介质导体复合目标电磁散射分析的表面积分方程方法
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摘要
导体与介质复合目标的电磁散射特性分析对于实际工程应用具有重要意义，尤其在雷达系统设计、雷达目标识别、遥感遥测以及军用目标的隐身、反隐身等应用上需求强烈。然而导体与介质间复杂的耦合与复杂的材料分布，导致这类问题的电磁散射求解面临计算时间长与所需计算机存储量大的困难。对此，本文主要研究了三维任意形状的介质以及均匀介质涂覆导电目标电磁散射的建模和高效求解方法。
本文按导体与介质的复合程度以及所使用的计算方法划分层次，对于导体介质复合目标的两种基本模型(全涂覆导体模型和局部涂覆导体模型)分章节进行了讨论，基于表面积分方程结合各种快速算法进行了比较。
第一部分首先回顾了计算全涂覆目标雷达散射截面(RCS)的几何建模和基于等效原理建立电场、磁场积分方程、PMCHW方程，通过不同组合构建TE+PMCHW和CFIE+PMCHW方程的过程，详细介绍了矩量法求解方程的过程及奇异性积分的处理方法，为后面的工作奠定了基础，并给出了相应的例子考察了程序的精确性。
第二部分本文结合了快速多极子方法加快矩量法的求解速度，验证了PMCHW表面积分方程对介质体RCS求解的精确性。
最后两章对于全涂覆导体目标和局部涂覆导体目标电磁散射的快速计算进行了推导，对局部涂敷目标分界面边缘的基函数处理进行了讨论，然后进一步采用多层快速多极子方法进一步加快求解速度，减少内存需求，使表面积分方程能适用于电大尺寸混合目标的计算。全文给出了大量算例检验了程序的精确性和高效性，对于基于表面积分方程的矩量法、快速多极子方法、多层快速多极子方法求解各类混合体目标的性能作了详细比较。结论得出基于表面积分方程方法的程序对于各种混合体目标具有较好的适用性，结合快速算法后对计算效率有很大提高且能保持矩量法所具有的精确性。
本文研究工作为三维介质体以及介质涂覆导电结构电磁散射特性研究提供了良好的分析手段，且程序具有较好的可移植性，便于再进一步优化以在工程上获得更广泛的应用。另外本文也给相关的研究提供了一个有意义的参考。
The analysis of the electromagnetic scattering character of the compositeconducting and dielectric object has great importance in the practical engineeringapplication, especially has strong requirement in the radar system design, radar targetidentify, remote sensing and measuring, stealth and anti-stealth. But the complexcoupling and materials distribution of the conductor and the dielectric body lead to thedifficulty of long computing time and large storage in this kind of problem. For thisproblem, the paper investigates the modeling and efficient solution method of 3Darbitrary shape conducting object coated by uniform dielectric.
The paper introduces the two basic models of the composite conducting anddielectric object, including entire coating and part coating, considering the difference ofthe combination construction and the solution method, and compared the different fastcomputing methods based on surface integral equation.
In the first section we recover the procedure of the geometry modeling of the RCScalculation of the entirely coated conductor and found the electromagnetic potentialequations. And the solution of the equations and the settlement of the singularityintegral is introduced in detail. The base of the latter work has been founded. Andcorresponding examples are given to prove the accuracy of the program.
In the next part the fast multipole method is presented to speed the solution, andvalidated the accuracy of the PMCHW equation to calculate the RCS of dielectric.
The paper introduces the solution of the RCS of the entirely-coated object and part-coated object, and deals with the basic function on the edge of the joint surface of thepart-coated object, and then uses the multilevel fast multipole algorithm accelerating thesolution and reducing the storage requirement in the final two chapters. Thus the surfaceintegral equation has the capability to solve the scattering problem of the electricallarge-scale composite targets. The whole paper gives abundant examples to test theaccuracy and efficiency of the programs. The detailed comparison in MoM, FMM,MLFMA based on surface integral equations in use of solution the electromagneticscattering of entirely-coated objects and part-coated objects and dielectric bodies can educe the conclusion the programs using fast computing method based on surfaceintegral equations has good applicability to most kind of composite objects and goodaccuracy close to MoM.
The research in the paper gives a good analysis method to the electromagneticscattering of 3D dielectric body and coated conductor construction, and the programsare transplantable well, and convenient to be optimized to be applied extensively inengineering. In addition, the work gives us a meaningful reference.
本文按导体与介质的复合程度以及所使用的计算方法划分层次，对于导体介质复合目标的两种基本模型(全涂覆导体模型和局部涂覆导体模型)分章节进行了讨论，基于表面积分方程结合各种快速算法进行了比较。
第一部分首先回顾了计算全涂覆目标雷达散射截面(RCS)的几何建模和基于等效原理建立电场、磁场积分方程、PMCHW方程，通过不同组合构建TE+PMCHW和CFIE+PMCHW方程的过程，详细介绍了矩量法求解方程的过程及奇异性积分的处理方法，为后面的工作奠定了基础，并给出了相应的例子考察了程序的精确性。
第二部分本文结合了快速多极子方法加快矩量法的求解速度，验证了PMCHW表面积分方程对介质体RCS求解的精确性。
最后两章对于全涂覆导体目标和局部涂覆导体目标电磁散射的快速计算进行了推导，对局部涂敷目标分界面边缘的基函数处理进行了讨论，然后进一步采用多层快速多极子方法进一步加快求解速度，减少内存需求，使表面积分方程能适用于电大尺寸混合目标的计算。全文给出了大量算例检验了程序的精确性和高效性，对于基于表面积分方程的矩量法、快速多极子方法、多层快速多极子方法求解各类混合体目标的性能作了详细比较。结论得出基于表面积分方程方法的程序对于各种混合体目标具有较好的适用性，结合快速算法后对计算效率有很大提高且能保持矩量法所具有的精确性。
本文研究工作为三维介质体以及介质涂覆导电结构电磁散射特性研究提供了良好的分析手段，且程序具有较好的可移植性，便于再进一步优化以在工程上获得更广泛的应用。另外本文也给相关的研究提供了一个有意义的参考。
The analysis of the electromagnetic scattering character of the compositeconducting and dielectric object has great importance in the practical engineeringapplication, especially has strong requirement in the radar system design, radar targetidentify, remote sensing and measuring, stealth and anti-stealth. But the complexcoupling and materials distribution of the conductor and the dielectric body lead to thedifficulty of long computing time and large storage in this kind of problem. For thisproblem, the paper investigates the modeling and efficient solution method of 3Darbitrary shape conducting object coated by uniform dielectric.
The paper introduces the two basic models of the composite conducting anddielectric object, including entire coating and part coating, considering the difference ofthe combination construction and the solution method, and compared the different fastcomputing methods based on surface integral equation.
In the first section we recover the procedure of the geometry modeling of the RCScalculation of the entirely coated conductor and found the electromagnetic potentialequations. And the solution of the equations and the settlement of the singularityintegral is introduced in detail. The base of the latter work has been founded. Andcorresponding examples are given to prove the accuracy of the program.
In the next part the fast multipole method is presented to speed the solution, andvalidated the accuracy of the PMCHW equation to calculate the RCS of dielectric.
The paper introduces the solution of the RCS of the entirely-coated object and part-coated object, and deals with the basic function on the edge of the joint surface of thepart-coated object, and then uses the multilevel fast multipole algorithm accelerating thesolution and reducing the storage requirement in the final two chapters. Thus the surfaceintegral equation has the capability to solve the scattering problem of the electricallarge-scale composite targets. The whole paper gives abundant examples to test theaccuracy and efficiency of the programs. The detailed comparison in MoM, FMM,MLFMA based on surface integral equations in use of solution the electromagneticscattering of entirely-coated objects and part-coated objects and dielectric bodies can educe the conclusion the programs using fast computing method based on surfaceintegral equations has good applicability to most kind of composite objects and goodaccuracy close to MoM.
The research in the paper gives a good analysis method to the electromagneticscattering of 3D dielectric body and coated conductor construction, and the programsare transplantable well, and convenient to be optimized to be applied extensively inengineering. In addition, the work gives us a meaningful reference.
引文
[1] 李世智，电磁散射与辐射问题的矩量法，电子工业出版社，1985．
[2] 王秉中，计算电磁学，电子科技大学出版社，2001．
[3] 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，电子科技大学，2000
[4] 胡俊，聂在平等，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
[5] 姚海英，介质以及涂覆介质结构电磁散射特性的基础研究—积分方程法及其快速求解，博士学位论文，电子科技大学，2002
[6] A. J. Pogglo and E. K. Miller. Integral equation solutions of three dimensional scattering problems in Computer Techniques for Electromagnetics. Oxford, U.K.:Permagon,1973,Chap.4
[7] J. R. Mautz and R. F. Harrington. Electromagnetic scattering from a homogenous material body of revolution.AEU,Feb. 1979,vol.33:71-80
[8] R. E Harrinton. Boundary integral formulations for homogeneous material bodies. J. Electromagnetics Wave Applicat.,1989,vol.3,no.1:1-15
[9] S. M. Rao and D. R. Wilton. E-field, H-field, and combined field solution for arbitrarily shaped three-dimensional dielectric bodies.Electromagn.,1990,vol.10,no.4:407-421
[10] K. R. Umashankar, A. Taflove, and S. M. Rao. Electromagnetic scattering by arbitrary shaped three-dimensional homogeneous lossy dielectric objects. IEEE Trans. Antennas Propagate., June1986, vol.AP-34:758-766
[11] S. M. Rao, C.C. Cha, R. L. Cravey, and D. Wilkes. Electromagnetic scattering from arbitrary shaped conducting bodies coated with lossy materials of arbitrary thickness. IEEE Trans. Antennas Propagate., May 1991,vol.Ap-39:627-631
[12] S. Velamparambil, W. C. Chew, and J. M. Song, 10 million unknowns: is it that big?, IEEE Trans. Antennas Propagate., 2003, 45:43-58
[13] V. Rokhlin. Rapid solution of integral equations of scattering theory in two dimensions. J. Compute. Phys., Feb. 1990, vol. 86:414-439
[14] 项铁铭梁昌洪，计算电磁学中稠密线性方程组的迭代求解，西安电子科技大学学报(自然科学版)，2003，30(6)：748-751
[15] J. M. Song and W. C. Chew. Multilevel fast-multipole algorithm for solving combined field integral equations of electromagnetic scattering. Microwave Opt. Tech. Lett., Sep. 1995, vol.10, no. 1:14-19
[16] 聂在平，徐利明，电磁散射数值分析中的特征基函数方法，电波科学学报，2004，19(增刊)：45-49
[17] 徐利明，分层介质中三维目标电磁散射的积分方程方法及其关键技术，博士学位论文，电子科技大学，2005．
[18] S. M. Rao, D. R. Wilton, A. W. Glisson, Electromagnetic scattering by surfaces of arbitrary shape[J], IEEE Trans. 1982, AP-30:409-418.
[19] 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 Propagate., Oct. 1993, vol. AP.41:1448-1455
[20] J. Dull, K.Gallivan, J. M. Song, and W. C. Chew. Parallel fast multipole capacitance solver. IEEE antennas Propagation Symposium, 1998,1766-1769
[21] J. M. Song. C. C. Lu, and W. C. Chew. Multilevel Fast Multipole Algorithm for Electromagnetic Scattering by Large Complex Objects. IEEE Trans. Antennas Propagate., Oct. 1997, vol. 45. no.10:1488-1493
[22] S. M. Rao, T. K.Sarkar, P. Midya and A. R. Djordevic. Electromagnetic radiation and scattering from finite conducting and dielectric structures: surface/surface formulation [J]. IEEE Trans on Antennas Propagate., 1991, 39(7): 1034-1037
[23] S. M. Rao, D. R. Wilton, and A. W. Glisson. Electromagnetic scattering by surfaces arbitrary shape. IEEE Trans. Antennas Propagate., May 1982, vol. AP-30:409-418
[24] 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 Opt. Tech. Lett., Feb. 2001, vol. 10,no.1: 221-224
[25] 胡俊，聂在平，二维多导电柱体电磁散射的快速算法，电子学报，1999年第6期
[26] 胡俊，聂在平，任意平面分层介质中正演计算的快速算法，电波科学学报，Vol．13，NO．2，1998，pp．113-116
[27] 胡俊，聂在平，“用快速多极子方法(FMM)求解二维介质柱电磁散射”，计算物理学会第二届计算电磁学研讨会(SCEM’98)，pp．47-50
[28] 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，No．12，1999
[29] 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, 1997, 45(10): 1488-1493
[30] J. M. Song, C. C. Lu., W. C. Chew. And S. W. Lee. Introduction to Fast Illinois Solver Code (FISC). IEEE Antennas Propagation Symposium, 1997,48-51
[31] Nader Engheta. William D. Murphy, ladimir Rokhlin, etc. The fast multipole method (FMM) for electromagnetic scattering problems. IEEE Transaction on Antennas and Propagation, 1992, 40(6): 634-641
[32] Qinglun Chen, Donald R.Wilton. Electromagnetic Scattering by Three-Dimensional Arbitrary Complex Material/Conducting Bodies. IEEE Transaction on Antennas and Propagation, 1990.
[33] Chung-Chi Cha, Debra Wilkes. Method of moments formulation for an arbitrary material configuration. IEEE Transaction on Antennas and Propagation, 1991.
[34] Ahmed A. Kishk, Allen W. Glisson, and Paul M. Goggans. Scattering from Conductors Coated with Materials of Arbitrary Thickness. IEEE Transaction on Antennas and Propagation, Vol. 40, No.1, January 1992.
[2] 王秉中，计算电磁学，电子科技大学出版社，2001．
[3] 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，电子科技大学，2000
[4] 胡俊，聂在平等，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
[5] 姚海英，介质以及涂覆介质结构电磁散射特性的基础研究—积分方程法及其快速求解，博士学位论文，电子科技大学，2002
[6] A. J. Pogglo and E. K. Miller. Integral equation solutions of three dimensional scattering problems in Computer Techniques for Electromagnetics. Oxford, U.K.:Permagon,1973,Chap.4
[7] J. R. Mautz and R. F. Harrington. Electromagnetic scattering from a homogenous material body of revolution.AEU,Feb. 1979,vol.33:71-80
[8] R. E Harrinton. Boundary integral formulations for homogeneous material bodies. J. Electromagnetics Wave Applicat.,1989,vol.3,no.1:1-15
[9] S. M. Rao and D. R. Wilton. E-field, H-field, and combined field solution for arbitrarily shaped three-dimensional dielectric bodies.Electromagn.,1990,vol.10,no.4:407-421
[10] K. R. Umashankar, A. Taflove, and S. M. Rao. Electromagnetic scattering by arbitrary shaped three-dimensional homogeneous lossy dielectric objects. IEEE Trans. Antennas Propagate., June1986, vol.AP-34:758-766
[11] S. M. Rao, C.C. Cha, R. L. Cravey, and D. Wilkes. Electromagnetic scattering from arbitrary shaped conducting bodies coated with lossy materials of arbitrary thickness. IEEE Trans. Antennas Propagate., May 1991,vol.Ap-39:627-631
[12] S. Velamparambil, W. C. Chew, and J. M. Song, 10 million unknowns: is it that big?, IEEE Trans. Antennas Propagate., 2003, 45:43-58
[13] V. Rokhlin. Rapid solution of integral equations of scattering theory in two dimensions. J. Compute. Phys., Feb. 1990, vol. 86:414-439
[14] 项铁铭梁昌洪，计算电磁学中稠密线性方程组的迭代求解，西安电子科技大学学报(自然科学版)，2003，30(6)：748-751
[15] J. M. Song and W. C. Chew. Multilevel fast-multipole algorithm for solving combined field integral equations of electromagnetic scattering. Microwave Opt. Tech. Lett., Sep. 1995, vol.10, no. 1:14-19
[16] 聂在平，徐利明，电磁散射数值分析中的特征基函数方法，电波科学学报，2004，19(增刊)：45-49
[17] 徐利明，分层介质中三维目标电磁散射的积分方程方法及其关键技术，博士学位论文，电子科技大学，2005．
[18] S. M. Rao, D. R. Wilton, A. W. Glisson, Electromagnetic scattering by surfaces of arbitrary shape[J], IEEE Trans. 1982, AP-30:409-418.
[19] 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 Propagate., Oct. 1993, vol. AP.41:1448-1455
[20] J. Dull, K.Gallivan, J. M. Song, and W. C. Chew. Parallel fast multipole capacitance solver. IEEE antennas Propagation Symposium, 1998,1766-1769
[21] J. M. Song. C. C. Lu, and W. C. Chew. Multilevel Fast Multipole Algorithm for Electromagnetic Scattering by Large Complex Objects. IEEE Trans. Antennas Propagate., Oct. 1997, vol. 45. no.10:1488-1493
[22] S. M. Rao, T. K.Sarkar, P. Midya and A. R. Djordevic. Electromagnetic radiation and scattering from finite conducting and dielectric structures: surface/surface formulation [J]. IEEE Trans on Antennas Propagate., 1991, 39(7): 1034-1037
[23] S. M. Rao, D. R. Wilton, and A. W. Glisson. Electromagnetic scattering by surfaces arbitrary shape. IEEE Trans. Antennas Propagate., May 1982, vol. AP-30:409-418
[24] 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 Opt. Tech. Lett., Feb. 2001, vol. 10,no.1: 221-224
[25] 胡俊，聂在平，二维多导电柱体电磁散射的快速算法，电子学报，1999年第6期
[26] 胡俊，聂在平，任意平面分层介质中正演计算的快速算法，电波科学学报，Vol．13，NO．2，1998，pp．113-116
[27] 胡俊，聂在平，“用快速多极子方法(FMM)求解二维介质柱电磁散射”，计算物理学会第二届计算电磁学研讨会(SCEM’98)，pp．47-50
[28] 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，No．12，1999
[29] 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, 1997, 45(10): 1488-1493
[30] J. M. Song, C. C. Lu., W. C. Chew. And S. W. Lee. Introduction to Fast Illinois Solver Code (FISC). IEEE Antennas Propagation Symposium, 1997,48-51
[31] Nader Engheta. William D. Murphy, ladimir Rokhlin, etc. The fast multipole method (FMM) for electromagnetic scattering problems. IEEE Transaction on Antennas and Propagation, 1992, 40(6): 634-641
[32] Qinglun Chen, Donald R.Wilton. Electromagnetic Scattering by Three-Dimensional Arbitrary Complex Material/Conducting Bodies. IEEE Transaction on Antennas and Propagation, 1990.
[33] Chung-Chi Cha, Debra Wilkes. Method of moments formulation for an arbitrary material configuration. IEEE Transaction on Antennas and Propagation, 1991.
[34] Ahmed A. Kishk, Allen W. Glisson, and Paul M. Goggans. Scattering from Conductors Coated with Materials of Arbitrary Thickness. IEEE Transaction on Antennas and Propagation, Vol. 40, No.1, January 1992.