电磁散射问题快速数值近似解法的研究
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摘要
积分方程法是求解电磁散射问题的重要方法之一,积分方程的矩量法的系数矩阵是一个满矩阵,求解该线性方程组是一个耗时的过程,通常采用迭代求解。基于积分方程的快速算法主要通过对系数矩阵的处理降低计算量和存储量。相对于数值解法,高频近似法在求解电磁散射问题,往往更有效率,但精度和对复杂结构适用性受限。研究将高频近似有机融合于数值求解方法中的数值近似法,将能在解决问题的效率与适用性方面取得更好的折衷。
本文研究基于高频照射照明区和阴影区概念、电磁场积分公式与数值迭代技术的混合算法。利用电磁场表面积分公式、高频近似和数值近似,提出了一种新的迭代方法,称为加窗测试迭代法。
首先,加窗测试迭代法应用于求解导体柱电磁散射问题:以表面感应电流为未知量建立积分方程求解散射场,在散射体表面构造单点测试方程,由电磁场边界条件与场关系式建立迭代式。依据高频近似概念在阴影区用实窗函数压缩迭代中产生的误差电流,窗函数应可根据散射体尺寸变化调整下降速度,故可利用凯塞窗的可调参数。文中讨论了窗函数参数的选取,并提出了改进的汉宁窗。区分不同的入射波情况,分别分析了柱体对TM和TE入射波的散射。在新方法中,迭代初始值选用物理光学电流,迭代过程中采用快速多极子法可加速矩阵向量乘积,减少计算开销。数值实验表明该方法快速、有效,仅需几次迭代就可收敛至足够精度,且迭代次数与散射体尺寸无关,适合于求解电大尺寸物体的电磁散射问题。
其次,加窗测试迭代法推广到均匀介质柱的电磁散射中。根据介质柱性质,提出了单测试方程和双测试方程两种情形下的加窗测试迭代法,并给出了单测试方程情形下的结果。
研究结果表明,本文提出的混合技术,有效融合了数值法和高频近似法的混合法,具有满意的精度、较好的适应性和较快的计算速度。
Integral equation method is one of important methods for solving electromagnetic scattering problems. Because the coefficient matrix of moment method (MM) is a dense matrix and solving the linear system is time-consuming, iterative methods are generally used for the solution. Fast algorithms based on integral equations are concentrating on dealing with the coefficient matrix to reduce the time consuming and memory space. Comparing with the numerical methods, high frequency approximation techniques are much more efficient in solving electromagnetic scattering problems, but it is limited in lower precision and applicability for scatterers with complex structures. Hybrid methods combined numerical methods with high frequency approximation would be better tradeoff between efficiency and applicability.
In this thesis, a hybrid technique using electromagnetic integral formulae and numerical iterative technique is investigated based on the regions of illumination and shadow in high frequency approximation. A novel iterative method is presented by combining numerical technique, high frequency approximation and surface integral formulae of the fields, which is called windowed iterative technique.
Windowed iterative technique is firstly applied to solve electromagnetic scattering problems of conducting cylinder. A single point measuring equation of a field is determined near the scatterer surface, and the iterative formula is established by use of the boundary conditions and field relationships. A window function is introduced to compress the error of current distribution in the shadow region. The descendent rate should be adjusted according to the scatterer sizes, so Kaiser window function is employed for its adjustable parameter. Parameter determination is discussed. Furthermore, a modified Hanning window is proposed. The scattering from cylinders under the TM and TE incidences are analyzed respectively. In the new technique, the solution is initialized with the physical optical current, and then is modified with the fast multipole method (FMM) to accelerate the matrix-vector multiplication and reduce computational costs. The numerical results demonstrate the efficiency and effectiveness. Sufficient accuracy can be reached after only several iterations which is independent of the sizes of the scatterers. It is can be employed to solve electromagnetic scattering problems of electrically large bodies.
Secondly, windowed iterative technique is extended to solve the scattering from homogeneous dielectric cylinders. Both single and double measuring equations are proposed. The results with the former are given.
It is concluded from the results that numerical methods and high frequency approximation can be syncretized in the hybrid technique proposed which possesses satisfactory precision, good applicability and less computational operations.
本文研究基于高频照射照明区和阴影区概念、电磁场积分公式与数值迭代技术的混合算法。利用电磁场表面积分公式、高频近似和数值近似,提出了一种新的迭代方法,称为加窗测试迭代法。
首先,加窗测试迭代法应用于求解导体柱电磁散射问题:以表面感应电流为未知量建立积分方程求解散射场,在散射体表面构造单点测试方程,由电磁场边界条件与场关系式建立迭代式。依据高频近似概念在阴影区用实窗函数压缩迭代中产生的误差电流,窗函数应可根据散射体尺寸变化调整下降速度,故可利用凯塞窗的可调参数。文中讨论了窗函数参数的选取,并提出了改进的汉宁窗。区分不同的入射波情况,分别分析了柱体对TM和TE入射波的散射。在新方法中,迭代初始值选用物理光学电流,迭代过程中采用快速多极子法可加速矩阵向量乘积,减少计算开销。数值实验表明该方法快速、有效,仅需几次迭代就可收敛至足够精度,且迭代次数与散射体尺寸无关,适合于求解电大尺寸物体的电磁散射问题。
其次,加窗测试迭代法推广到均匀介质柱的电磁散射中。根据介质柱性质,提出了单测试方程和双测试方程两种情形下的加窗测试迭代法,并给出了单测试方程情形下的结果。
研究结果表明,本文提出的混合技术,有效融合了数值法和高频近似法的混合法,具有满意的精度、较好的适应性和较快的计算速度。
Integral equation method is one of important methods for solving electromagnetic scattering problems. Because the coefficient matrix of moment method (MM) is a dense matrix and solving the linear system is time-consuming, iterative methods are generally used for the solution. Fast algorithms based on integral equations are concentrating on dealing with the coefficient matrix to reduce the time consuming and memory space. Comparing with the numerical methods, high frequency approximation techniques are much more efficient in solving electromagnetic scattering problems, but it is limited in lower precision and applicability for scatterers with complex structures. Hybrid methods combined numerical methods with high frequency approximation would be better tradeoff between efficiency and applicability.
In this thesis, a hybrid technique using electromagnetic integral formulae and numerical iterative technique is investigated based on the regions of illumination and shadow in high frequency approximation. A novel iterative method is presented by combining numerical technique, high frequency approximation and surface integral formulae of the fields, which is called windowed iterative technique.
Windowed iterative technique is firstly applied to solve electromagnetic scattering problems of conducting cylinder. A single point measuring equation of a field is determined near the scatterer surface, and the iterative formula is established by use of the boundary conditions and field relationships. A window function is introduced to compress the error of current distribution in the shadow region. The descendent rate should be adjusted according to the scatterer sizes, so Kaiser window function is employed for its adjustable parameter. Parameter determination is discussed. Furthermore, a modified Hanning window is proposed. The scattering from cylinders under the TM and TE incidences are analyzed respectively. In the new technique, the solution is initialized with the physical optical current, and then is modified with the fast multipole method (FMM) to accelerate the matrix-vector multiplication and reduce computational costs. The numerical results demonstrate the efficiency and effectiveness. Sufficient accuracy can be reached after only several iterations which is independent of the sizes of the scatterers. It is can be employed to solve electromagnetic scattering problems of electrically large bodies.
Secondly, windowed iterative technique is extended to solve the scattering from homogeneous dielectric cylinders. Both single and double measuring equations are proposed. The results with the former are given.
It is concluded from the results that numerical methods and high frequency approximation can be syncretized in the hybrid technique proposed which possesses satisfactory precision, good applicability and less computational operations.
引文
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[3]谢处方,高新技术与电磁场理论[J],安徽大学学报,1998,22(3):59-63
[4]任吉林,电磁无损检测的新进展[J],无损探伤,2001,5:1-5
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[15]赵维江,龚书喜,刘其中,复杂目标多次散射计算方法的高频混合方法研究[J],微波学报,1999,15(4):386-390
[16]李明之,王长清,徐承和,迭代物理光学法(IPO)求解高频部件互相耦合问题[J],电波科学学报,1997,12(2):176-179
[17]聂小春,葛德彪,闫玉波,IPO-MoM混合法分析开槽电大目标德电磁散射[J],电子学报,1999,27(9),108-110
[18] U. Jakobus and F. M. Landstorfer, Imporved PO-MM hybrid Formulation for scattering from three-dimensional perfectly conducting bodies of arbitray sharp[J],IEEE Trans. Antennas and propagat, 1995, 43(2):192-196
[19]崔索民,汪茂光,混合法在二维导体目标散射中的应用[J],电波科学学报,1995,10(1):57-62
[20]刘英,赵维江,龚书喜,计算物理光学积分的几种数值方法的分析[J],西安电子科技大学学报,2001,28(4):542-545
[21]张孟阳,冯孔豫,高频近似下新月形导体的散射场计算和散射体轮廓的投影重建[J],电子科学学刊,1996,18(11):620-626
[22]徐敬波,电大尺寸物体电磁散射的数值近似解法[D],无锡:江南大学,2003
[23] Hu Jun, Nie Zaiping, Solving electromagnetic scattering from two-dimensional cavity by FMM with complexifying k-technique[J], Microwave and optical technique letters, 1999, 20(6): 430-433
[24]胡俊,聂在平,二维多柱体电磁散射的快速算法[J],电子学报,1999,27(6):123-125
[25]胡俊,聂在平,王军,姚海英,王浩刚,三维大纵横比电磁散射的快速精确求解算法,电波科学学报[J],2000,15(2):235-237
[26]聂在平,胡俊,姚海英,王浩刚,用于复杂目标的三维矢量散射分析的快速多极子方法[J],1999,27(6):104-108
[27] R. L. wagner and W. C. Chew. A ray-propagation fast multipole algorithm. Microwave and Opt. Tech. Lett, 1994, 7(10):435-438
[28] V. Jandhyala, B. Shanker, E. Michielssen and W. C. Chew. A combined steepest descent-fast multipole algorithm for the analysis of three-dimensinal scattering by rough surfaces[A], Inter. IEEE Antennas and propagat symposium, 1997: 2308-2311
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[30] K. K. MEI, R. Pous, Z. Chen, Y. Liu, and M. Prouty, The measured equation of invariance-A new concept in field computation[J], IEEE Trans.Antennas Propagat., 1994, 42(3):320-28
[31]孙国安,电磁场与电磁波理论基础[M],南京,东南大学出版社,1999
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