本文選題：有限元　切入點：ABC吸收邊界條件　出處：《電子科技大學》2017年碩士論文

【摘要】：隨著社會的發(fā)展,以及國際形勢的不斷變化,科技的作用已經(jīng)越來越凸顯。而這其中,雷達無疑是發(fā)展的重點,因為它被稱為現(xiàn)代戰(zhàn)爭的眼鏡。而在雷達系統(tǒng)的設計中,目標的電磁散射特性研究是一項重要的共性基礎(chǔ)研究,它對于現(xiàn)代戰(zhàn)機的隱形設計、目標分類與識別、遠程預警和跟蹤等軍事應用都有著極其重要的參考價值。在研究電磁散射的數(shù)值計算方法中,有限元法被廣泛應用。而在實際應用中,很多電磁散射問題和輻射問題都涉及到無限區(qū)域,這時有限元法需要在離開目標一段距離的位置設置合適的邊界條件,導致計算量的急劇增加。雖然邊界積分法在積分方程的基礎(chǔ)上可以直接分析目標問題,但是最終要生成一個滿秩矩陣,這對計算機的內(nèi)存和計算要求較高,不能應用到尺寸較大的電磁問題中。為了更好地應用這兩種數(shù)值仿真方法,發(fā)展出了有限元-邊界積分法。通過引入一個虛構(gòu)的邊界可以將這種方法應用到實際的電磁問題中,以邊界面分割,邊界內(nèi)部應用有限元法,邊界外應用邊界積分法,并根據(jù)場的連續(xù)性進行耦合。有限元-邊界積分法對于處理大型無限域問題有著較大的優(yōu)勢,因此有必要對其進行研究和應用。本文主要工作分為以下三點:1首先介紹了矢量有限元方法的基本原理,并通過對波導問題的分析加深對有限元法的理解。在這個過程中,通過離散網(wǎng)格、添加插值函數(shù)、強加邊界條件、矩陣稀疏存儲以及對矩陣求解等過程得到最后的場圖和透射系數(shù)。并通過與HFSS仿真結(jié)果進行比較,計算誤差大小,進而對有限元法的過程進行一個詳細的概述。2在電磁散射和輻射等問題中,它們關(guān)心的是無限空間,而應用有限元法必須將無限大區(qū)域通過人工截斷邊界截斷為有限大區(qū)域,包括吸收邊界條件(ABC)和完全匹配層(PML),本文采用一階矢量吸收邊界條件計算三維結(jié)構(gòu)目標的散射問題。通過對規(guī)則模型的收斂性判斷,與HFSS仿真結(jié)果進行對比,并計算出其雷達截面RCS與解析解對比驗證自己的程序,并得到一些復雜模型的RCS,從而完成一套適用于任意三維結(jié)構(gòu)模型的程序。3最后,引入有限元邊界積分解決電磁散射問題,通過Ez極化和Hz極化兩種方式對其進行推導,得出最后的矩陣方程組和矩陣元素的表達式,并對一般的二維模型進行了計算,包括其雙站RCS,并和資料的結(jié)果進行了詳細的比對。
[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.
【學位授予單位】：電子科技大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：TN011

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