介质目标散射和载体天线辐射的电磁问题研究

发布时间：2018-05-27 17:16

本文选题：矩量法 + 介质目标　；参考：《西安电子科技大学》2016年博士论文

【摘要】：雷达在第二次世界大战中得到了迅速的发展,时至今日发展成为能够代表一个国家军事工业先进水平的典型案例。雷达系统的设计和目标电磁散射特性的预估与系统前端天线辐射特性的分析是紧密相关的。目标电磁散射特性的预估是以电磁计算方法为基础的,其最终要求则是能够对外形复杂和电大尺寸的目标进行精确且快速的分析。另一方面,天线辐射特性分析的难点之一在于能够有效计算各种复杂载体平台对天线性能的影响。本文基于以上背景并结合国防预研项目,着重研究了电磁算法中有关介质目标的矩量法及其快速算法,并结合扫频算法实现了针对介质目标的快速宽带散射分析。此外,对载体平台上天线辐射特性的快速分析进行了相关研究。本文的主要工作可以概括为以下六个方面：1.详细研究了电场积分方程的矩量法。介绍了矩量法的数学原理,根据理想导体边界条件建立了电场积分方程。着重讨论了RWG基函数的特点、伽略金检验过程和高斯数值积分,对奇异性问题进行了细致的公式推导。2.详细研究了基于PMCHWT方程和体积分方程的矩量法。从均匀介质目标散射模型的等效外问题和等效内问题出发,阐述了PMCHWT方程的形成过程。用矩量法对PCMHWT方程进行求解,并讨论了子阻抗矩阵的对称性和其奇异性问题。介绍了基于四面体剖分的SWG基函数及其的特点。用矩量法对适用于一般介质目标的体积分方程进行求解,并对奇异性问题给出了详细的公式推导。对介质金属混合目标的矩量法进行了拓展研究。3.介绍了积分方程-快速傅里叶变换方法(IE-FFT)中均匀笛卡尔网格的建立和自由空间格林函数的拉格朗日多项式插值技术,形象地展示了离散格林函数矩阵的三重Toeplitz特性,完整的阐述了具有三重Toeplitz特性的矩阵和向量乘积的快速傅里叶变换(FFT)加速原理。针对矩量法内存需求大和求解矩阵方程计算复杂度较高的问题,研究了基于PMCHWT方程的IE-FFT技术,并比较了两种可能的FFT加速策略,将内存和计算复杂度降低到O(N1.5)和O(N1.5log N)。同样,研究了基于体积分方程的IE-FFT方法,有效的将内存和计算复杂度降低到O(N)和O(N log N)。4.提出将体积分方程矩量法分别结合渐近波形估计和最佳一致有理逼近来快速预估一般介质目标的宽带电磁散射特性。第一种方法在给定频点对矩阵方程中的阻抗矩阵、激励向量和未知向量进行泰勒展开,对关于频率的多项式进行合并同类项来求解未知向量的泰勒展开系数,通过Pad6逼近对未知向量做进一步展开来延展带宽。第二种方法在给定的整个带宽内选定切比雪夫节点,计算其对应波数上的等效体电流密度,并通过梅利逼近来提高计算精度。将PMCHWT-IE-FFT和最佳一致有理逼近相结合来快速分析均匀介质目标的宽带散射特性,通过FFT加速技术缩短了最佳一致有理逼近方法中电磁流密度的求解时间。5.针对矩量法物理光学混合算法(MoM-PO)中修正阻抗矩阵填充计算复杂度较大的问题,提出将MoM-PO和IE-FFT相结合的IE-FFT-PO方法。首先对修正阻抗矩阵进行矩阵分解得到矩量法区和物理光学区之间互阻抗矩阵和耦合矩阵的乘积。稀疏存储自阻抗矩阵、互阻抗矩阵和耦合矩阵的阻抗元素,并对矩阵方程求解每一步迭代中的三次矩阵向量积运算进行FFT加速。6.针对载体平台上多天线的辐射问题,提出基于MoM-PO方法的分区技术,将每一个天线及其附近区域划分为一个矩量法区,剩余部分为物理光学区。该方法在考虑每一个矩量法区和物理光学区之间耦合作用的基础上,进一步考虑多个矩量法区之间的相互作用。相比传统MoM-PO方法,其结果是修正阻抗元素个数的大幅减少,从而缩短自阻抗矩阵需要的修正时间。借鉴迭代MoM-PO的思想,提出了分区迭代的MoM-PO方法,相比分区MoM-PO方法,进一步缩短了载体平台多线天线辐射问题分析所需要的时间。
[Abstract]:Radar has developed rapidly in the Second World War, and today it has developed into a typical case that can represent the advanced level of a country's military industry. The design of the radar system and the prediction of the target electromagnetic scattering characteristics are closely related to the analysis of the radiation characteristics of the front end of the system. The prediction of the target electromagnetic scattering characteristics It is based on the electromagnetic calculation method, and its final requirement is to be able to accurately and quickly analyze the complex and large size targets. On the other hand, one of the difficulties of antenna radiation analysis is to effectively calculate the influence of various complex carrier platforms on the performance of the antenna. This paper is based on the background and the national defense. In the pre research project, the moment method and its fast algorithm about the medium target in the electromagnetic algorithm are emphatically studied, and the fast broadband scattering analysis for medium targets is realized with the sweep frequency algorithm. In addition, the rapid analysis of the antenna radiation characteristics on the carrier platform is studied. The main work of this paper can be summarized as the following six parties Surface: 1. the method of moment of the electric field integral equation is studied in detail. The mathematical principle of the moment method is introduced. The integral equation of the electric field is established according to the ideal conductor boundary condition. The characteristics of the RWG basis function, the Galerkin test process and the Gauss numerical integration are emphatically discussed. The detailed formula derivation of the singularity problem is carried out in the.2. detailed study based on the P The method of moment of the MCHWT equation and the body integral equation. Based on the equivalent external problem and the equivalent internal problem of the uniform medium target scattering model, the formation process of the PMCHWT equation is expounded. The PCMHWT equation is solved by the moment method, and the symmetry and singularity of the sub impedance matrix are discussed. The SWG base function based on the tetrahedral partition is introduced. The method of moment method is used to solve the volume equation applicable to the general medium target, and the detailed formula derivation is given to the singularity problem. The expansion of the moment method for the medium metal mixed target is extended..3. introduces the establishment of the uniform Cartesian grid in the integral equation fast Fourier transform square method (IE-FFT). The Lagrange polynomial interpolation technique of the free space Green function shows the three Toeplitz properties of the discrete Green function matrix, and expounds the fast Fu Liye transform (FFT) acceleration principle of the matrix and the vector product of the three heavy Toeplitz properties. The problem of high complexity is to study the IE-FFT technology based on PMCHWT equation, and compare two possible FFT acceleration strategies to reduce the memory and computational complexity to O (N1.5) and O (N1.5log N). Also, the IE-FFT method based on the body integral equation is studied. The memory and computational complexity are effectively reduced to O (N) and O (O). The method of moment of the body integral equation combines the Asymptotic Waveform Estimation and the best uniform rational approximation to quickly estimate the wide-band electromagnetic scattering characteristics of the general medium target. The first method is carried out by Taylor expansion of the impedance matrix, the excitation vector and the unknown vector in the matrix equation at a given frequency point, and the polynomial of the frequency is merged with the same kind. The Taylor expansion coefficient of the unknown vector is solved by the term, and the unknown vector is further expanded to extend the bandwidth by Pad6 approximation. The second methods select the Chebyshev node in the given whole bandwidth, calculate the equivalent body current density on the corresponding wave number, and improve the calculation precision by Melly approximation. Combining rational approximation to fast analysis the wide-band scattering characteristics of uniform medium targets, the time.5. for solving the electromagnetic flow density in the best uniform rational approximation method is shortened by FFT acceleration technology. The problem of calculating the complexity of the modified impedance matrix in the moment method physical optical mixing algorithm (MoM-PO) is solved, and MoM-PO and I are proposed. The IE-FFT-PO method combined with E-FFT. First, the matrix decomposition of the modified impedance matrix is used to obtain the product of the mutual impedance matrix and the coupling matrix between the moment method region and the physical optical region. The impedance matrix of the self impedance matrix, the mutual impedance matrix and the coupling matrix are sparsely stored, and the matrix formula is used to solve the three matrix vectors in each iteration of the matrix. The product operation is carried out by FFT acceleration.6. to solve the radiation problem of multi antenna on the carrier platform. The partition technique based on the MoM-PO method is proposed. Each antenna and its nearby region are divided into a moment method region, and the remaining part is the physical optical region. In one step, the interaction between the multiple moment method regions is considered. Compared with the traditional MoM-PO method, the result is a significant reduction in the number of impedance elements, thus shortening the correction time needed for the self impedance matrix. Using the idea of iterative MoM-PO, a MoM-PO method of partition iteration is proposed. The phase is compared to the partition MoM-PO method, and the carrier platform is further shortened. The time needed for the analysis of the radiation problem of a multiwire antenna.
【学位授予单位】：西安电子科技大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：TN011

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