese Journal of Electronics.2003,12(3):457-460.
[70]K.C.Donepudi,K.Gang,J.M.Song,etc.Higher-order MoM implement to solve integral equations.IEEEAP-S 1999,1716-1719.
[71]J.M.Song and W.C.Chew.Moment method solution using parametric geometry.Journal of Electromagnetic Wave and Applications,1995,9(1/2):71-83.
[72]M.I.Sancer,R.L.Mcclary and K.J.Glover.Electromagnetic computation using parametric geometry.Electromagnetics,1990,10:85-103.
[73]J.Perez,J.A.Saiz and O.M.Conde.Analysis of antennas on board arbitrary structures modeled by NURBS surfaces.IEEE Trans.Antennas Propagat.,1997,45(6):1045-1053.
[74]M.Chen,Y.Zhang,X.W.Zhao and C.H.Liang.Analysis of antenna around NURBS surface with hybrid MoM-PO technique.IEEE Trans.Antennas Propagat.,55(2):407-412.
[75]L.Valle,F.Rivas and M.F.Catedra.Combining the moment method with geometrical modeling by NURBS surfaces and Bezier patches.IEEE Trans.Antennas Propagat.,1994,42(3):373-381.
[76]陈维恒.微分几何初步.北京大学出版社,1990.
[77]L.Matekovits,G.Vecchi,G.Dassano and M.Orefice.Synthetic function analysis of large printed structures:the solution space sampling approach.2001 IEEE AP-S Int.Symp.,Jul.2001,pp.568-571,Boston,MA.
[78]V.V.S.Prakash and R.Mittra.Characteristic basis function method:a new technique for fast solution of integral equations.Microwave and Optical Technology Letters,2003,36(2):95-100.
[79]W.B.Lu,T.J.Cui,Z.G.Qian,X.X.Yin and W.Hong.Accurate analysis of large-scale periodic structures using an efficient sub-entire-domain basis function method.IEEE Trans.Antennas Propagat.,2004,52(11):3078-3085.
[80]J.M.Song and W.C.Chew.Moment method solution using parametric geometry.Journal of Electromagnetic Wave and Applications,1995,9(1/2):71-83.
[81]E.H.Newman,P.Alexandropoulos,E.K.Walton.Polygonal plate modeling of realistic structure.IEEE Tram.Antennas Propagat.,1984,32(7):742-747.
[82]E.H.Newman.Polygonal plate modeling.Electroomagnetics,1990,10(2):65-83.
[83]E.Jorgensen,J.L.Volakis,P.Meincke,et al.Higher order hierarchical discretization scheme for surface integral equations for layered media.IEEE Trans.Geoscience and Remote Sensing,2004,42(4):764-772.
[84]D.R.Wilton,S.M.Rao and A.W.Glisson.Potential integrals for uniform and linear source distributions on polygonal and polyhedral domains.IEEE Trans.Antennas Propagat.,1984,32(3):276-281.
[85]R.D.Graglia.On the numerical integration of the linear shape functions times the 3-D Green's function or its gradient on a plane triangle.IEEE Trans.Antennas Propagat.,1993,41(10):1448-1455.
[86]M.G.Duffy.Quadrature over a pyramid or cube of integrands with a singularity at a vertex.J.Numer.Anal,1982,19(6):1260-1262.
[87]王浩刚,聂在平.三维矢量散射积分方程中奇异性分析.电子学报,27(12):68-71.
[88]姚海英,聂在平.三维矢量散射分析中奇异积分的准确积分方法.电子与信息学报.2000,22(3):471-477.
[89]C.Esmith,A.Epeterson and R.Mittra.The biconjugate gradient method for electromagnetic scattering.IEEE Trans.Antennas Propagat.,1990,938-940.
[90]T.K.Sarkar.On the application of the generalized biconjugate gradient method.Journal of electromagnetic waves and applications,1987,1(3):223-242.
[91]Y.Saad,Iterative methods for sparse linear systems,PWS Publishing Company,Boston,1996.
[92]A.C.Woo,H.T.G.Wang,M.J.Schuh and M.L.Sander.Benchmark radar targets for the validation of computational electromagnetics programs.IEEE Trans.Antennas and Propagation Magazine,1993,35(1):84-89.
[93]姚海英.介质以及涂敷介质结构电磁散射特性的基础研究.积分放出法及其快速求解。博士学位论文.成都:电子科技大学,2002.
[94]S.M.Rao,T.K.Sarkar,E Midya and A.R.Djordevic.Electromagnetic radiation and scattering from finite conducting and dielectric structures:surface/surface formulation.IEEE Trans.Antennas Propagat.,1991,39(7):1034-1037.
[95]A.Taflove and K.Umashankar.Radar cross section of general three-dimensional scatterers.IEEE Trans.Eleetromagn.Compat.,1983,vol.EMC-25(4):433-440.
[96] X. Q. Sheng, J. M. Jin, J. M. Song, W. C. Chew and C. C. Lu. On the formulation of hybrid finite-element and boundary-integral methods for 3-D scattering. IEEE Trans. Antennas Propagat., 1998,46(3): 303-311.
[97] S. Y. Chen, W. C. Chew, J. M. Song and J. S. Zhao. Analysis of low freqency scattering from penetrable scatterers. IEEE Trans on Geoscience and Remote Sensionng, 39(4): 726-735.
[98] J. S. Zhao and W. C. Chew. Integral equation solution of maxwell's equations from zero frequency to microwave frequencies. IEEE Trans. Antennas Propagat., 2000, 48(1):1635-1645.
[99] Y. H. Chu and W. C. Chew. A surface integral equation method for solving complicated electrically small structures. Electrical Performance of Electronic Packeaging 2003, pp:341-344.
[100] Y. Chu and W. C. Chew. A multi-level fast multipole algorithm for low-frequency scattering from a composite object. IEEE AP-S, 2003: 43-46
[101] Y. Chu, W. C. Chew, J. S. Zhao and S. Y. Chen. A surface integral equation formulation for low-frequency scattering from a composite object. IEEE Trans. Antennas Propagat., 2003,51(10): 2837-2844
[102] S. D. Gedney and R. Mittra. The use of the FFT for the efficient solution of the problem of electromagnetic scattering by a body of revolution. Microwave and Optical Technology Letters, 1990,15(3): 313-322.
[103] Z. Q. Zhang, Q. H. Liu, X. M. Xu. RCS computation of large inhomogeneous objets using a fast integral equation solver. IEEE Trans. Antennas Propagat., 2003,51(3): 613-618.
[104] J. R. Phillips and J. K. White. A precorrected-FFT method for electrostatic analysis of complicated 3-D strucures. IEEE Trans Computer-Aided Design Integr Circ Sys. 1997, 16:1059-1072.
[105] X. C. Nie, L. W. Li and N. Yuan. Fast analysis of scattering by arbitrarily shaped three-Dimensional objects using the precorected-FFT method. Microwave and Optical Technology Letters, 2002, 34: 438-44.
[106] X. C. Nie, L. W. Li, N. Yuan, etc. A fast analysis of electromagnetic scattering by arbitrarily shaped homogeneous dielectric objects. 2003, 38(1): 30-35.
[107] C. C. Lu. Dielectric radome analysis using multilevel fast multipole algorithm. IEEE AP-S,2000,pp:730-733.
[108] C. C. Lu and W. C. Chew. A coupled surface-volume integral equation approach for the calculation of Electromagnetic scattering from composite metallic and material targets. IEEE Trans. Antennas Propagat., 2001,48(12): 1866-1868.
[109] S. Koc, J. M. Song and W. C. Chew. Error analysis for the multilevel fast multipole algorithm.IEEE AP-S, 1998, vol. 3, pp: 1758-1761.
[110] M. Abramowitz and I. A. Stegun, Handbook of mathematical functions. New York: Dover,1970.
[111] N. Geng, A.. Sullivan and L. Carin. Fast multipole method for scatering from an arbitrary PEC target above or buried in a lossy half space, IEEE Trans. Antennas Propagat., 2001,49(5):740-748.
[112] N. Geng, A. Sullivan and L. Carin. Multilevel fast-multipole algorithm for Scatering from conducting target s above or embedded in a lossy half space, IEEE Trans. Antennas Propagat.,2000, 38(4): 1561-1573.
[113] J. F. Lee, J. Zhang and C. C. Lu. Sparse inverse preconditioning of multilevel fast multipole algorithm for hybrid integral equations in electromagnetics. IEEE Trans. Antennas Propagat.,2004, 52(9): 2277-2286.
[114] Y. J. Xie, J. He, A. Sullivan and L Carin. A simple preonditioner for electric-field integral equations. Microwave and Optical Technology Letters, 2001,30(1): 51-54.
[115] Z. Y. Niu and J. P. Xu. Near-field sparse inverse preconditioning of multilevel fast multipole algorithm for electric field integral equations. APMC 2005, vol. 3, pp: 1879-1883.
[116] P. L. Rui and R. S. Chen. An efficient sparse approximate inverse preconditioning for FMM implementation. Microwave and Optical Technology Letters, 2006,49(7): 1746-1750.
[117] E. Chow. A priori sparsity patterns for parallel sparse approximate inverse preconditioners.SIAM J.. Sci. Stat. Comput., 2000, 21(5): 1804-1822.
[118] M. Grote and T. Huckle. Parallel preconditioning with sparse approximate inverses. SIAM J.Sci. Stat. Comput., 1997,18(3): 838-853.
[119] B. Carpentieri, I. S. Duff and L. Giraud. Experiments with sparse preconditioning of dense problems from electromagnetic applications. Technical Report TR/PA/00/04, CEPFACS,Toulouse, France, 2000.
[120] K. Sertel, J. L. Volakis. Incomplete LU preconditioner for FMM implementation. Micro. Opt.Tech. Lett., 2000, 26(7): 265-267.
[121] Y. Saad. ILUT: a dual threshold incomplete LU factorization. Numer. Linear Algebra Appl,1994,1(4): 387-402.
[122] J. F. Lee, J. Zhang and C. C. Lu. Incomplete LU preconditioner for large scale dense complex linear systems from electromagnetic wave scattering problems. J. Comput. Phys., 2003,185(1): 158-175.
[123] P. L. Rui, R. S. Chen, Z. H. Fan. Perturbed incomplete ILU preconditioner for efficient solution of electric field integral equations. IET Microw. Antennas Propag., 2007, 1(5):1059-1063.
[124] R. D. Graglia, D. R. Wilton and A. F. Peterson. Higher order interpolatory Vector Bases for Computational Electromagnetics. IEEE Trans. Antennas Propagat., 1997,45(3):329-342.
[125] J. D. Savage and A. F. Peterson. Higher-order vector finite elements for tetrahedral cells.IEEE Trans. Microwave Theory and Techniques, 1996,44(6): 874-879.
[126] L. S. Andersen and J. L. Volakis. Development and application of a novel class of hierarchical tangential vector finite elements for electromagnetics. IEEE Trans. Antennas Propagat.,1999,47(1): 112-120.
[127] J. Liu and J. M. Jin. A novel hybridization of higher order finite element and boundary integral methods for electromagnetic scattering and radiation problems. IEEE Trans. Antennas Propagat., 2001,49(11): 1794-1806.
[128] J. P. Webb. Hierarchical vector basis functions of arbitrary order for triangular and tetrahedral finite elements. IEEE Trans. Antennas Propagat., 1999,47(8): 1244-1253.
[129] L. R. Hamilton, P. A. Macdonald, et al, Electromagnetic scattering computations using high-order basis functions in the method of moments. IEEE AP-S, vol.3, pp: 2166-2169.
[130] G Kang, J. M. Song, W. C. Chew, etc. Grid-robust higher-order vector basis functions for solving integral equations. IEEE AP-S 2001, Salt Lake City, pp: 468-471.
[131] K. C. Donepudi, J. M. Jin, J. M. Song and W. C. Chew. A higher order parallelized multilevel fast multipole algorithm for 3-D scattering, IEEE Trans. Antennas Propagat., 2001, 49(7):1069-1078.
[132]K.C.Donepudi,J.M.Jin and W.C.Chew.A higher order multilevel fast multipole algorithm for scattering from mixed conducting/dielectric bodies.IEEE Trans.Antennas Propagat.,2003,51(10):2814-2821.
[133]K.Sertel and J.L.Volakis.Method of moments solution of volume integral equations using parametric geometry modeling.Radio Science,2002,37(1):1-7.
[134]E.Jorgensen,J.L.Volakis,P.Meincke,et al.Higher order hierarchical Legendre basis functions for electromagnetic modeling.IEEE Trans.Antennas Propagat.,2004,52(11):2985-2995.
[135]E.Jorgensen,J.L.Volakis,P.Meineke,et al.Higher order hierarchical discretization scheme for surface integral equations for layered media.IEEE Trans.Geoscience and Remote Sensing,2004,42(4):764-772.
[136]E.Jorgensen,J.L.Volakis,P.Meineke,et al.Higher order hierarchical Legendre basis functions for iterative integral equation solvers with curvilinear surface modeling.IEEE AP-S,2002,vol:4,pp:618-621.
[137]E.Jorgensen,P.Meincke,and O.Breinbjerg.A hybrid Po-higher-order hierarchical MoM formulation using curvilinear geometry modeling.IEEE AP-S,2003,pp:98-101.
[138]D.S.Sumic and B.M.Kolundzija.Efficient iterative solution of surface integral equations based on maximally orthogonalized higher order basis functions.IEEE AP-S,2005.
[139]任仪,聂在平,赵延文,马文敏.矩量法中阻抗矩阵的稀疏化研究.电子学报.2007,35(12):2354-2358.
[140]A.F.Peterson,S.L.Ray and R.Mittra.Computational methods for electromagnetics.New York:IEEE Press,1998.
[141]R.J.Adams.Physical and analytical properties of a stabilized electric field integral equation.IEEE Trans.Antennas Propagat.,2004,52(2):362-372.
[142]R.J.Adams and N.J.Champagne.A numerical implementation of a modified form of the electric field integral equation.IEEE Trans.Antennas Propagat.,2004,52(9):2262-2266.
[143]H.Contopanagos,B.Dembart,M.Epton.,etc.Well-conditioned boundary integral equations for three-dimensional electromagnetic scattering.IEEE Trans.Antennas Propagat.,2003,50(12):1824-1830.
[144]J.Hu,Z.P.Nie,L.Lei,etc.A modified electric field integral equation for 3D electromagnetic scattering.Asia-Pacific Microwave Conference Proceedings,Suzhou,China:2005:2216-2219.
[145]Jun Hu,Z P Nie,etc.A modified electric field integral equation for 3D electromagnetic scattering.IEEE AP-S 2005.
[146]L.J.Tian,J.Hu,Z.P.Nie.An improved EFIE for composite geometries involving open and closed conducing surfaces.IEEE AP-S 2007:4873-4876.
[147]闫玉波,李清亮,复杂载体短波天线特性的FDTD模拟与分析.电波科学学报,2004,19(2):135-142.
[148]邓维波,刘永坦.FDTD法计算高频单极天线特性.电波科学学报,2000,15(4):491-495.
[149]I.Tekin and E.H.Newman.Method of moments solution for a wire attached to an arbitrary faceted surface.IEEE Trans.Antennas Propagat.,1998,46(4):559-562.
[150]Z.P.Nie,W.C.Chew and Y.Z.Lo.Analysis of the annular -ring-loaded circular-disk mierostrip antenna.IEEE Trans.Antennas Propagat.,1990,38(6):806-813.
[151]W.C.Chew.Analysis of a probe-fed microstrip disk antenna.IEE Proceedings-H.1991,138(2):185-191.
[152]B.M.Kolundzija and B.D.Popovic.General localized junction model in the analysis of wire-to plate junctions.IEE Proe.-Microw.AE,141(1):1-7.
[153]H.Y.Chao,J.S.Zhao and W.C.Chew.Application of curvilinear basis functions and MLFMA for radiation and scattering problems involving curved PEC structures.IEEE Trans.Antennas Propagat.,2003,51(2):331-336.
[154]万继响,张玉,梁吕洪,任意导体与线大线连接问题的MoM分析.电波科学学报,2003,18(5):523-528.
[155]宗卫华,万继响,梁昌洪.导体线面连接问题中奇异函数积分的计算.微波学报,2004,20(1):6-9.
[156]J.M.Taboada.Evaluation of galerkin integrals involving triangular-type wire-surface junctions in the method of moments.IEEE Trans.Antennas Propagat.,2004,52(10):2785-2789.
[157]郭景丽,刘其中,纪奕才,精确分析任意导体地面上的套简单极子天线,电波科学学报,2004,19(5):613-617.
[158]H.Y.Chao,J.M.Song,E.Michielssen and W.C.Chew.The MLFMA for analyzing electromagnetic radiation from complex surface-wire structures.In Proc.of Antenna Appl.Syrup.1998:291-303.
[159]H.Y.Chao,K.Pirapaharan,W.C.Chew,et al.Simulation of vehicle antennas by the MLFMA.IEEE AP-S,2002,pp:18-20.
[160]H.Y.Chao.The multilevel fast multipole algorithm for electromagnetic compatibility analysis.IEEE International Symposium on Electromagnetic Compatibility,1999,vol.2,pp:844-847.
[161]H.Y.Chao,W.C.Chew,J.M.Song and E.Michielssen.Impedance calculation of complex surfaces-wire structures with multilevel fast multipole algorithm and variational formulation.IEEE AP-S,1999,vol.3,pp:1848-1850.
[162]H.Y.Chao,S.Y.Chen,W.C.Chew,etc.An application-independent multilevel fast multipole code for the analysis of eurvilinear surfaces with wire attachment.IEEE AP-S,2000,vol.4,pp:1880-1883.
[163]E.P.Ekelman,G.A.Thiele.A hybrid technique for combining the moment method treatment of wire antenna with the GTD for curved surfaces.IEEE Trans.Antennas Propagat.,1980,28(11):831-839.
[164]F.Obelleiro,J.M.Taoada,J.L.Rodriguez and J.M.Bertolo.HEMCUVI:A software package for the electromagnetic analysis and design of radiating systems on board real platforms.IEEE AP Magazine,2002,44(5):44-61.
[165]U.Jakobus and F.J.C.Meyer.A hybrid physical optics/method of moments numerical technique:theory,investigation and application.IEEE 4th Africon Symposium,vol.1,pp:24-27.
[166]U.Jakobus and F.M.Landstoffer.Improved PO-MM hybrid formulation for scattering from three-dimensional perfectly conducting bodies of arbitrary shape.IEEE Trans.Antennas Propagnt.,1995,43(2):162-169.
[167]J.Erik,M.Peter and B.Olav.A hybrid PO-higher-order hierarchical MoM formulation using eurvilinear geometry modeling.IEEE A.P-S,2003,pp:98-101.
[168]M.Djordjevic and B.M.Notaros.Higher order hybrid method of moments-physical optics modeling technique for radiation and scattering from large perfectly conducting surfaces.IEEE Trans.Antennas Propagat.,2005,53(2):800-813.
[169]J.M.taboada,F.Obelleiro and J.L.Rodriguez.Improvement of the hybrid moment-method-physical-optics method through a novel evaluation of the physical optics operator.Microwave and Optical Technology Letters,2001,30(5):357-363.
[170]E.H.Rcihard and R.S.Yahya.An iterative current-based hybrid method for complex structures.IEEE Trans.Antennas Propagat.,1997,45(2):265-276.
[171]华夷和,徐金平,牛臻弋.FAFFA加速的PO-MM研究复杂金属载体上线天线电磁特性.电子学报,2003,31(12):2045-2049.
[172]牛臻弋,王文博,徐金平.PO-MoM结合近场预条件技术分析复杂载体上线天线辐射特性.东南大学学报,2005,35(4)514-518.
[173]R.W.P.King,The Theory of Linear Antenna.Boston,MA:Harvard Univ.Press,1956,p.20.
[174]S.Bhattacharya,S.A.Long,and D.R.Wilton,The input impedance ofa monopole antenna mounted on a cubical conducting box.IEEE Trans.Antennas Propagat.,1987,35(7):756-762.
[175]J.C.G.Matthews and G.G.Cook,An efficient method for attaching thin wire monopoles to surfaces modeled using triangular patch segmentation.IEEE Trans.Antennas Propagat.,2003,51(7):1623-1629.
[176]T.J.Cui,W.C.Chew,J.S.Zhao and H.Y.Chao.Full-wave analysis of complicated transmission line circuits using wire models.IEEE Trans.Antennas Propagat.,2002,50(10):1350-1360.
[177]G.P.Junker,A.W.Glisson and A.A.Kishk.Accurate impedance model for antiresonant monopoles on finite group planes.Electronic Letters,1996,32(18):1632-1633.
[178]L.L.Tsai.A numerical solution for the near and far fields of an annular ring of magnetic current.IEEE Trans.Antennas Propagat.,1972,20(5):569-576.
[179]K.C.Donepudi,J.M.Song,J.M.Jin and W.C.Chew.Point-based implementation of multilevel fast multipole algorithm for higher-order Galerkin's method.IEEE AP-S,2000,pp:476-479.
[2]K.S.Yee,J.S.Chen,and A.H.Chang.Conformal finite-difference time-domain(FDTD) with overlapping grids.IEEE Trans.Antennas Propagat.,1992,40(2):1068-1075.
[3]A.Taflve.Computational electrodynamics:the finite-difference time-domain Method.Norwood,MA:Artech House,1995.
[4]金建铭.电磁场有限元方法.西安电子科技大学出版社,1998.
[5]R.F.Harrington.Time-harmonic electromagnetic fields.McGraw-Hill Book Company,New York,1961.
[6]R.F.Harrington.Field computation by moment methods.McMillan,New York,1968.
[7]李世智.电磁散射与辐射问题的矩量法.电子工业出版社,1985.
[8]A.W.Glisson and D.R.Wilton.Simple and efficient numerical methods for problems of electromagnetic radiation and scattering from surfaces.IEEE Trans.Antennas Propagat.,1980,28(5):593-603.
[9]S.M.Rao,D.R.Wilton and A.W.Glisson.Electromagnetic scattering by surfaces of arbitrary shape.IEEE Trans.Antennas Propagat.,1982,30(5):409-418.
[10]J.J.H.Wang.Generalized moment methods in electromagnetics:formulation and computer solution of integral equations.John Wiley & Sons,Inc.,1991.
[11]H.Schaubert,D.R.Wilton and A.W.Glisson.A tetrahedral modeling method for electromagnetic scattering by arbitrary shaped inhomogeneous dielectric bodies.IEEE Trans.Antennas Propagat.,1984,32(1):77-85.
[12]M.F.Catedra,E.Gago and L.Nulo.A numerical scheme to obtain the RCS of three dimensional bodies of resonant size using the conjugate gradient method and the fast fourier transform.IEEE Trans.Antennas Propagat.,1989,37(5):528-537.
[13]H.Gan and W.C.Chew.A discrete BCG-FFT algorithm for solving 3D inhomogeneous scatter problems.J.Electromag.Waves Appl.,1995,9(10):1339-1357.
[14]C.C.Lu,J.M.Song and W.C.Chew.Multilevel fast multipole algorithm for solving 3D volume integral equations of electromagnetic scattering.AP-S,2000(4):1864-1867.
[15]J.L.Guo,J.Y.Li and Q.Z.Liu.Analysis of arbitrarily shaped dielectric radomes using adaptive integral method based on volume integral equation.IEEE Trans.Antennas Propagat.,2006,54(7):1910-1916.
[16]H.Y.Yao,X.Q.Sheng,K.N.Yung and Z.P.Nie.Analysis of scattering by finite periodic dielectric structures using TFQMR-FFT.Microwave and Optical Technology Letters,2001,10(1):221-224.
[17]C.Muller.Foundations of the Mathematical Theory of Electromagnetic Waves.New York:Spinger,1969.
[18]J.R.Mautz and R.F.Harrington.Electromagnetic scattering from a homogeneous materical body of revolution.AEU,1979,33(2):71-80.
[19]A.J.Poggio and E.K.Miller.Integral equation solutions of three-dimensional scattering problems.In Computer Techniques for Electromagnetics,R.Mittra,Ed.Oxford:Pergamon Press,1973,Chap.4.
[20]T.K.Wu and L.L.Tsai.Scattering from arbitrarily-shaped lossy dielectric bodies of revolution.Radio Sci.,1997,vol.12,709-718.
[21]R.F.Harrington.Boundary integral formulations for homogeneous material bodies.J.Electromagn.Waves Applicat.,1989,3(1):1-15.
[22]Y.Chung and R.F.Harrington.A surface formulation for characteristic modes of material bodies.IEEE Trans.Antennas Propagat.,1977,25(11):789-795.
[23]S.M.Rao and D.R.Wilton.E-field,H-field,and combined field solution for arbitrarily shaped three-dimensional dielectric bodies.Electromagn.,1990,10(4):407-421.
[24]X.Q.Sheng,J.M.Jin,J.M.Song,W.C.Chew and C.C.Lu.Solution of combined-field integral equation using multilevel fast multipole algorithm for scattering by homogeneous bodies.IEEE Trans.Antennas Propagat.,1998,46(11):1718-1726.
[25]P.Yla-Oijala.Application of a novel CFIE for electromagnetic scattering by dielectric objects.Microwave and Optical Technology Letters,2002,35(10):3-5.
[26]P.Yla-Oijala and T Matti.Applieatinn of combined field integral equation for electromagnetic scattering by dielectric and composite objects.IEEE Trans.Antennas Propagat.,2003,53(3):1168-1173.
[27]P.Yla-Oijala and T Matti.Improving conditioning of electromagnetic surface integral equations using normalized field quantifies.IEEE Trans.Antennas Propagat.,2007,55(1):178-185.
[28]P.Yla-Oijala,M Taskinen and J Sarvas.Surface integral equation method for general composite metallic and dielectric structures with junctions.Progress in Electromagnetic Research,2005,52:81-108.
[29]P.Yla-Oijala and M.Taskinen.Well-conditioned Muller formulation for electromagnetic scattering by dielectric objects.IEEE Trans.Antennas Propagat.,2005.53(10):3316-3323.
[30]A.W.Glisson.An integral equation for electromagnetic scattering from homogeneous dielectric bodies.IEEE Trans.Antennas Propagat.,1984,32(2):172-175.
[31]M.S.Yeung.Single integral equation for electromagnetic scattering by three-dimensional homogeneous dielectric objects.IEEE Trans.Antennas Propagat.,1999,47(10):1615-1622.
[32]阙肖峰,聂在平,胡俊.基于混合场积分方程MLFMA分析导体介质复合目标电磁散射问题.电子学报,2007,35(11):2062-2066.
[33]J.M.Putman and L.N.Medgyesi-Mitschang.Combined field integral equation for inhomogeneous two- and three-dimensional bodies:The junction problem.IEEE Trans.Antennas Propagat.,1991,39(5):667-672.
[34]M.Carr,E.Topsakal and J.L.Volakis.A procedure for modeling material junctions in 3-D surface integral equation approaches.IEEE Trans.Antennas Propagat.,2004,52(5):1374-1379.
[35]B.M.Kolundzija.Electromagnetic modeling of composite metallic and dielectric structures.IEEE Trans.Microwave Theory and Techniques,1999,47(7):1021-1032.
[36]S.Y.Chen,J.S.Zhao and W.C.Chew.Analyzing low-frequency electromagnetic scattering from a composite object.IEEE Trans.Geoscience and Remot Sensing,2002,40(2):426-433.
[37]W.C.Chew,J.M.Jin,E.Miehielssen and J.M.Song.Fast and efficient algorithms in computational electromagnetics.Artech House,Boston,2001.
[38]J.Hu and Z.P.Nie.Improved electric field integral equation for analysis of scattering from 3-D conducting structures.IEEE Trans Electromagnetic Compatibility,2007,49(3):644-648.
[39]E.H.Newman and D.M.Pozar,Electromagnetic modeling of composite wire and surface geometries.IEEE Trans.Antennas Propagat.,1978,26(6):784-789.
[40]E.H.Newman and D.M.Pozar.Considerations for efficient wire/surface modeling.IEEE Trans.Antennas Propagat.,1980,28(1):121-125.
[41]D.M.Pozar and E.H.Newman.Analysis ofa monopole mounted near an edge or a vertex.IEEE Trans.Antennas Propagat.,1982,30(5):401-408.
[42]M.E Costa,R.F.Harrington,Minimization of radiation from computer systems.Int.Elect.Electron.Conference and Exposition Proc.,1983:660-665.
[43]S.U.Hwu,D.R.Wilton and S.M.Rao.Electromagnetic scattering and radiation by arbitrary conducting wire/surface configurations.IEEE AP-S,1988.
[44]逯贵祯,刘永俊,毛志及.位于任意形状导体上的天线输入阻抗分析.电波科学学报,1995,10(1):128-130.
[45]V.Rokhlin.Rapid solution of integral equations of scattering theory in two dimensions.Journal of Computational physics,1990,86:414-437.
[46]B.Dembart and E.Yip.A 3-D fast multipole method for electromagnetics with multipole levels.11~(th) Annu.Rev.progress Appl.Computat.Electromagn.,Monterery,CA,1995:621-628.
[47]N.Engheta,W.D.Murphy,V.Rokhlin,etc.The fast multipole method(FMM) for electromagnetic scattering problems.IEEE Trans.Antennas Propagat.,1992,40(6):634-641.
[48]R.Coifman,V.Rokhlin,S.Wandzura.The fast multipole method for the wave equation:a pedestrian prescription.IEEE AP magazine.1993,25(3):7-12.
[49]Sunil S.Bindiganavale and J.L.Volakis.Guidelines for using the fast multipole method to calculate the RCS of large objects.Microwave and Optical Technology Letters,1996,11(4):190-194.
[50]C.C.Lu,W.C.Chew.Fast algorithm for solving hybrid integral equations.IEEE proceedings-H,1993,140(6):455-460.
[51]J.M.Song and W.C.Chew.Fast multipole method solution using parametric geometry.Microwave and Optical Technology Letters,1994,7(16):760-765.
[52]J.M.Song,C.C.Lu and W.C.Chew.Multilevel fast multipole algorithm for electromagnetic scattering by large complex objects.IEEE Trans.Antennas Propagat.,1997,45(10):1488-1498.
[53]J.M.Song and W.C.Chew.Multilevel fast-multipole algorithm for solving combined field integral equations of electromagnetic scattering.Microwave and Optical Technology Letters,1995,8(1):14-19.
[54]J.M.Song and W.C.Chew.A multilevel algorithm for solving a boundary integral equation of wave scattering.Microwave and Optical Technology Letters,1994,7(10):466-470.
[55]J.M.Song,C.C.Lu and W.C.Chew.Fast Illinois Solver Code(FISC).IEEE Trans.Antennas Propagat.,1998,40(3):27-34.
[56]E.Bleszynski.AIM:adaptive integral method for solving large-scale electromagnetic scattering and radiation problems.Radio Science,1996,31(5):1225-1251.
[57]胡俊.复杂目标矢量电磁散射的高效方法-快速多极子方法及其应用.博士学位论文.成都:电子科技大学,2000.
[58]王浩刚.电大尺寸含腔复杂目标矢量电磁散射一体化精确建模与高效算法研究.博士学位论文,成都:电子科技大学,2001.
[59]胡俊,聂在平,王军.三维电大目标散射求解的多层快速多极子方法.电波科学学报,2004,19(5):509-514.
[60]聂在平,胡俊,姚海英,王浩刚.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.
[61]陆卫兵.复杂电磁问题的快速算法研究和软件实现.博士学位论文.南京:东南大学,2005.
[62]盛新庆.计算电磁学要论.科学出版社,2004.
[63]W.C.Chew,T.J.Cui,J.M.Song.A FAFFA-MLFMA algorithm for electromagnetic scattering.IEEE Tram Antennas and Propagat.,2002,50(11):1641-1649.
[64]T.J.Cui,W.C.Chew,G.Chen and J.J.Song.Efficient MLFMA,RPFMA,and FAFFA algorithm for EM scattering by very large:structures.IEEE Trans.Antennas Propagat.,2004,52(3):759-770.
[65]胡俊,聂在平,雷霖,王军.三维局部快速多极子算法.系统工程与电子技术,2006,28(3):329-330.
[66]J.H.Richmond.A wire-grid for scattering by conducting bodies.IEEE Trans.Antennas Propagat.,1966,14(6):782-786.
[67]Y.T.Lin and J.H.Richmond.EM modeling of aircraft at low frequencies.IEEE Trans.Antennas Propagat.,1975,23(1):53-56.
[68]J.H.Richmonda dn D.M.Pozar.Rigorous near-zone field expressions for rectangular sinusoidal surface monopole.IEEE Trans.Antennas Propagat.,1978,26(3):509-510.
[69]J.Hu,Z.P.Nie and X.D.Gong.Sovling electromagnetic scattering and radiation by FMM with curvilinear RWG basis.Chinese Journal of Electronics.2003,12(3):457-460.
[70]K.C.Donepudi,K.Gang,J.M.Song,etc.Higher-order MoM implement to solve integral equations.IEEEAP-S 1999,1716-1719.
[71]J.M.Song and W.C.Chew.Moment method solution using parametric geometry.Journal of Electromagnetic Wave and Applications,1995,9(1/2):71-83.
[72]M.I.Sancer,R.L.Mcclary and K.J.Glover.Electromagnetic computation using parametric geometry.Electromagnetics,1990,10:85-103.
[73]J.Perez,J.A.Saiz and O.M.Conde.Analysis of antennas on board arbitrary structures modeled by NURBS surfaces.IEEE Trans.Antennas Propagat.,1997,45(6):1045-1053.
[74]M.Chen,Y.Zhang,X.W.Zhao and C.H.Liang.Analysis of antenna around NURBS surface with hybrid MoM-PO technique.IEEE Trans.Antennas Propagat.,55(2):407-412.
[75]L.Valle,F.Rivas and M.F.Catedra.Combining the moment method with geometrical modeling by NURBS surfaces and Bezier patches.IEEE Trans.Antennas Propagat.,1994,42(3):373-381.
[76]陈维恒.微分几何初步.北京大学出版社,1990.
[77]L.Matekovits,G.Vecchi,G.Dassano and M.Orefice.Synthetic function analysis of large printed structures:the solution space sampling approach.2001 IEEE AP-S Int.Symp.,Jul.2001,pp.568-571,Boston,MA.
[78]V.V.S.Prakash and R.Mittra.Characteristic basis function method:a new technique for fast solution of integral equations.Microwave and Optical Technology Letters,2003,36(2):95-100.
[79]W.B.Lu,T.J.Cui,Z.G.Qian,X.X.Yin and W.Hong.Accurate analysis of large-scale periodic structures using an efficient sub-entire-domain basis function method.IEEE Trans.Antennas Propagat.,2004,52(11):3078-3085.
[80]J.M.Song and W.C.Chew.Moment method solution using parametric geometry.Journal of Electromagnetic Wave and Applications,1995,9(1/2):71-83.
[81]E.H.Newman,P.Alexandropoulos,E.K.Walton.Polygonal plate modeling of realistic structure.IEEE Tram.Antennas Propagat.,1984,32(7):742-747.
[82]E.H.Newman.Polygonal plate modeling.Electroomagnetics,1990,10(2):65-83.
[83]E.Jorgensen,J.L.Volakis,P.Meincke,et al.Higher order hierarchical discretization scheme for surface integral equations for layered media.IEEE Trans.Geoscience and Remote Sensing,2004,42(4):764-772.
[84]D.R.Wilton,S.M.Rao and A.W.Glisson.Potential integrals for uniform and linear source distributions on polygonal and polyhedral domains.IEEE Trans.Antennas Propagat.,1984,32(3):276-281.
[85]R.D.Graglia.On the numerical integration of the linear shape functions times the 3-D Green's function or its gradient on a plane triangle.IEEE Trans.Antennas Propagat.,1993,41(10):1448-1455.
[86]M.G.Duffy.Quadrature over a pyramid or cube of integrands with a singularity at a vertex.J.Numer.Anal,1982,19(6):1260-1262.
[87]王浩刚,聂在平.三维矢量散射积分方程中奇异性分析.电子学报,27(12):68-71.
[88]姚海英,聂在平.三维矢量散射分析中奇异积分的准确积分方法.电子与信息学报.2000,22(3):471-477.
[89]C.Esmith,A.Epeterson and R.Mittra.The biconjugate gradient method for electromagnetic scattering.IEEE Trans.Antennas Propagat.,1990,938-940.
[90]T.K.Sarkar.On the application of the generalized biconjugate gradient method.Journal of electromagnetic waves and applications,1987,1(3):223-242.
[91]Y.Saad,Iterative methods for sparse linear systems,PWS Publishing Company,Boston,1996.
[92]A.C.Woo,H.T.G.Wang,M.J.Schuh and M.L.Sander.Benchmark radar targets for the validation of computational electromagnetics programs.IEEE Trans.Antennas and Propagation Magazine,1993,35(1):84-89.
[93]姚海英.介质以及涂敷介质结构电磁散射特性的基础研究.积分放出法及其快速求解。博士学位论文.成都:电子科技大学,2002.
[94]S.M.Rao,T.K.Sarkar,E Midya and A.R.Djordevic.Electromagnetic radiation and scattering from finite conducting and dielectric structures:surface/surface formulation.IEEE Trans.Antennas Propagat.,1991,39(7):1034-1037.
[95]A.Taflove and K.Umashankar.Radar cross section of general three-dimensional scatterers.IEEE Trans.Eleetromagn.Compat.,1983,vol.EMC-25(4):433-440.
[96] X. Q. Sheng, J. M. Jin, J. M. Song, W. C. Chew and C. C. Lu. On the formulation of hybrid finite-element and boundary-integral methods for 3-D scattering. IEEE Trans. Antennas Propagat., 1998,46(3): 303-311.
[97] S. Y. Chen, W. C. Chew, J. M. Song and J. S. Zhao. Analysis of low freqency scattering from penetrable scatterers. IEEE Trans on Geoscience and Remote Sensionng, 39(4): 726-735.
[98] J. S. Zhao and W. C. Chew. Integral equation solution of maxwell's equations from zero frequency to microwave frequencies. IEEE Trans. Antennas Propagat., 2000, 48(1):1635-1645.
[99] Y. H. Chu and W. C. Chew. A surface integral equation method for solving complicated electrically small structures. Electrical Performance of Electronic Packeaging 2003, pp:341-344.
[100] Y. Chu and W. C. Chew. A multi-level fast multipole algorithm for low-frequency scattering from a composite object. IEEE AP-S, 2003: 43-46
[101] Y. Chu, W. C. Chew, J. S. Zhao and S. Y. Chen. A surface integral equation formulation for low-frequency scattering from a composite object. IEEE Trans. Antennas Propagat., 2003,51(10): 2837-2844
[102] S. D. Gedney and R. Mittra. The use of the FFT for the efficient solution of the problem of electromagnetic scattering by a body of revolution. Microwave and Optical Technology Letters, 1990,15(3): 313-322.
[103] Z. Q. Zhang, Q. H. Liu, X. M. Xu. RCS computation of large inhomogeneous objets using a fast integral equation solver. IEEE Trans. Antennas Propagat., 2003,51(3): 613-618.
[104] J. R. Phillips and J. K. White. A precorrected-FFT method for electrostatic analysis of complicated 3-D strucures. IEEE Trans Computer-Aided Design Integr Circ Sys. 1997, 16:1059-1072.
[105] X. C. Nie, L. W. Li and N. Yuan. Fast analysis of scattering by arbitrarily shaped three-Dimensional objects using the precorected-FFT method. Microwave and Optical Technology Letters, 2002, 34: 438-44.
[106] X. C. Nie, L. W. Li, N. Yuan, etc. A fast analysis of electromagnetic scattering by arbitrarily shaped homogeneous dielectric objects. 2003, 38(1): 30-35.
[107] C. C. Lu. Dielectric radome analysis using multilevel fast multipole algorithm. IEEE AP-S,2000,pp:730-733.
[108] C. C. Lu and W. C. Chew. A coupled surface-volume integral equation approach for the calculation of Electromagnetic scattering from composite metallic and material targets. IEEE Trans. Antennas Propagat., 2001,48(12): 1866-1868.
[109] S. Koc, J. M. Song and W. C. Chew. Error analysis for the multilevel fast multipole algorithm.IEEE AP-S, 1998, vol. 3, pp: 1758-1761.
[110] M. Abramowitz and I. A. Stegun, Handbook of mathematical functions. New York: Dover,1970.
[111] N. Geng, A.. Sullivan and L. Carin. Fast multipole method for scatering from an arbitrary PEC target above or buried in a lossy half space, IEEE Trans. Antennas Propagat., 2001,49(5):740-748.
[112] N. Geng, A. Sullivan and L. Carin. Multilevel fast-multipole algorithm for Scatering from conducting target s above or embedded in a lossy half space, IEEE Trans. Antennas Propagat.,2000, 38(4): 1561-1573.
[113] J. F. Lee, J. Zhang and C. C. Lu. Sparse inverse preconditioning of multilevel fast multipole algorithm for hybrid integral equations in electromagnetics. IEEE Trans. Antennas Propagat.,2004, 52(9): 2277-2286.
[114] Y. J. Xie, J. He, A. Sullivan and L Carin. A simple preonditioner for electric-field integral equations. Microwave and Optical Technology Letters, 2001,30(1): 51-54.
[115] Z. Y. Niu and J. P. Xu. Near-field sparse inverse preconditioning of multilevel fast multipole algorithm for electric field integral equations. APMC 2005, vol. 3, pp: 1879-1883.
[116] P. L. Rui and R. S. Chen. An efficient sparse approximate inverse preconditioning for FMM implementation. Microwave and Optical Technology Letters, 2006,49(7): 1746-1750.
[117] E. Chow. A priori sparsity patterns for parallel sparse approximate inverse preconditioners.SIAM J.. Sci. Stat. Comput., 2000, 21(5): 1804-1822.
[118] M. Grote and T. Huckle. Parallel preconditioning with sparse approximate inverses. SIAM J.Sci. Stat. Comput., 1997,18(3): 838-853.
[119] B. Carpentieri, I. S. Duff and L. Giraud. Experiments with sparse preconditioning of dense problems from electromagnetic applications. Technical Report TR/PA/00/04, CEPFACS,Toulouse, France, 2000.
[120] K. Sertel, J. L. Volakis. Incomplete LU preconditioner for FMM implementation. Micro. Opt.Tech. Lett., 2000, 26(7): 265-267.
[121] Y. Saad. ILUT: a dual threshold incomplete LU factorization. Numer. Linear Algebra Appl,1994,1(4): 387-402.
[122] J. F. Lee, J. Zhang and C. C. Lu. Incomplete LU preconditioner for large scale dense complex linear systems from electromagnetic wave scattering problems. J. Comput. Phys., 2003,185(1): 158-175.
[123] P. L. Rui, R. S. Chen, Z. H. Fan. Perturbed incomplete ILU preconditioner for efficient solution of electric field integral equations. IET Microw. Antennas Propag., 2007, 1(5):1059-1063.
[124] R. D. Graglia, D. R. Wilton and A. F. Peterson. Higher order interpolatory Vector Bases for Computational Electromagnetics. IEEE Trans. Antennas Propagat., 1997,45(3):329-342.
[125] J. D. Savage and A. F. Peterson. Higher-order vector finite elements for tetrahedral cells.IEEE Trans. Microwave Theory and Techniques, 1996,44(6): 874-879.
[126] L. S. Andersen and J. L. Volakis. Development and application of a novel class of hierarchical tangential vector finite elements for electromagnetics. IEEE Trans. Antennas Propagat.,1999,47(1): 112-120.
[127] J. Liu and J. M. Jin. A novel hybridization of higher order finite element and boundary integral methods for electromagnetic scattering and radiation problems. IEEE Trans. Antennas Propagat., 2001,49(11): 1794-1806.
[128] J. P. Webb. Hierarchical vector basis functions of arbitrary order for triangular and tetrahedral finite elements. IEEE Trans. Antennas Propagat., 1999,47(8): 1244-1253.
[129] L. R. Hamilton, P. A. Macdonald, et al, Electromagnetic scattering computations using high-order basis functions in the method of moments. IEEE AP-S, vol.3, pp: 2166-2169.
[130] G Kang, J. M. Song, W. C. Chew, etc. Grid-robust higher-order vector basis functions for solving integral equations. IEEE AP-S 2001, Salt Lake City, pp: 468-471.
[131] K. C. Donepudi, J. M. Jin, J. M. Song and W. C. Chew. A higher order parallelized multilevel fast multipole algorithm for 3-D scattering, IEEE Trans. Antennas Propagat., 2001, 49(7):1069-1078.
[132]K.C.Donepudi,J.M.Jin and W.C.Chew.A higher order multilevel fast multipole algorithm for scattering from mixed conducting/dielectric bodies.IEEE Trans.Antennas Propagat.,2003,51(10):2814-2821.
[133]K.Sertel and J.L.Volakis.Method of moments solution of volume integral equations using parametric geometry modeling.Radio Science,2002,37(1):1-7.
[134]E.Jorgensen,J.L.Volakis,P.Meincke,et al.Higher order hierarchical Legendre basis functions for electromagnetic modeling.IEEE Trans.Antennas Propagat.,2004,52(11):2985-2995.
[135]E.Jorgensen,J.L.Volakis,P.Meineke,et al.Higher order hierarchical discretization scheme for surface integral equations for layered media.IEEE Trans.Geoscience and Remote Sensing,2004,42(4):764-772.
[136]E.Jorgensen,J.L.Volakis,P.Meineke,et al.Higher order hierarchical Legendre basis functions for iterative integral equation solvers with curvilinear surface modeling.IEEE AP-S,2002,vol:4,pp:618-621.
[137]E.Jorgensen,P.Meincke,and O.Breinbjerg.A hybrid Po-higher-order hierarchical MoM formulation using curvilinear geometry modeling.IEEE AP-S,2003,pp:98-101.
[138]D.S.Sumic and B.M.Kolundzija.Efficient iterative solution of surface integral equations based on maximally orthogonalized higher order basis functions.IEEE AP-S,2005.
[139]任仪,聂在平,赵延文,马文敏.矩量法中阻抗矩阵的稀疏化研究.电子学报.2007,35(12):2354-2358.
[140]A.F.Peterson,S.L.Ray and R.Mittra.Computational methods for electromagnetics.New York:IEEE Press,1998.
[141]R.J.Adams.Physical and analytical properties of a stabilized electric field integral equation.IEEE Trans.Antennas Propagat.,2004,52(2):362-372.
[142]R.J.Adams and N.J.Champagne.A numerical implementation of a modified form of the electric field integral equation.IEEE Trans.Antennas Propagat.,2004,52(9):2262-2266.
[143]H.Contopanagos,B.Dembart,M.Epton.,etc.Well-conditioned boundary integral equations for three-dimensional electromagnetic scattering.IEEE Trans.Antennas Propagat.,2003,50(12):1824-1830.
[144]J.Hu,Z.P.Nie,L.Lei,etc.A modified electric field integral equation for 3D electromagnetic scattering.Asia-Pacific Microwave Conference Proceedings,Suzhou,China:2005:2216-2219.
[145]Jun Hu,Z P Nie,etc.A modified electric field integral equation for 3D electromagnetic scattering.IEEE AP-S 2005.
[146]L.J.Tian,J.Hu,Z.P.Nie.An improved EFIE for composite geometries involving open and closed conducing surfaces.IEEE AP-S 2007:4873-4876.
[147]闫玉波,李清亮,复杂载体短波天线特性的FDTD模拟与分析.电波科学学报,2004,19(2):135-142.
[148]邓维波,刘永坦.FDTD法计算高频单极天线特性.电波科学学报,2000,15(4):491-495.
[149]I.Tekin and E.H.Newman.Method of moments solution for a wire attached to an arbitrary faceted surface.IEEE Trans.Antennas Propagat.,1998,46(4):559-562.
[150]Z.P.Nie,W.C.Chew and Y.Z.Lo.Analysis of the annular -ring-loaded circular-disk mierostrip antenna.IEEE Trans.Antennas Propagat.,1990,38(6):806-813.
[151]W.C.Chew.Analysis of a probe-fed microstrip disk antenna.IEE Proceedings-H.1991,138(2):185-191.
[152]B.M.Kolundzija and B.D.Popovic.General localized junction model in the analysis of wire-to plate junctions.IEE Proe.-Microw.AE,141(1):1-7.
[153]H.Y.Chao,J.S.Zhao and W.C.Chew.Application of curvilinear basis functions and MLFMA for radiation and scattering problems involving curved PEC structures.IEEE Trans.Antennas Propagat.,2003,51(2):331-336.
[154]万继响,张玉,梁吕洪,任意导体与线大线连接问题的MoM分析.电波科学学报,2003,18(5):523-528.
[155]宗卫华,万继响,梁昌洪.导体线面连接问题中奇异函数积分的计算.微波学报,2004,20(1):6-9.
[156]J.M.Taboada.Evaluation of galerkin integrals involving triangular-type wire-surface junctions in the method of moments.IEEE Trans.Antennas Propagat.,2004,52(10):2785-2789.
[157]郭景丽,刘其中,纪奕才,精确分析任意导体地面上的套简单极子天线,电波科学学报,2004,19(5):613-617.
[158]H.Y.Chao,J.M.Song,E.Michielssen and W.C.Chew.The MLFMA for analyzing electromagnetic radiation from complex surface-wire structures.In Proc.of Antenna Appl.Syrup.1998:291-303.
[159]H.Y.Chao,K.Pirapaharan,W.C.Chew,et al.Simulation of vehicle antennas by the MLFMA.IEEE AP-S,2002,pp:18-20.
[160]H.Y.Chao.The multilevel fast multipole algorithm for electromagnetic compatibility analysis.IEEE International Symposium on Electromagnetic Compatibility,1999,vol.2,pp:844-847.
[161]H.Y.Chao,W.C.Chew,J.M.Song and E.Michielssen.Impedance calculation of complex surfaces-wire structures with multilevel fast multipole algorithm and variational formulation.IEEE AP-S,1999,vol.3,pp:1848-1850.
[162]H.Y.Chao,S.Y.Chen,W.C.Chew,etc.An application-independent multilevel fast multipole code for the analysis of eurvilinear surfaces with wire attachment.IEEE AP-S,2000,vol.4,pp:1880-1883.
[163]E.P.Ekelman,G.A.Thiele.A hybrid technique for combining the moment method treatment of wire antenna with the GTD for curved surfaces.IEEE Trans.Antennas Propagat.,1980,28(11):831-839.
[164]F.Obelleiro,J.M.Taoada,J.L.Rodriguez and J.M.Bertolo.HEMCUVI:A software package for the electromagnetic analysis and design of radiating systems on board real platforms.IEEE AP Magazine,2002,44(5):44-61.
[165]U.Jakobus and F.J.C.Meyer.A hybrid physical optics/method of moments numerical technique:theory,investigation and application.IEEE 4th Africon Symposium,vol.1,pp:24-27.
[166]U.Jakobus and F.M.Landstoffer.Improved PO-MM hybrid formulation for scattering from three-dimensional perfectly conducting bodies of arbitrary shape.IEEE Trans.Antennas Propagnt.,1995,43(2):162-169.
[167]J.Erik,M.Peter and B.Olav.A hybrid PO-higher-order hierarchical MoM formulation using eurvilinear geometry modeling.IEEE A.P-S,2003,pp:98-101.
[168]M.Djordjevic and B.M.Notaros.Higher order hybrid method of moments-physical optics modeling technique for radiation and scattering from large perfectly conducting surfaces.IEEE Trans.Antennas Propagat.,2005,53(2):800-813.
[169]J.M.taboada,F.Obelleiro and J.L.Rodriguez.Improvement of the hybrid moment-method-physical-optics method through a novel evaluation of the physical optics operator.Microwave and Optical Technology Letters,2001,30(5):357-363.
[170]E.H.Rcihard and R.S.Yahya.An iterative current-based hybrid method for complex structures.IEEE Trans.Antennas Propagat.,1997,45(2):265-276.
[171]华夷和,徐金平,牛臻弋.FAFFA加速的PO-MM研究复杂金属载体上线天线电磁特性.电子学报,2003,31(12):2045-2049.
[172]牛臻弋,王文博,徐金平.PO-MoM结合近场预条件技术分析复杂载体上线天线辐射特性.东南大学学报,2005,35(4)514-518.
[173]R.W.P.King,The Theory of Linear Antenna.Boston,MA:Harvard Univ.Press,1956,p.20.
[174]S.Bhattacharya,S.A.Long,and D.R.Wilton,The input impedance ofa monopole antenna mounted on a cubical conducting box.IEEE Trans.Antennas Propagat.,1987,35(7):756-762.
[175]J.C.G.Matthews and G.G.Cook,An efficient method for attaching thin wire monopoles to surfaces modeled using triangular patch segmentation.IEEE Trans.Antennas Propagat.,2003,51(7):1623-1629.
[176]T.J.Cui,W.C.Chew,J.S.Zhao and H.Y.Chao.Full-wave analysis of complicated transmission line circuits using wire models.IEEE Trans.Antennas Propagat.,2002,50(10):1350-1360.
[177]G.P.Junker,A.W.Glisson and A.A.Kishk.Accurate impedance model for antiresonant monopoles on finite group planes.Electronic Letters,1996,32(18):1632-1633.
[178]L.L.Tsai.A numerical solution for the near and far fields of an annular ring of magnetic current.IEEE Trans.Antennas Propagat.,1972,20(5):569-576.
[179]K.C.Donepudi,J.M.Song,J.M.Jin and W.C.Chew.Point-based implementation of multilevel fast multipole algorithm for higher-order Galerkin's method.IEEE AP-S,2000,pp:476-479.