电磁场数值计算中的内插和外推
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摘要
内插和外推算法是电磁场领域的常用算法，它在天线设计、微波技术、雷达目标散射建模等各种电磁场计算领域都要用到。因此内插和外推算法的成功应用，直接关系到电磁场数值计算技术的计算效率。
本文主要介绍了内插和外推算法在电磁场数值计算中的应用背景；提出了当前所面临的问题：研究了电磁场数值计算中的经典算法——矩量法(MoM)并编写了相应的程序；研究发展了Neville算法和模基参数估计算法(MBPE)；探讨和创新性的改进了渐近波形估计技术(AWE)。
具体工作主要包括：
1．编写了大量的矩量法程序，这是研究内插外推算法的基础。这些程序包括：
采用点匹配法和磁场积分方程计算三维目标的矩量法程序；
采用矢量三角基和全波离散镜象分析微带贴片的矩量法程序；
研究频率选择面(FSS)结构电磁散射特性的应用程序；
独立完成了对基本目标的表面三角剖分方法；
与计算机系合作完成了对任意目标的表面三角剖分程序。
2．研究和发展了一些有效的内插方法：
研究了MBPE方法对天线方向图，目标散射等问题进行二维内插的应用；
深入研究了Neville算法，并将其作为一种优秀的内插算法在目标建模当中应用。
3．深入研究并改进了AWE算法：
设计微带贴片时，首次采用AWE技术以微带衬底的相对介电常数为变量进行外推；
进行目标建模时，采用AWE技术将二维涂敷介质圆柱的雷达散射截面(RCS)数据的求解速度大幅提高；
在一维的AWE技术上发展了二维的AWE技术，同时在天线分析、目标建模当中应用，取得了较好的效果；
将神经网络技术和二维AWE技术相结合，使AWE的计算速度进一步提高。
Interpolation and extrapolation are in common use in the field of computational electromagnetics, such as antenna designing, microwave technique, radar scattering model, and so on. The reasonable and suitable application of the interpolation and extrapolation can make computation in electromagnetics more efficient.
The main work includes:
1. To develop several programs based on the method of moment (MoM):
The method of moment in conjunction with the magnetic field integral equation and pulse basis function for calculating the radar cross section (RCS) of the three-dimensional metal object
The method of moment in conjunction with the hybrid field integral equation, vector triangular basis function and full-wave discrete imaging (FWDI) for calculating the input characteristics of the microstrip antenna
The method of moment in conjunction with the free space periodic Green's function for calculating the one -dimensional frequency selective surfaces (FSS)
Software for meshing the surface of the object with triangular faces
2. To develop and improve some interpolation methods:
MBPE technique has been discussed, and been used to interpolate the radiation pattern of antenna and object scattering in the frequency and angular domain simultaneously.
Neville algorithm has been developed to interpolate the RCS data of the object in the frequency and angular domain simultaneously.
3. To develop and improve AWE method:
AWE method is applied to calculating the input characteristics of the microstrip antenna at f first time, as the relative permittivity of the substrate is variable.
AWE method is applied to calculating medium coated object, and makes the procession of the computing more efficiently.
AWE method has been developed into the two-dimensional AWE method and been used in the analysis of the microstrip antenna and RCS modeling. The results show the two-dimensional AWE is very efficient.
AWE method is combined with the neural networks. The hybrid technique can be used in the condition of multi-variables, even one or more variables are related with the dimension.
本文主要介绍了内插和外推算法在电磁场数值计算中的应用背景；提出了当前所面临的问题：研究了电磁场数值计算中的经典算法——矩量法(MoM)并编写了相应的程序；研究发展了Neville算法和模基参数估计算法(MBPE)；探讨和创新性的改进了渐近波形估计技术(AWE)。
具体工作主要包括：
1．编写了大量的矩量法程序，这是研究内插外推算法的基础。这些程序包括：
采用点匹配法和磁场积分方程计算三维目标的矩量法程序；
采用矢量三角基和全波离散镜象分析微带贴片的矩量法程序；
研究频率选择面(FSS)结构电磁散射特性的应用程序；
独立完成了对基本目标的表面三角剖分方法；
与计算机系合作完成了对任意目标的表面三角剖分程序。
2．研究和发展了一些有效的内插方法：
研究了MBPE方法对天线方向图，目标散射等问题进行二维内插的应用；
深入研究了Neville算法，并将其作为一种优秀的内插算法在目标建模当中应用。
3．深入研究并改进了AWE算法：
设计微带贴片时，首次采用AWE技术以微带衬底的相对介电常数为变量进行外推；
进行目标建模时，采用AWE技术将二维涂敷介质圆柱的雷达散射截面(RCS)数据的求解速度大幅提高；
在一维的AWE技术上发展了二维的AWE技术，同时在天线分析、目标建模当中应用，取得了较好的效果；
将神经网络技术和二维AWE技术相结合，使AWE的计算速度进一步提高。
Interpolation and extrapolation are in common use in the field of computational electromagnetics, such as antenna designing, microwave technique, radar scattering model, and so on. The reasonable and suitable application of the interpolation and extrapolation can make computation in electromagnetics more efficient.
The main work includes:
1. To develop several programs based on the method of moment (MoM):
The method of moment in conjunction with the magnetic field integral equation and pulse basis function for calculating the radar cross section (RCS) of the three-dimensional metal object
The method of moment in conjunction with the hybrid field integral equation, vector triangular basis function and full-wave discrete imaging (FWDI) for calculating the input characteristics of the microstrip antenna
The method of moment in conjunction with the free space periodic Green's function for calculating the one -dimensional frequency selective surfaces (FSS)
Software for meshing the surface of the object with triangular faces
2. To develop and improve some interpolation methods:
MBPE technique has been discussed, and been used to interpolate the radiation pattern of antenna and object scattering in the frequency and angular domain simultaneously.
Neville algorithm has been developed to interpolate the RCS data of the object in the frequency and angular domain simultaneously.
3. To develop and improve AWE method:
AWE method is applied to calculating the input characteristics of the microstrip antenna at f first time, as the relative permittivity of the substrate is variable.
AWE method is applied to calculating medium coated object, and makes the procession of the computing more efficiently.
AWE method has been developed into the two-dimensional AWE method and been used in the analysis of the microstrip antenna and RCS modeling. The results show the two-dimensional AWE is very efficient.
AWE method is combined with the neural networks. The hybrid technique can be used in the condition of multi-variables, even one or more variables are related with the dimension.
引文
[1] W.C.Chew et al. Recent Advances in Fast Solvers for Computational EM [M].Proceedings of ISAE'2000, Fukuoka, Japan, 2000, 871-874.
[2] V.V.Veremey and R.Mittra. Domain Decomposition Approach for Capacifance Computation of Nonorthogonal Interconnect Structures[J]. IEEE Trans. On Microwave Theory & Tech, 2000, 48(9): 1428-1434.
[3] R.S.Chen, D.G.Fang, K.F.Tsang, and E.K.N.Yung. Analysis of electromagnetic wave scattering by an electrically Large metallic grating using wavelet-based algebraic multigrid preconditioned CG method——abstract [J]. J. of EM Waves & Appl., 2000, 14: 1559-1561.
[4] E. K. Miller. Model-based parameter estimation in electromagnetic Pt. 1[J]. IEEE Antennas and Propagation Magazine, 1998, 40(1): 40-52.
[5] E. K. Miller. Model-based parameter estimation in electromagnetic Pt. 2[J]. IEEE Antennas and Propagation Magazine, 1998, 40(2): 51-65.
[6] E. K. Miller. Model-based parameter estimation in electromagnetic Pt. 3 [J]. IEEE Antennas and Propagation Magazine, 1998, 40(3): 49-66.
[7] E.Chiprout and M.Nakhla. Asymptotic Waveform Evaluation and Moment Matching for Interconnect Analysis [M]. Boston, MA:Kluwer Academic Publishers, 1994.
[8] W.T.Smith,R.D.Slone, and S.K.Das. Recent progress in reduced-order modeling of electrical interconnects using asymptotic waveform evaluation and Pad é approximation via the Lanczos process [J]. Appl. Comput. Electromagn. Soc. Newslett., 1997, 12: 46-71.
[9] 章创明，洪伟．渐近波形估计技术用于介质柱宽角度RCS的计算[J]．电波科学学报，2001，16(1)：72-75．
[10] 汪杰，洪伟．三维散射体宽角度RCS的快速算法[J]．电波科学学报，2001，16(2)：241-244
[11] W.X.Sheng, D.G.Fang, J.Zhuang, T.J.Liu and Z.L.Yang. Data Compression in RCS modelingby TDFT[J]. 电子学报(英文版), 2001, 10(4): 557-559.
[12] Doualas H. Werner and Rene J.Allard. The Simultaneous Interpolation of Antenna Radiation Patterns in Both the Spatial and Frequency Domains Using Model-Based Parameter Estimation [J]. IEEE Trans. On Antennas Propagat., 2000, 48(3): 383-391.
[13] D.Jiao and J.M.Jin. Asymptotic Waveform Evaluation for Scattering by a Dispersive Dielectric Object [J]. Microwave Opt. Tech Lett., 2000, 24(4): 232-234.
[14] 熊邺，方大纲，盛卫星．雷达散射截面基于MBPE模型的在频空两域的双内插[J]．电波科学学报，2001，16(3)：287-290．
[15] Zhengshe Liu and Jian Li. Implementation of the RELAX Algorithm[J]. IEEE Transactions on Aerospace and Electronic Systems, 1998, 34(2): 657-664.
[16] Kay, S.M. and S.L.Marple. Spectrum ananlysis: A modern perspective [J].Proc.IEEE, 1981, 69: 1380-1419.
[17] Roy, R. and T. Kailath. Total least squares ESPRIT [M]. in Proc. 21st Asilomar conf. Singnals, Syst., Comput., 1987, 297-301.
[18] Schmidt, R.O.. Multiple emitter location and signal parameter estimation[J]. IEEE Trans. on Antennas Propagat., 1986, 34: 276-280.
[19] R.L.Wagner and W.C.Chew. A Study of Wavelets for the Solution of Electromagnetic Integral Equations [J]. IEEE Trans. Antennas and Propagat., 43(8): 802-810.
[20] Q.J.Zhang, K.C.Kupta. Neural Networks for RF and Microwave Design [M]. Artech House, 2000.
[21] D.X.Jin, S.M.Cui and D.G. Fang. An efficient representation for radar scattering with use of the genetic algorithm [J]. Microwave Optical Tech. Lett., 1997, 15: 36-39.
[22] Q.Li, E.J. Rothwell, K.Chen and D.P.Nyquist. Scattering Center Analysis of Radar Targets Using Fitting Scheme and Genetic Algorithm [J]. IEEE Trans. Antennas Propagat., 1996, 44: 198-207.
[23] C.J.Reddy, M.D.Deshpande, C.R.Cockrell, and F.B.Beck. Fast RCS Computation over a Frequency Band Using Method of Moments in Conjunction with Asymptotic Waveform Evaluation Technique [J]. IEEE Trans. Antennas Propagat., 1998, 46: 1129-1233.
[24] Ahmad Hoorfar. Simple Closed-Form Expressions For Microstrip Green's Functions in a Magneto-dielectric Substrate [J]. Mircrowave Opt. Tech. Letters, 1995, 8(1): 33-36.
[25] William H.Press, Saul A.Teukolsky, William T. Vetterling and Brian P.Flannery. Numerical Recipes in FORTRAN, Chapter 3[M]. Cambridge University Press, 1992.
[26] 熊邺，方大纲，吴克利，盛卫星．雷达散射截面频空两域双内插的研究[M]．电波科学学报增刊，2001，79-85．
[27] Yuanxun Wang and Hao Ling. Radar signature prediction using moment method codes via a frequency extrapolation technique [J]. IEEE Transactions on Antennas and Propagation, 1999, 47(6): 1008-1015.
[28] Yuanxun Wang and Hao Ling. A model-based angular extrapolation technique for iterative method-of-moments solves [J]. Microwave and Optical Technology Letters,
1999，20(4)：229-233．
[29]王浩刚，聂在平．一种求解单站RCS的高效算法[J]．电子学报，1999，27(9)： 28-31．
[30]Raviraj S. Adve and Tapan K. Sarkar. Simultaneous Time-and Frequency-Domain Extrapolation [J]. IEEE Trans. on Antennas and Propagation, 1998, 46(4): 484-493.
[31]Tapan K. Sarkar. Simultaneous Exptraolation in Time and Frequency Domain Using Hermite Expansions[J]. IEEE Trans. on Antennas and Propagation, 1999, 47(6): 1108-1115.
[32]N.Shahid, W.X.Sheng, D.G.Fang and X.D.Ye. The high resolution estimate—A comparative study [M]. Inter. Conf. on Comput. EM and its Appl. (ICCEA), 1999, 262-265.
[33]M.A.Kolbehdari, M.Srinivasan, M.S.Nakhla, Q.J.Zhang, and R.Achar. Simultaneous time and frequency domain solutions of EM problems using finite element and CFH techniques [J]. IEEE Trans. Microwave Theory Tech., 1996, 44: 1526-1534.
[34]T.Dhaene etal. Adaptive sampling algorithm for fast and accurate S-parameter modeling of genered planar structures [M]. IEEE MTT-S, 1995, 1427-1430.
[2] V.V.Veremey and R.Mittra. Domain Decomposition Approach for Capacifance Computation of Nonorthogonal Interconnect Structures[J]. IEEE Trans. On Microwave Theory & Tech, 2000, 48(9): 1428-1434.
[3] R.S.Chen, D.G.Fang, K.F.Tsang, and E.K.N.Yung. Analysis of electromagnetic wave scattering by an electrically Large metallic grating using wavelet-based algebraic multigrid preconditioned CG method——abstract [J]. J. of EM Waves & Appl., 2000, 14: 1559-1561.
[4] E. K. Miller. Model-based parameter estimation in electromagnetic Pt. 1[J]. IEEE Antennas and Propagation Magazine, 1998, 40(1): 40-52.
[5] E. K. Miller. Model-based parameter estimation in electromagnetic Pt. 2[J]. IEEE Antennas and Propagation Magazine, 1998, 40(2): 51-65.
[6] E. K. Miller. Model-based parameter estimation in electromagnetic Pt. 3 [J]. IEEE Antennas and Propagation Magazine, 1998, 40(3): 49-66.
[7] E.Chiprout and M.Nakhla. Asymptotic Waveform Evaluation and Moment Matching for Interconnect Analysis [M]. Boston, MA:Kluwer Academic Publishers, 1994.
[8] W.T.Smith,R.D.Slone, and S.K.Das. Recent progress in reduced-order modeling of electrical interconnects using asymptotic waveform evaluation and Pad é approximation via the Lanczos process [J]. Appl. Comput. Electromagn. Soc. Newslett., 1997, 12: 46-71.
[9] 章创明，洪伟．渐近波形估计技术用于介质柱宽角度RCS的计算[J]．电波科学学报，2001，16(1)：72-75．
[10] 汪杰，洪伟．三维散射体宽角度RCS的快速算法[J]．电波科学学报，2001，16(2)：241-244
[11] W.X.Sheng, D.G.Fang, J.Zhuang, T.J.Liu and Z.L.Yang. Data Compression in RCS modelingby TDFT[J]. 电子学报(英文版), 2001, 10(4): 557-559.
[12] Doualas H. Werner and Rene J.Allard. The Simultaneous Interpolation of Antenna Radiation Patterns in Both the Spatial and Frequency Domains Using Model-Based Parameter Estimation [J]. IEEE Trans. On Antennas Propagat., 2000, 48(3): 383-391.
[13] D.Jiao and J.M.Jin. Asymptotic Waveform Evaluation for Scattering by a Dispersive Dielectric Object [J]. Microwave Opt. Tech Lett., 2000, 24(4): 232-234.
[14] 熊邺，方大纲，盛卫星．雷达散射截面基于MBPE模型的在频空两域的双内插[J]．电波科学学报，2001，16(3)：287-290．
[15] Zhengshe Liu and Jian Li. Implementation of the RELAX Algorithm[J]. IEEE Transactions on Aerospace and Electronic Systems, 1998, 34(2): 657-664.
[16] Kay, S.M. and S.L.Marple. Spectrum ananlysis: A modern perspective [J].Proc.IEEE, 1981, 69: 1380-1419.
[17] Roy, R. and T. Kailath. Total least squares ESPRIT [M]. in Proc. 21st Asilomar conf. Singnals, Syst., Comput., 1987, 297-301.
[18] Schmidt, R.O.. Multiple emitter location and signal parameter estimation[J]. IEEE Trans. on Antennas Propagat., 1986, 34: 276-280.
[19] R.L.Wagner and W.C.Chew. A Study of Wavelets for the Solution of Electromagnetic Integral Equations [J]. IEEE Trans. Antennas and Propagat., 43(8): 802-810.
[20] Q.J.Zhang, K.C.Kupta. Neural Networks for RF and Microwave Design [M]. Artech House, 2000.
[21] D.X.Jin, S.M.Cui and D.G. Fang. An efficient representation for radar scattering with use of the genetic algorithm [J]. Microwave Optical Tech. Lett., 1997, 15: 36-39.
[22] Q.Li, E.J. Rothwell, K.Chen and D.P.Nyquist. Scattering Center Analysis of Radar Targets Using Fitting Scheme and Genetic Algorithm [J]. IEEE Trans. Antennas Propagat., 1996, 44: 198-207.
[23] C.J.Reddy, M.D.Deshpande, C.R.Cockrell, and F.B.Beck. Fast RCS Computation over a Frequency Band Using Method of Moments in Conjunction with Asymptotic Waveform Evaluation Technique [J]. IEEE Trans. Antennas Propagat., 1998, 46: 1129-1233.
[24] Ahmad Hoorfar. Simple Closed-Form Expressions For Microstrip Green's Functions in a Magneto-dielectric Substrate [J]. Mircrowave Opt. Tech. Letters, 1995, 8(1): 33-36.
[25] William H.Press, Saul A.Teukolsky, William T. Vetterling and Brian P.Flannery. Numerical Recipes in FORTRAN, Chapter 3[M]. Cambridge University Press, 1992.
[26] 熊邺，方大纲，吴克利，盛卫星．雷达散射截面频空两域双内插的研究[M]．电波科学学报增刊，2001，79-85．
[27] Yuanxun Wang and Hao Ling. Radar signature prediction using moment method codes via a frequency extrapolation technique [J]. IEEE Transactions on Antennas and Propagation, 1999, 47(6): 1008-1015.
[28] Yuanxun Wang and Hao Ling. A model-based angular extrapolation technique for iterative method-of-moments solves [J]. Microwave and Optical Technology Letters,
1999，20(4)：229-233．
[29]王浩刚，聂在平．一种求解单站RCS的高效算法[J]．电子学报，1999，27(9)： 28-31．
[30]Raviraj S. Adve and Tapan K. Sarkar. Simultaneous Time-and Frequency-Domain Extrapolation [J]. IEEE Trans. on Antennas and Propagation, 1998, 46(4): 484-493.
[31]Tapan K. Sarkar. Simultaneous Exptraolation in Time and Frequency Domain Using Hermite Expansions[J]. IEEE Trans. on Antennas and Propagation, 1999, 47(6): 1108-1115.
[32]N.Shahid, W.X.Sheng, D.G.Fang and X.D.Ye. The high resolution estimate—A comparative study [M]. Inter. Conf. on Comput. EM and its Appl. (ICCEA), 1999, 262-265.
[33]M.A.Kolbehdari, M.Srinivasan, M.S.Nakhla, Q.J.Zhang, and R.Achar. Simultaneous time and frequency domain solutions of EM problems using finite element and CFH techniques [J]. IEEE Trans. Microwave Theory Tech., 1996, 44: 1526-1534.
[34]T.Dhaene etal. Adaptive sampling algorithm for fast and accurate S-parameter modeling of genered planar structures [M]. IEEE MTT-S, 1995, 1427-1430.