基于阻抗边界条件的电场积分方程分析介质涂覆目标电磁散射
摘要
涂敷目标的电磁散射分析在实际应用中一直具有十分重要的意义。尤其在雷达隐身和反隐身、雷达识别和反识别、精密制导及仿真技术领域起着极其重要的作用。因此如何准确、快速地分析涂敷目标的电磁特性,长期以来一直是计算电磁学领域的研究重点。然而由于导体与介质之间存在复杂的耦合问题使得这类问题的电磁散射存在计算复杂,计算量过大和计算机所需内存大的困难。为此,本文开展了三维任意形状介质涂敷导体目标电磁散射分析中高效求解方法的研究。
本文阐述了电磁场积方程以及快速多极子算法(FMM, the Fast Multipole Method)用于加速求解导体散射问题,并介绍了求解介质问题的PMCHW (Poggio-Miller-Chang-Harrington-Wu-Tsai)积分方程方法以及其快速多极子算法的实现。
传统的积分方程方法结合快速多极子算法虽然能够精确计算普通介质目标的电磁散射特性,但是对于复杂介质涂敷目标,计算时消耗的资源仍然非常多。为此本文以阻抗边界条件(IBC, Impedance Boundary Condition)为理论基础,采用三角面元网格剖分模型,通过介质涂敷目标表面上等效电流和磁流之间的关系,建立表面电场积分方程,并使用快速多极子算法来加速求解过程和降低存储需求,从而快速计算电大尺寸介质涂敷目标的散射特性。
本文的研究工作为计算三维介质涂敷导电结构的电磁散射特性提供了良好的分析手段,并且文中给出了一些数值算例证明此方法的正确性与有效性,便于阻抗边界条件优化在工程中得到应用。此外,本文还讨论了涂覆介质参数特性不同时对目标的雷达散射特性的影响,给相关研究提供一个有意义的参考。
本文阐述了电磁场积方程以及快速多极子算法(FMM, the Fast Multipole Method)用于加速求解导体散射问题,并介绍了求解介质问题的PMCHW (Poggio-Miller-Chang-Harrington-Wu-Tsai)积分方程方法以及其快速多极子算法的实现。
传统的积分方程方法结合快速多极子算法虽然能够精确计算普通介质目标的电磁散射特性,但是对于复杂介质涂敷目标,计算时消耗的资源仍然非常多。为此本文以阻抗边界条件(IBC, Impedance Boundary Condition)为理论基础,采用三角面元网格剖分模型,通过介质涂敷目标表面上等效电流和磁流之间的关系,建立表面电场积分方程,并使用快速多极子算法来加速求解过程和降低存储需求,从而快速计算电大尺寸介质涂敷目标的散射特性。
本文的研究工作为计算三维介质涂敷导电结构的电磁散射特性提供了良好的分析手段,并且文中给出了一些数值算例证明此方法的正确性与有效性,便于阻抗边界条件优化在工程中得到应用。此外,本文还讨论了涂覆介质参数特性不同时对目标的雷达散射特性的影响,给相关研究提供一个有意义的参考。
引文
[1]R. F. Harrington. Field Computation by Moment Methods. Krieger Publishing Company, Malabar, Florida,1983.
[2]李世智.电磁散射与辐射问题的矩量法.成都：电子工业出版社.1985.
[3]Johnson J. H. Wang. Generalized Moment Methods In Electromagnetic Formulation and Computer Solution of Integral Equations. John Wiley Sons, Inc,1991.
[4]A. W. Glisson, D.R.Wilton. Simple and Efficient Numerical Methods for Problems of Electromagnetic Radiation and Scattering from Surfaces. IEEE Trans. on Antennas Propagat, vol. AP-28, pp.593-603, No.5, September 1980.
[5]S. M. Rao, D. R. Wilton, A. W. Glisson. Electromagnetic Scattering by Surfaces of Arbitrary Shape. IEEE Trans. on Antennas Propagat, AP-30, No.3, pp.409-419, May 1982.
[6]J. M. Song, W. C. Chew. Moment Method Solution Using Parametric Geometry. Journal of Electromagnetic Waves and Applications, vol.9, No.112, pp.71-83,1995.
[7]R. Coifman, V. Rokhlin and S. Wandzura. The Fast Multipole Method for The Wave Equation:A Pedestrian Prescription. IEEE Trans. on Antennas Propagat, vol.35, No.3, pp.7-12,1993.
[8]A. J. Pogglo and E. K. Miller. Integral equation solution of three dimensional scattering problems in Computer Techniques for Electromagnetic. Oxford, U.K.Permagon,1973.chap.4
[9]J.R. Mauta and R.F. Harrington. Electromagnetic scattering from a homogenous material body of revolution. Aeu,feb.1979,vol.33:71-80
[10]盛新庆.计算电磁学要论.第一版,北京：科学出版社,2004.
[11]曾渊.阻抗边界条件理论与应用,西安：西北工业大学硕士论文,2004.
[12]阙肖峰,聂在平,胡俊.三维导体介质复合结构电磁辐射与散射的MLFMA分析：电波科学学报,2007
[13]杨星华.介质导体复合目标电磁散射分析的表面积分方程方法,成都：电子科技大学硕士论文,2007
[14]姚海英.介质以及涂敷介质结构电磁散射特性的基础研究-积分方程方法及其快速求解, 成都：电子科技大学硕士论文,2002
[15]李江,傅君眉.平面分层介质结构的空间域格林函数近似解,微波学报,1999.9..15( 3)：221-226
[16]J. M. Song. W. C. Chew. Fast Multipole Method Solution Using Parametric Geometry. Microwave and Optical Technology Letters, vol.7, No.16. pp.760-765,1994.
[17]J. M. Song, C.C. Lu., W. C. Chew. Multilevel fast multipole algorithm for Electromagnetic scattering by large complex objects. IEEE Transaction on Antennas Propagation, vol.45, No.10, pp.1488-1493,1997
[18]J. M. Song, C.C. Lu., W. C. Chew. and S. W. Lee. Fast Illinois Solver Code (FSIC),IEEE Transactions on Antennas and Propagation,1998,40(3):27-34
[19]J. M. Song, C. C. Lu, W. C. Chew and S. W. Lee. Introduction to Fast Illinois Solver Code (FISC). IEEE Trans. on Antennas Propagat, pp.48-51,1997.
[20]J. M. Song, C. C. Lu, W. C. Chew, S. W. Lee. Fast Illinois Solver Code (FISC). IEEE Trans. on Antennas Propagat, vol.40, No.3, pp.27-34,1998.
[21]J. M. Song, W. C. Chew. Multilevel Fast-Multipole Algorithm For Solving Combined Field Integral Equations of Electromagnetic Scattering. Microwave and Optical Tech. Lett., 10(10):pp.14-19,1995.
[22]金建铭著,王建国译,葛德彪校.电磁场有限元方法.西安：西安电子科技大学出版社,1991年.
[23]R. F. Harrington, Time-harmonic electromagnetic fields. McGraw-Hill Book Company, Newyork,1961.
[24]J. M. Song, W. C. Chew. Fast Multipole Method Solution of Three Dimensional Integral Equations. IEEE Trans. on Antennas Propagat, pp.1528-1531,1995.
[25]E. Marx. Scattering by an arbitrary cylinder at a plane interface:Broadside incidence. IEEE Trans. Antennas Propagat., vol.37, pp.1823-1828, May.1989.
[26]H. S. Chang and K. K. Mei. Scattering of electromagnetic waves by buried and partly buried bodies of revolution. IEEE Trans. Geosci. Remote Sensing, vol.23, pp.592-596, July 1985.
[27]J. R. Mosig, F. Gardiol. General integral equation formulation for microstrip antennas and scatterers. Inst. Elect. Eng. Proc., pt. H, vol.132, pp.424-432, Dec.1985.
[28]K. A. Michalski. On the scalar potential of a point charge associated with a time-harmonic dipole in a layered medium. IEEE Trans. Antennas Propagat., vol.AP-35, pp.1299-1301,Nov.1987.
[29]A.W. Glisson, D.R.Wilton. Simple and efficient numerical methods for problems of electromagnetic radiation and scattering from surfaces. IEEE Trans. on Antennas Propagat. vol.AP-28,pp.593-603,No.5,1980
[30]J.M.Song, W. C. Chew. Multilevel fast-multipole algorithm for solving combined field integral equations of electromagnetic scattering. Microwave and Optical Tech. Lett..10(10):pp.14-19.1995
[31]L. Carin, N. Geng, M. McClure, J. Sichina, and L. Nguyen. Ultra wide-band synthetic-aperture radar for mine-field detection. IEEE Antennas Propagat., Mag., vol.41, pp. 18-33, Feb.1999.
[32]N.G eng and L. Carin. Wide band electromagnetic scattering form adielectric BOR buried in a layered, dispersive medium. IEEE Trans. Antennas Propagat, vol.47, pp.610-619, Apr.1999.
[33]U mashankar K R, Taflove A, Rao S M. Electromagnetic scattering by arbitrary shaped three-dimensional homogeneous lossy dielectric objects [J]. IEEE Trans Antennas Propagat, 1986,34(6):758-766
[34]J. R. Mosig, F. Gardiol. General integral equation formulation for micro strip antennas and scatterers. Inst. Elect. Eng. Proc., pt.H,vol.132, pp.424-432.1985
[35]Pasi Yla-Oijala and Matti Taskinen. Application of Combined Field Integral Equation for Electromagnetic Scattering by Dielectric and Composite Objects. IEEE Trans. Antennas Propag., vol.53, no.3, March 2005.
[36]P. Yla-Oijala, M. Taskinen, and S. Jarvenpaa. Surface integral equation formulations for solving electromagnetic scattering problems with iterative methods. Radio Sci., vol.40, no. 6, Nov.2005.
[37]X.Q. Sheng and J.-M Jin et. al. Solution of Combined-Field Integral Equation Using Multilevel Fast Multipole Algorithm for Scattering by Homogeneous Bodies. IEEE Trans.,2005
[38]A. Helaly and H. M. Fahmy. Combined-field integral equation. Electronics Letters. 1993(29):1678-1679,1993
[39]Zaiping Nie,Haogang Wang,Tun Wang. A Combined Field Solution With Single Operator for Electromagnetic Scattering From Conductive Targets With Open Cavities. IEEE Trans. Antennas Propagat 1998(46):1718-1726,1998
[40]S. M. Rao, T. K. Sarkar, P. Midya, A. R. Djordevic, Electromagnetic Radiation and Scattering from Finite Conducting and Dielectric Structures:Surface/Surface Formulation. IEEE Tran on Antennas and Propagation.1991,39(7):10341037,1991
[41]J. M. Song, C. C. Lu, W. C. Chew, and S. W. Lee. Fast Illinois Solver Code (FISC), IEEE Transactions on Antennas and Propagation,1998,40(3):27-34
[42]Louis N. Medgyesi-Mitschang and John M. Putnam. Integral equation formulations for imperfectly conducting scatters. IEEE Transactions on Antennas and Propagation.1985, 33(2):206-214
[43]Louis N. Medgyesi-Mitschang and Dau-sing Wang. Hybrid solution for large impedance coated bodies of revolution. IEEE Transactions on Antennas and Propagation. 1986,33(2):206-214
[2]李世智.电磁散射与辐射问题的矩量法.成都：电子工业出版社.1985.
[3]Johnson J. H. Wang. Generalized Moment Methods In Electromagnetic Formulation and Computer Solution of Integral Equations. John Wiley Sons, Inc,1991.
[4]A. W. Glisson, D.R.Wilton. Simple and Efficient Numerical Methods for Problems of Electromagnetic Radiation and Scattering from Surfaces. IEEE Trans. on Antennas Propagat, vol. AP-28, pp.593-603, No.5, September 1980.
[5]S. M. Rao, D. R. Wilton, A. W. Glisson. Electromagnetic Scattering by Surfaces of Arbitrary Shape. IEEE Trans. on Antennas Propagat, AP-30, No.3, pp.409-419, May 1982.
[6]J. M. Song, W. C. Chew. Moment Method Solution Using Parametric Geometry. Journal of Electromagnetic Waves and Applications, vol.9, No.112, pp.71-83,1995.
[7]R. Coifman, V. Rokhlin and S. Wandzura. The Fast Multipole Method for The Wave Equation:A Pedestrian Prescription. IEEE Trans. on Antennas Propagat, vol.35, No.3, pp.7-12,1993.
[8]A. J. Pogglo and E. K. Miller. Integral equation solution of three dimensional scattering problems in Computer Techniques for Electromagnetic. Oxford, U.K.Permagon,1973.chap.4
[9]J.R. Mauta and R.F. Harrington. Electromagnetic scattering from a homogenous material body of revolution. Aeu,feb.1979,vol.33:71-80
[10]盛新庆.计算电磁学要论.第一版,北京：科学出版社,2004.
[11]曾渊.阻抗边界条件理论与应用,西安：西北工业大学硕士论文,2004.
[12]阙肖峰,聂在平,胡俊.三维导体介质复合结构电磁辐射与散射的MLFMA分析：电波科学学报,2007
[13]杨星华.介质导体复合目标电磁散射分析的表面积分方程方法,成都：电子科技大学硕士论文,2007
[14]姚海英.介质以及涂敷介质结构电磁散射特性的基础研究-积分方程方法及其快速求解, 成都：电子科技大学硕士论文,2002
[15]李江,傅君眉.平面分层介质结构的空间域格林函数近似解,微波学报,1999.9..15( 3)：221-226
[16]J. M. Song. W. C. Chew. Fast Multipole Method Solution Using Parametric Geometry. Microwave and Optical Technology Letters, vol.7, No.16. pp.760-765,1994.
[17]J. M. Song, C.C. Lu., W. C. Chew. Multilevel fast multipole algorithm for Electromagnetic scattering by large complex objects. IEEE Transaction on Antennas Propagation, vol.45, No.10, pp.1488-1493,1997
[18]J. M. Song, C.C. Lu., W. C. Chew. and S. W. Lee. Fast Illinois Solver Code (FSIC),IEEE Transactions on Antennas and Propagation,1998,40(3):27-34
[19]J. M. Song, C. C. Lu, W. C. Chew and S. W. Lee. Introduction to Fast Illinois Solver Code (FISC). IEEE Trans. on Antennas Propagat, pp.48-51,1997.
[20]J. M. Song, C. C. Lu, W. C. Chew, S. W. Lee. Fast Illinois Solver Code (FISC). IEEE Trans. on Antennas Propagat, vol.40, No.3, pp.27-34,1998.
[21]J. M. Song, W. C. Chew. Multilevel Fast-Multipole Algorithm For Solving Combined Field Integral Equations of Electromagnetic Scattering. Microwave and Optical Tech. Lett., 10(10):pp.14-19,1995.
[22]金建铭著,王建国译,葛德彪校.电磁场有限元方法.西安：西安电子科技大学出版社,1991年.
[23]R. F. Harrington, Time-harmonic electromagnetic fields. McGraw-Hill Book Company, Newyork,1961.
[24]J. M. Song, W. C. Chew. Fast Multipole Method Solution of Three Dimensional Integral Equations. IEEE Trans. on Antennas Propagat, pp.1528-1531,1995.
[25]E. Marx. Scattering by an arbitrary cylinder at a plane interface:Broadside incidence. IEEE Trans. Antennas Propagat., vol.37, pp.1823-1828, May.1989.
[26]H. S. Chang and K. K. Mei. Scattering of electromagnetic waves by buried and partly buried bodies of revolution. IEEE Trans. Geosci. Remote Sensing, vol.23, pp.592-596, July 1985.
[27]J. R. Mosig, F. Gardiol. General integral equation formulation for microstrip antennas and scatterers. Inst. Elect. Eng. Proc., pt. H, vol.132, pp.424-432, Dec.1985.
[28]K. A. Michalski. On the scalar potential of a point charge associated with a time-harmonic dipole in a layered medium. IEEE Trans. Antennas Propagat., vol.AP-35, pp.1299-1301,Nov.1987.
[29]A.W. Glisson, D.R.Wilton. Simple and efficient numerical methods for problems of electromagnetic radiation and scattering from surfaces. IEEE Trans. on Antennas Propagat. vol.AP-28,pp.593-603,No.5,1980
[30]J.M.Song, W. C. Chew. Multilevel fast-multipole algorithm for solving combined field integral equations of electromagnetic scattering. Microwave and Optical Tech. Lett..10(10):pp.14-19.1995
[31]L. Carin, N. Geng, M. McClure, J. Sichina, and L. Nguyen. Ultra wide-band synthetic-aperture radar for mine-field detection. IEEE Antennas Propagat., Mag., vol.41, pp. 18-33, Feb.1999.
[32]N.G eng and L. Carin. Wide band electromagnetic scattering form adielectric BOR buried in a layered, dispersive medium. IEEE Trans. Antennas Propagat, vol.47, pp.610-619, Apr.1999.
[33]U mashankar K R, Taflove A, Rao S M. Electromagnetic scattering by arbitrary shaped three-dimensional homogeneous lossy dielectric objects [J]. IEEE Trans Antennas Propagat, 1986,34(6):758-766
[34]J. R. Mosig, F. Gardiol. General integral equation formulation for micro strip antennas and scatterers. Inst. Elect. Eng. Proc., pt.H,vol.132, pp.424-432.1985
[35]Pasi Yla-Oijala and Matti Taskinen. Application of Combined Field Integral Equation for Electromagnetic Scattering by Dielectric and Composite Objects. IEEE Trans. Antennas Propag., vol.53, no.3, March 2005.
[36]P. Yla-Oijala, M. Taskinen, and S. Jarvenpaa. Surface integral equation formulations for solving electromagnetic scattering problems with iterative methods. Radio Sci., vol.40, no. 6, Nov.2005.
[37]X.Q. Sheng and J.-M Jin et. al. Solution of Combined-Field Integral Equation Using Multilevel Fast Multipole Algorithm for Scattering by Homogeneous Bodies. IEEE Trans.,2005
[38]A. Helaly and H. M. Fahmy. Combined-field integral equation. Electronics Letters. 1993(29):1678-1679,1993
[39]Zaiping Nie,Haogang Wang,Tun Wang. A Combined Field Solution With Single Operator for Electromagnetic Scattering From Conductive Targets With Open Cavities. IEEE Trans. Antennas Propagat 1998(46):1718-1726,1998
[40]S. M. Rao, T. K. Sarkar, P. Midya, A. R. Djordevic, Electromagnetic Radiation and Scattering from Finite Conducting and Dielectric Structures:Surface/Surface Formulation. IEEE Tran on Antennas and Propagation.1991,39(7):10341037,1991
[41]J. M. Song, C. C. Lu, W. C. Chew, and S. W. Lee. Fast Illinois Solver Code (FISC), IEEE Transactions on Antennas and Propagation,1998,40(3):27-34
[42]Louis N. Medgyesi-Mitschang and John M. Putnam. Integral equation formulations for imperfectly conducting scatters. IEEE Transactions on Antennas and Propagation.1985, 33(2):206-214
[43]Louis N. Medgyesi-Mitschang and Dau-sing Wang. Hybrid solution for large impedance coated bodies of revolution. IEEE Transactions on Antennas and Propagation. 1986,33(2):206-214