介质目标电磁散射的高效积分方程方法研究
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摘要
由于在通信、雷达等领域的重要应用价值,介质目标电磁散射特性备受关注。积分方程方法由于其求解严格、计算结果精度高,成为了分析介质目标电磁散射特性的主要方法。本文主要围绕介质目标电磁散射特性的高效积分方程开展研究工作。针对传统方法求解介质目标所需未知量数目太多,矩阵方程迭代求解收敛很慢的问题,着重研究了单积分方程(SIE)和基于体无散基函数的体积分方程,并采用矩阵交叉近似技术(ACA)和多层快速多极子方法(MLFMA),进一步减少了存储量,提高了单积分方程和体积分方程的计算效率。
首先,本文详细介绍了求解介质结构的面积分方程方法及目标模型的建立。研究了面积分方程方法:PMCHW,TENENH,JMCFIE。给出了公式推导,开发了PMCHW,TENENH,JMCFIE三种面积分方程的数值程序,为后面的工作打下了基础。
然后,为了减少待求未知量的个数,提高矩阵求解迭代收敛速度,本文详细研究了一种高效的面积分方程方法——单积分方程方法,给出了详细的公式推导,阐述了其物理意义。并将该方法的思想分别应用于PMCHW,TENENH,JMCFIE中,推导出相应的单积分方程形式。数值研究表明,采用单积分方程方法求解介质目标电磁散射,数值结果准确,并能提高矩阵迭代收敛求解速度。接着研究了电大尺寸介质目标电磁散射分析的高效方法。由于矩量法的内存需求和计算复杂度都是O ( N 2)( N为待求未知量数目),当处理电大尺寸的介质时,采用矩量法求解需要昂贵的内存开销和CPU计算时间。本文采用高效方法——ACA算法,成功地解决了单积分方程矩量法求解所带来的内存消耗大和计算复杂度高的问题。
最后,本文分析了用于体积分方程的体无散基函数,详细推导了基于此基函数矩量法的具体公式,重点介绍了求解过程中的奇异性处理技术,成功实现了基于体无散基函数的多层快速多极子方法,为三维非均匀介质电磁散射提供了高效的数值分析工具。
The electromagnetic scattering of dielectric bodies has been extensively studied because of its importance in the area of wireless communication and radar. The integral equation is widely applied to analyze the electromagnetic scattering of dielectric objects for its high precision. In this thesis, the research work is based on efficient integral equations for electromagnetic scattering property of dielectric materials. Single integral equation(SIE) and volume integral equation with the solenoidal basis function are investigated. The number of the unknowns is reduced and the iterative solution of the matrix equation is more efficient than the traditional methods. Two efficient methods including adaptive cross approximation (ACA) algorithm and multilevel fast multipole algorithm (MLFMA) are adopted to reduced the storage requirement and computational cost successfully.
Firstly, the surface integral equation method for dielectric objects is introduced. Surface integral equations for dielectric objects based on equivalent principle, such as PMCHW, TENENH, JMCFIE are presented in detail. Numerical results show that the programs are correct.
Secondly, a novel surface integral equation called single integral equation is presented to realize efficient solution of scattering from dielectric objects. Further, the SIE is extended successfully into the PMCHW,TENENH and JMCFIE. Numerical results by this method are in good agreement with the exact results. And, the convergence speed of the iterative solution of the matrix equation in SIE method is significantly better than that of the traditional coupled integral equations method. Then, the efficient integral method for electromagnetic scattering property of electrically-large object is investigated. Since the memory requirement and computational complexity are both O ( N 2), where N is the number of unknowns. It requires very expensive storage and CPU time when dealing with the electrically-large object. In this thesis, a efficient method called ACA algorithm is adopted to further reduce the storage requirement and computational complexity successfully.
Finally, the solenoidal basis function for the volume integral equation is studied. The detailed formulations for implementation, especially the technique for treating singular integration in the method of moment are given. Numerical results show that the proposed approach is valid. The MLFMA algorithm is successfully realized for the volume integral equation solution. It provides an efficient analysis tool for numerical solution of scattering from 3D inhomogeneous dielectric.
首先,本文详细介绍了求解介质结构的面积分方程方法及目标模型的建立。研究了面积分方程方法:PMCHW,TENENH,JMCFIE。给出了公式推导,开发了PMCHW,TENENH,JMCFIE三种面积分方程的数值程序,为后面的工作打下了基础。
然后,为了减少待求未知量的个数,提高矩阵求解迭代收敛速度,本文详细研究了一种高效的面积分方程方法——单积分方程方法,给出了详细的公式推导,阐述了其物理意义。并将该方法的思想分别应用于PMCHW,TENENH,JMCFIE中,推导出相应的单积分方程形式。数值研究表明,采用单积分方程方法求解介质目标电磁散射,数值结果准确,并能提高矩阵迭代收敛求解速度。接着研究了电大尺寸介质目标电磁散射分析的高效方法。由于矩量法的内存需求和计算复杂度都是O ( N 2)( N为待求未知量数目),当处理电大尺寸的介质时,采用矩量法求解需要昂贵的内存开销和CPU计算时间。本文采用高效方法——ACA算法,成功地解决了单积分方程矩量法求解所带来的内存消耗大和计算复杂度高的问题。
最后,本文分析了用于体积分方程的体无散基函数,详细推导了基于此基函数矩量法的具体公式,重点介绍了求解过程中的奇异性处理技术,成功实现了基于体无散基函数的多层快速多极子方法,为三维非均匀介质电磁散射提供了高效的数值分析工具。
The electromagnetic scattering of dielectric bodies has been extensively studied because of its importance in the area of wireless communication and radar. The integral equation is widely applied to analyze the electromagnetic scattering of dielectric objects for its high precision. In this thesis, the research work is based on efficient integral equations for electromagnetic scattering property of dielectric materials. Single integral equation(SIE) and volume integral equation with the solenoidal basis function are investigated. The number of the unknowns is reduced and the iterative solution of the matrix equation is more efficient than the traditional methods. Two efficient methods including adaptive cross approximation (ACA) algorithm and multilevel fast multipole algorithm (MLFMA) are adopted to reduced the storage requirement and computational cost successfully.
Firstly, the surface integral equation method for dielectric objects is introduced. Surface integral equations for dielectric objects based on equivalent principle, such as PMCHW, TENENH, JMCFIE are presented in detail. Numerical results show that the programs are correct.
Secondly, a novel surface integral equation called single integral equation is presented to realize efficient solution of scattering from dielectric objects. Further, the SIE is extended successfully into the PMCHW,TENENH and JMCFIE. Numerical results by this method are in good agreement with the exact results. And, the convergence speed of the iterative solution of the matrix equation in SIE method is significantly better than that of the traditional coupled integral equations method. Then, the efficient integral method for electromagnetic scattering property of electrically-large object is investigated. Since the memory requirement and computational complexity are both O ( N 2), where N is the number of unknowns. It requires very expensive storage and CPU time when dealing with the electrically-large object. In this thesis, a efficient method called ACA algorithm is adopted to further reduce the storage requirement and computational complexity successfully.
Finally, the solenoidal basis function for the volume integral equation is studied. The detailed formulations for implementation, especially the technique for treating singular integration in the method of moment are given. Numerical results show that the proposed approach is valid. The MLFMA algorithm is successfully realized for the volume integral equation solution. It provides an efficient analysis tool for numerical solution of scattering from 3D inhomogeneous dielectric.
引文
[1]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.
[2]金建铭.电磁场有限元方法.西安电子科技大学出版社, 1998.
[3]R. F. Harrington. Field computation by moment methods. McMillan, New York, 1968.
[4]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.
[5]P. L. Huddleston, L. N. Medgyesi-Mitschang, and J. M. Putnam.Combined field integral equation formulation for scattering by dielectrically coated conducting bodies. IEEE Trans. Antennas Propag., 1986,34(4): 510–520.
[6]J. M. Putnam and L. N. Medgyesi-Mitschang. Combined field integral equation for inhomogeneous two-and three-dimensional bodies: The junction problem. IEEE Trans. Antennas Propag., 1991,39(5): 667–672
[7]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 Propag., 2003,51(10): 2814–2821.
[8]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.
[9]盛新庆.计算电磁学要论.科学出版社, 2004.
[10]Pasi Yla-Oijala. Application Of A Novel CFIE For Electromagnetic Scattering Bydielectric Objects. Microwave And Optical Technology Letters , 2002,35(1).
[11]P.Yla-Oijala and T Matti. Application of combined field integral equation for electromagnetic scattering by dielectric and composite objects. IEEE Trans. Antennas Propagat., 2003, 53(3): 1168-1173.
[12]A. W. Glisson. An integral equation for electromagnetic scattering from homogeneous dielectric bodies. IEEE Trans. Antennas Propagat., 1984, 32(2): 172-175.
[13]M. S. Yeung.Single integral equation for electromagnetic scattering by three-dimensional homogeneous dielectric objects. IEEE Trans. Antennas Propagat., 1999, 47(10): 1615-1622.
[14]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.
[15]S. Kulkarni, R. Lemdiasov, R. Ludwig, and S. Makarov. Comparison of Two Sets of Low-Order Basis Functions for Tetrahedral VIE Modeling. IEEE Trans. Antennas Propagat,2004,52(10).
[16]L. Mendes and S. Carvalho. Scattering of EM Waves by Homogeneous Dielectrics with the Use of the Method of Moments and 3D Solenoidal Basis Functions,. Microw Opt Tech Lett, 1996,12: 327-331.
[17]S.A. Carvalho and L.S. Mendes, Scattering of EM waves by inhomogeneous dielectrics with the use of the method of moments and 3D solenoidal basis functions, Microwave Opt Tech Lett,1999, 23(1).
[18]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. Antenna Propagat.,1989,37(5):528一537
[19]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.
[20]阙肖峰.导体介质组合目标电磁问题的精确建模和快速算法研究:[博士学位论文].成都:电子科技大学,2008
[21]Kezhong Zhao, Marinos N. Vouvakis and Jin-Fa Lee. The Adaptive Cross Approximation Algorithm for Accelerated Method of Moments Computations of EMC Problems. IEEE Trans. Elecnomagn. Compat., 2005,47(4).
[22]S. Kurz, O. Rain, and S. Rjasanow. The adaptive cross-approximation technique for the 3-D boundary element method. IEEE Trans. Magn., 38(2):421–424
[23]The multilevel adaptive cross-approximation algorithm for modeling electromagnetic radiation and scattering problems. PIERs, Nanjing,China, Aug. 2004.
[24]K. C. Donepudi, J.M. Jin, Jiming Song, W.C. Chew. A Higher Order Parallelized Multilevel Fast Multipole Algorithm for 3-D Scattering. IEEE Trans. Antennas Propagat., 1994, 49(7):1069-1078
[25]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.
[26]E. H. Newman, P. Alexandropoulos, E. K. Walton. Polygonal plate modeling of realisticstructure. IEEE Trans. Antennas Propagat., 1984, 32(7): 742-747.
[27]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.
[28]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:[博士学位论文].成都:电子科技大学, 2002.
[29]Roberto 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).
[30]J. R. Phillips and J. K. White. A precorrected-FFT method for electrostatic analysis of complicated 3-D structures. IEEE Trans. Comput. Aided Des. Integr. Circuits Syst.,1997,16(10): 1059–1072
[31]M. A. Morgan and K. K. Mei. Finite element computation of scattering by inhomogeneous penetrable bodies of revolution. IEEE Trans. Antennas Propagat,1979,27: 202-214.
[32]R. Holland, L. Simpson, and K. S. Kunz. Finite-difference analysis of EMP coupling to lossy dielectric structures. IEEE Trans. Elecnomagn. Compat., vol. EMC-22, pp. 203-209, Aug. 1980.
[33]E. H. Newman and P. Tulyathan. Wire antennas in the presence of a dielectric/ferrite inhomogeneity. IEEE Trans. Antennas Propagat., vol. AP-26, pp. 587-593, July 1978.
[34]D. E. Livesay and K-M Cheo. Electromagnetic fields induced inside arbitrarily shaped biological bodies. IEEE Trans. Microwave Theory Tech., vol. MTT-22, pp. 1273-1280
[35]Mao-Kun Li and Weng Cho Chew. A Study on Applying Divergence-Free Condition in Solving the Volume Integral Equation with Loop Basis. IEEE Antennas and Propagation Society Int. Symp, 2006:4107–4110.
[36]Z. H. Fan, Jian Bao, Edward K. N. Yung, and R. S. Chen. Volume Integral Equation using Solenoidal Basis Functions. IEEE Antennas, Propagation and EM Theory, 2006:1-5.
[2]金建铭.电磁场有限元方法.西安电子科技大学出版社, 1998.
[3]R. F. Harrington. Field computation by moment methods. McMillan, New York, 1968.
[4]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.
[5]P. L. Huddleston, L. N. Medgyesi-Mitschang, and J. M. Putnam.Combined field integral equation formulation for scattering by dielectrically coated conducting bodies. IEEE Trans. Antennas Propag., 1986,34(4): 510–520.
[6]J. M. Putnam and L. N. Medgyesi-Mitschang. Combined field integral equation for inhomogeneous two-and three-dimensional bodies: The junction problem. IEEE Trans. Antennas Propag., 1991,39(5): 667–672
[7]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 Propag., 2003,51(10): 2814–2821.
[8]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.
[9]盛新庆.计算电磁学要论.科学出版社, 2004.
[10]Pasi Yla-Oijala. Application Of A Novel CFIE For Electromagnetic Scattering Bydielectric Objects. Microwave And Optical Technology Letters , 2002,35(1).
[11]P.Yla-Oijala and T Matti. Application of combined field integral equation for electromagnetic scattering by dielectric and composite objects. IEEE Trans. Antennas Propagat., 2003, 53(3): 1168-1173.
[12]A. W. Glisson. An integral equation for electromagnetic scattering from homogeneous dielectric bodies. IEEE Trans. Antennas Propagat., 1984, 32(2): 172-175.
[13]M. S. Yeung.Single integral equation for electromagnetic scattering by three-dimensional homogeneous dielectric objects. IEEE Trans. Antennas Propagat., 1999, 47(10): 1615-1622.
[14]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.
[15]S. Kulkarni, R. Lemdiasov, R. Ludwig, and S. Makarov. Comparison of Two Sets of Low-Order Basis Functions for Tetrahedral VIE Modeling. IEEE Trans. Antennas Propagat,2004,52(10).
[16]L. Mendes and S. Carvalho. Scattering of EM Waves by Homogeneous Dielectrics with the Use of the Method of Moments and 3D Solenoidal Basis Functions,. Microw Opt Tech Lett, 1996,12: 327-331.
[17]S.A. Carvalho and L.S. Mendes, Scattering of EM waves by inhomogeneous dielectrics with the use of the method of moments and 3D solenoidal basis functions, Microwave Opt Tech Lett,1999, 23(1).
[18]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. Antenna Propagat.,1989,37(5):528一537
[19]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.
[20]阙肖峰.导体介质组合目标电磁问题的精确建模和快速算法研究:[博士学位论文].成都:电子科技大学,2008
[21]Kezhong Zhao, Marinos N. Vouvakis and Jin-Fa Lee. The Adaptive Cross Approximation Algorithm for Accelerated Method of Moments Computations of EMC Problems. IEEE Trans. Elecnomagn. Compat., 2005,47(4).
[22]S. Kurz, O. Rain, and S. Rjasanow. The adaptive cross-approximation technique for the 3-D boundary element method. IEEE Trans. Magn., 38(2):421–424
[23]The multilevel adaptive cross-approximation algorithm for modeling electromagnetic radiation and scattering problems. PIERs, Nanjing,China, Aug. 2004.
[24]K. C. Donepudi, J.M. Jin, Jiming Song, W.C. Chew. A Higher Order Parallelized Multilevel Fast Multipole Algorithm for 3-D Scattering. IEEE Trans. Antennas Propagat., 1994, 49(7):1069-1078
[25]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.
[26]E. H. Newman, P. Alexandropoulos, E. K. Walton. Polygonal plate modeling of realisticstructure. IEEE Trans. Antennas Propagat., 1984, 32(7): 742-747.
[27]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.
[28]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:[博士学位论文].成都:电子科技大学, 2002.
[29]Roberto 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).
[30]J. R. Phillips and J. K. White. A precorrected-FFT method for electrostatic analysis of complicated 3-D structures. IEEE Trans. Comput. Aided Des. Integr. Circuits Syst.,1997,16(10): 1059–1072
[31]M. A. Morgan and K. K. Mei. Finite element computation of scattering by inhomogeneous penetrable bodies of revolution. IEEE Trans. Antennas Propagat,1979,27: 202-214.
[32]R. Holland, L. Simpson, and K. S. Kunz. Finite-difference analysis of EMP coupling to lossy dielectric structures. IEEE Trans. Elecnomagn. Compat., vol. EMC-22, pp. 203-209, Aug. 1980.
[33]E. H. Newman and P. Tulyathan. Wire antennas in the presence of a dielectric/ferrite inhomogeneity. IEEE Trans. Antennas Propagat., vol. AP-26, pp. 587-593, July 1978.
[34]D. E. Livesay and K-M Cheo. Electromagnetic fields induced inside arbitrarily shaped biological bodies. IEEE Trans. Microwave Theory Tech., vol. MTT-22, pp. 1273-1280
[35]Mao-Kun Li and Weng Cho Chew. A Study on Applying Divergence-Free Condition in Solving the Volume Integral Equation with Loop Basis. IEEE Antennas and Propagation Society Int. Symp, 2006:4107–4110.
[36]Z. H. Fan, Jian Bao, Edward K. N. Yung, and R. S. Chen. Volume Integral Equation using Solenoidal Basis Functions. IEEE Antennas, Propagation and EM Theory, 2006:1-5.