【作者】 阙肖峰；

【导师】 聂在平；

【作者基本信息】 电子科技大学 ， 电磁场与微波技术， 2008， 博士

【摘要】 本文主要研究了具有电大尺寸和复杂材料组分的目标三维矢量电磁辐射与散射的精确建模和高效数值求解问题。针对这一问题,本文分别研究了复杂目标的精确几何建模和电磁建模方法、复杂导体介质组合目标快速求解算法,以及复杂不规则几何结构目标的快速算法。首先,本文系统地阐述了矩量法的基本原理和关键步骤。采用曲面三角形单元和曲RWG基函数模拟曲面目标的几何形状以及曲面上的电流分布,运用Duffy变换方法处理积分方程的奇异性问题,采用广义最小残差算法(GMRES)对线性方程组进行迭代求解。数值算例验证了代码的可靠性。接着本文着重讨论了用于任意导体介质组合目标电磁特性分析的表面积分方程方法。根据等效原理,推导得到多种形式的表面积分方程,提出了CFIE-JMCFIE组合形式的混合场积分方程,与其他组合形式的方程在迭代求解收敛性以及实用性方面进行了系统、全面地比较。证明该方程构造的阻抗矩阵形式对角线元素占优,条件数好,迭代求解具有良好的收敛性。CFIE-JMCFIE方程的提出为准确、高效地运用积分方程求解组合目标的散射问题打下基础。本文还研究了多个导体、介质材料的组合结构,分析了积分方程和基函数在多个分界面连接处的定义以及积分方程的组合形式。另外还研究了一类简化多区域分界面处理的电磁建模方法—连接域方法(CRM)。为实现电大尺寸目标的高效求解,本文提出了基于CFIE-JMCFIE的多层快速多极子算法(MLFMA)。在全面阐述MLFMA的基本原理和数值实现过程的基础上,重点研究了介质域内MLFMA的参数选取和预条件技术。数值算例表明,利用CFIE-JMCFIE阻抗矩阵对角元素占优的特点,采用块对角预条件技术的MLFMA能实现对电大尺寸导体介质组合目标电磁特性分析的快速计算。在此基础上,进一步研究了基于MLFMA的稀疏近似逆(SAI)预条件技术。提出一类改进分组策略的SAI预条件方法,降低了构造预条件器的计算复杂度,提高了积分方程求解的收敛速度。然后提出了基于高阶叠层矢量基函数的高阶MLFMA用于组合目标电磁散射分析。采用基于修正勒让德多项式的最大正交化高阶叠层矢量基函数减少未知量数目,降低阻抗矩阵条件数。针对大贴片剖分单元,详细分析了高阶MLFMA的分组策略,提出了参数最优化选取原则。数值算例表明在合理选择基函数阶数和剖分单元大小的情况下,高阶MLFMA具有较高的计算精度和计算效率。针对含开放结构的导体介质组合目标问题,我们提出了一类新的混合场积分方程形式IEFIE-IPMCHW。通过引入积分方程的主值项,有效地改善了原积分方程算子的条件数。该方程利用内外两层迭代逼近真解,对分析开放、不规则目标的电磁问题具有较高的计算效率。最后,本文研究具有线面连接结构的载体上天线问题。研究了线面连接结构的面面等效方法,对天线加载或者移动时仅对加载点附近剖分单元进行重新划分,准确地得到天线阻抗和辐射特性。进一步研究了Costa连接基函数,分别采用迭代矩量法-物理光学法(MoM-PO)以及结合预条件技术的MLFMA实现了复杂平台上天线问题的高效求解。本文的研究工作为具有复杂形状和结构、复杂材料组分的目标电磁辐射与散射问题的精确建模和快速求解提供了有效的方法途径,也为该课题的进一步深入开展打下了坚实的基础。更多还原

【Abstract】 The rigorous modeling and high efficient calculation of electromagnetic radiation and scattering from complex electrically-large targets is studied in this dissertation. It is discussed from three points. First, accurate geometrical and electromagnetic modeling for complex targets; secondly, the details of effectively solving the integral equations by fast numerical methods; thirdly, analyzing the fast algorithms for complex irregular objects.Firstly, the crux techniques of the basic method for solving the integral equations-method of moment (MoM) have been studied. Curvilinear triangular patches and curvilinear RWG basis function are used to model the shape of the curved surface and the current distribution on the curved surface, respectively. A Duffy’s transformation method is used to solve the singularity of integral equation and the general minimum residual method (GMRES) is used to solve linear equations. Numerical examples validate our codes.Then, the surface integral equations (SIEs) for composite conducting and dielectric objects are presented. Some formulations of SIEs are derived from equivalent principle. A new CFIE-JMCFIE formulation is proposed and compared with other equations from iterative characteristics and the applicability. CFIE-JMCFIE requires fewer iterations than other formulations because its impedance matrix is diagonally dominant and has low condition number. A treatment for SIEs and basis functions on the junctions of composite objects with multiple metallic and dielectric regions is discussed. A new contact region method (CRM) is proposed to simplify the treatment for complex composite objects.As key techniques for solving the scattering by electrically-large object efficiently, extensive study of the multilevel fast multipole algorithm (MLFMA) based on CFIE-JMCFIE has been carried out. The principles and the numerical realization in dielectric regions of MLFMA have been described. The numerical examples show that MLFMA with block-diagonal preconditioner can solve electrically-large problems accurately and efficiently. Where after, some other preconditioners based on MLFMA have been studied. A new grouped sparse approximate inverse (SAI) preconditioner is proposed to save the construction cost significantly and reduce the iteration number.For the sake of reducing unknowns, a higher order MLFMA, using the maximally orthogonalized higher order hierarchical vector basis functions based on modified Legendre polynomials, is proposed. To improve the efficiency of higher order MLFMA with large patches, a detailed discussion for grouping and parameters and the referenced principle are given. Through reasonably chousing the order of basis function and the size of the patches, higher order MLFMA can solve scattering problem for composite objects efficiently and accurately.Aimed at resolving the scattering by composite object with open metallic structure with high efficient solution, a new IEFIE-IPMCHW formulation has been proposed. By adding the principal value term into EFIE-PMCHW operator, a well-conditioned IEFIE-IPMCHW operator is constructed. To achieve a reasonable accuracy, several update steps for the current vector are required. This method attains much faster convergence of iterations than conventional methods, particularly for 3-D structures with open or sharp surface.Finally, detailed work has been done for the problems of complicated objects attached with wires, such as wire monopoles on platform. A surface/surface junction mode has been used to model the wire/surface junction. When the monopole is added or moved on the surface, accurate results of impedance and radiation properties have been achieved and only a few triangular patches need to be resegmented near the attachment point. Then, a Costa’s junction basis function is described. An iterative MoM-PO method and a preconditioned MLFMA are employed to solve the electrically-large problems, respectively.As a basic research work for electromagnetic radiation and scattering characteristics of the 3-D electrically-large objects with arbitrary shape and materials, this research work presented in the dissertation provides the powerful way in rigorous modeling and effective solution, as well as a solid foundation for the further development in this subject.更多还原