基于有限元方法对三维结构电磁散射问题的研究

发布时间：2018-04-06 00:23

本文选题：有限元　切入点：ABC吸收边界条件　出处：《电子科技大学》2017年硕士论文

【摘要】：随着社会的发展,以及国际形势的不断变化,科技的作用已经越来越凸显。而这其中,雷达无疑是发展的重点,因为它被称为现代战争的眼镜。而在雷达系统的设计中,目标的电磁散射特性研究是一项重要的共性基础研究,它对于现代战机的隐形设计、目标分类与识别、远程预警和跟踪等军事应用都有着极其重要的参考价值。在研究电磁散射的数值计算方法中,有限元法被广泛应用。而在实际应用中,很多电磁散射问题和辐射问题都涉及到无限区域,这时有限元法需要在离开目标一段距离的位置设置合适的边界条件,导致计算量的急剧增加。虽然边界积分法在积分方程的基础上可以直接分析目标问题,但是最终要生成一个满秩矩阵,这对计算机的内存和计算要求较高,不能应用到尺寸较大的电磁问题中。为了更好地应用这两种数值仿真方法,发展出了有限元-边界积分法。通过引入一个虚构的边界可以将这种方法应用到实际的电磁问题中,以边界面分割,边界内部应用有限元法,边界外应用边界积分法,并根据场的连续性进行耦合。有限元-边界积分法对于处理大型无限域问题有着较大的优势,因此有必要对其进行研究和应用。本文主要工作分为以下三点:1首先介绍了矢量有限元方法的基本原理,并通过对波导问题的分析加深对有限元法的理解。在这个过程中,通过离散网格、添加插值函数、强加边界条件、矩阵稀疏存储以及对矩阵求解等过程得到最后的场图和透射系数。并通过与HFSS仿真结果进行比较,计算误差大小,进而对有限元法的过程进行一个详细的概述。2在电磁散射和辐射等问题中,它们关心的是无限空间,而应用有限元法必须将无限大区域通过人工截断边界截断为有限大区域,包括吸收边界条件(ABC)和完全匹配层(PML),本文采用一阶矢量吸收边界条件计算三维结构目标的散射问题。通过对规则模型的收敛性判断,与HFSS仿真结果进行对比,并计算出其雷达截面RCS与解析解对比验证自己的程序,并得到一些复杂模型的RCS,从而完成一套适用于任意三维结构模型的程序。3最后,引入有限元边界积分解决电磁散射问题,通过Ez极化和Hz极化两种方式对其进行推导,得出最后的矩阵方程组和矩阵元素的表达式,并对一般的二维模型进行了计算,包括其双站RCS,并和资料的结果进行了详细的比对。
[Abstract]:With the development of society and the changing international situation, the role of science and technology has become more and more prominent.Among them, radar is undoubtedly the focus of development, because it is called the spectacles of modern war.In the design of radar system, the study of electromagnetic scattering characteristics of target is an important general basic research, it is for the stealth design of modern fighter, target classification and recognition,Military applications such as long-range early warning and tracking have extremely important reference value.Finite element method is widely used in the numerical calculation of electromagnetic scattering.However, in practical applications, many electromagnetic scattering and radiation problems are related to the infinite region. In this case, the finite element method needs to set appropriate boundary conditions at a distance from the target, resulting in a sharp increase in computation.Although the boundary integral method can directly analyze the target problem on the basis of the integral equation, a full rank matrix should be generated in the end, which requires high memory and computation of the computer, and can not be applied to the larger size electromagnetic problem.In order to better apply these two numerical simulation methods, a finite element-boundary integration method is developed.By introducing a fictitious boundary, this method can be applied to practical electromagnetic problems. The boundary surface is divided, the finite element method is applied within the boundary, the boundary integral method is applied outside the boundary, and the coupling is carried out according to the continuity of the field.The finite element-boundary integration method has great advantages in dealing with large infinite domain problems, so it is necessary to study and apply it.The main work of this paper is as follows: 1. Firstly, the basic principle of vector finite element method is introduced, and the understanding of finite element method is deepened through the analysis of waveguide problem.In this process, the final field diagram and transmission coefficient are obtained by discrete mesh, adding interpolation function, imposing boundary condition, sparse storage of matrix and solving matrix.By comparing with the results of HFSS simulation, the error is calculated, and then the process of finite element method is summarized in detail. 2 in the problems of electromagnetic scattering and radiation, they are concerned with infinite space.However, the finite element method must be used to truncate the infinite region into a finite area by artificial truncation, including the absorbing boundary condition (ABC) and the perfectly matched layer (PML). In this paper, the first-order vector absorbing boundary condition is used to calculate the scattering problem of three-dimensional structural targets.By judging the convergence of the regular model and comparing it with the HFSS simulation results, the radar cross section (RCS) of the model is compared with the analytical solution to verify its own program.Finally, the finite element boundary integral is introduced to solve the electromagnetic scattering problem. It is deduced by two ways of z polarization and Hz polarization.Finally, the expressions of matrix equations and matrix elements are obtained, and the general two-dimensional model is calculated, including its bistatic RCS, and the results are compared in detail with the data.
【学位授予单位】：电子科技大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TN011

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