矩量法及其加速算法研究一维粗糙面与目标复合电磁散射
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摘要
本论文采用矩量法(Method of Moment, MOM)及其相关加速算法深入系统地研究了一维粗糙面及其与二维目标的复合电磁散射问题。首先研究了一维理想导体和介质粗糙面的电磁散射特性;然后分析了一维单(分)层介质粗糙面与二维理想导体目标的复合电磁散射特性;最后给出了并行技术和多区域分解技术在一维粗糙面及其与目标复合电磁散射求解中的应用。主要工作如下:
1、介绍了矩量法(Method of Moment, MOM)和快速多极子(Fast Multipole Method, FMM)的基本原理和基本知识,给出了MOM求解一维理想导体粗糙面电磁散射的积分方程和矩阵方程建立的详细过程,并对采用FMM计算一维理想导体粗糙面电磁散射的具体实施过程进行了详细说明。
2、利用FMM快速求解了一维介质粗糙面的双站电磁散射,给出了二维理想导体目标放置在一维介质粗糙面的上方、下方和半掩埋时复合电磁散射矩量法求解的详细过程,并讨论粗糙面的特征参数和目标的几何参数对复合散射的影响。
3、推导了一维多层粗糙面及其与二维理想导体目标复合电磁散射MOM求解的积分方程和矩阵方程,讨论了分层粗糙面在不同极化下的电磁散射特性,以及目标放置在分层粗糙面的上方、下方或者两层之间时的复合电磁散射特性,讨论了粗糙面的特征参数、目标的几何参数以及两层粗糙面之间填充的媒质和厚度对电磁散射特性的影响。
4、将并行技术和多区域分解技术引入到一维粗糙面及其与目标的复合电磁散射的快速求解中,给出了加速算法在粗糙面及其与目标复合电磁散射应用的详细过程,并说明了加速算法在计算时间方面的优势,讨论了粗糙面的特征参数及目标的几何参数对复合散射的影响。
In this thesis, the properties of the composite scattering from a one-dimensional (1-D) rough surface with or without a two-dimensional (2-D) object are investigated by the method of moment (MOM) and its fast algorithms. Firstly, the characteristics of the electromagnetic (EM) scattering from a 1-D perfectly electric contour (PEC) or a 1-D dielectric rough surface is examined. The composite scattering from a 1-D single-layered or two-layered dielectric rough surface and a 2-D object is calculated. Finally, the parallel algorithm and the multiregion technique are applied to compute the composite scattering of the 1-D rough surface and the 2-D object. Main works of this thesis are as following:
1. The fundamental of the MOM and the fast multipole method (FMM) are presented. The integral equations and the matrix equations for calculating the EM scattering from a 1-D PEC rough surface are provided in detail. The implementation of calculating EM scattersing from the 1-D PEC rough surface has been described in detail.
2. The bistatic scattering from a 1-D dielectric rough surface is calculated by the fast FMM. The processes of obtaining the composite scattering from a 2-D PEC object located above, below or embedded in the 1-D dielectric rough surface through the MOM are given in detail. The influences of the parameters of the rough surface and the object on the composite scattering are illustrated.
3. The integral equations and the matrix equations for calculating the EM scattering from a 1-D multi-layered rough surface with or without 2-D PEC object are derived. The properties of the EM scattering from two-layered rough surface are discussed. The composite scattering from the 2-D object located above, below and between the two rough surfaces is computed. Finally, the influences of the parameters of the rough surfaces and the object, as well as the average height between the two rough surfaces and the medium on the composite scattering are discussed.
4. The parallel algorithm and the multiregion technique have been introduced to compute the composite scattering of the 1-D rough surface and the 2-D object. The solution to the above scattering problem by these fast algorithms has been presented in detail. The advantage in the computing time of these fast algorithms is presented, and the influences of the parameters of the rough surface and the object are discussed.
1、介绍了矩量法(Method of Moment, MOM)和快速多极子(Fast Multipole Method, FMM)的基本原理和基本知识,给出了MOM求解一维理想导体粗糙面电磁散射的积分方程和矩阵方程建立的详细过程,并对采用FMM计算一维理想导体粗糙面电磁散射的具体实施过程进行了详细说明。
2、利用FMM快速求解了一维介质粗糙面的双站电磁散射,给出了二维理想导体目标放置在一维介质粗糙面的上方、下方和半掩埋时复合电磁散射矩量法求解的详细过程,并讨论粗糙面的特征参数和目标的几何参数对复合散射的影响。
3、推导了一维多层粗糙面及其与二维理想导体目标复合电磁散射MOM求解的积分方程和矩阵方程,讨论了分层粗糙面在不同极化下的电磁散射特性,以及目标放置在分层粗糙面的上方、下方或者两层之间时的复合电磁散射特性,讨论了粗糙面的特征参数、目标的几何参数以及两层粗糙面之间填充的媒质和厚度对电磁散射特性的影响。
4、将并行技术和多区域分解技术引入到一维粗糙面及其与目标的复合电磁散射的快速求解中,给出了加速算法在粗糙面及其与目标复合电磁散射应用的详细过程,并说明了加速算法在计算时间方面的优势,讨论了粗糙面的特征参数及目标的几何参数对复合散射的影响。
In this thesis, the properties of the composite scattering from a one-dimensional (1-D) rough surface with or without a two-dimensional (2-D) object are investigated by the method of moment (MOM) and its fast algorithms. Firstly, the characteristics of the electromagnetic (EM) scattering from a 1-D perfectly electric contour (PEC) or a 1-D dielectric rough surface is examined. The composite scattering from a 1-D single-layered or two-layered dielectric rough surface and a 2-D object is calculated. Finally, the parallel algorithm and the multiregion technique are applied to compute the composite scattering of the 1-D rough surface and the 2-D object. Main works of this thesis are as following:
1. The fundamental of the MOM and the fast multipole method (FMM) are presented. The integral equations and the matrix equations for calculating the EM scattering from a 1-D PEC rough surface are provided in detail. The implementation of calculating EM scattersing from the 1-D PEC rough surface has been described in detail.
2. The bistatic scattering from a 1-D dielectric rough surface is calculated by the fast FMM. The processes of obtaining the composite scattering from a 2-D PEC object located above, below or embedded in the 1-D dielectric rough surface through the MOM are given in detail. The influences of the parameters of the rough surface and the object on the composite scattering are illustrated.
3. The integral equations and the matrix equations for calculating the EM scattering from a 1-D multi-layered rough surface with or without 2-D PEC object are derived. The properties of the EM scattering from two-layered rough surface are discussed. The composite scattering from the 2-D object located above, below and between the two rough surfaces is computed. Finally, the influences of the parameters of the rough surfaces and the object, as well as the average height between the two rough surfaces and the medium on the composite scattering are discussed.
4. The parallel algorithm and the multiregion technique have been introduced to compute the composite scattering of the 1-D rough surface and the 2-D object. The solution to the above scattering problem by these fast algorithms has been presented in detail. The advantage in the computing time of these fast algorithms is presented, and the influences of the parameters of the rough surface and the object are discussed.
引文
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