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摘要有限元法作为计算电磁领域的一个高效数值方法，以其对各种电磁结构强大的拟合性，分析处理各种复杂媒质电磁问题的优越性在各种数值方法中脱颖而出[1]。但是使用有限元法求解大规模问题，如文中所涉及到的天线阵列时，未知量会急剧增加，导致内存消耗急剧增大，解方程的速度会受到计算机内存的限制而变慢，甚至无法计算下去。为了解决单机内存和速度限制的问题，本文在有限元法的基础上引入了区域分解法，采用“分而治之”的思想将目标区域分解成若干互不重叠的子区域单独求解，然后再通过在相邻子区域分界面上施加特定的连续的边界条件将它们重新联结在一起，克服了有限元法在处理大规模问题时因内存消耗过大而导致运算困难的缺点。19792
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本文首先介绍了有限元区域分解法的基本理论；然后运用有限元区域分解法分析了具有周期结构的微带阵列天线；接着分别分析了微带阵列天线，矩形波导阵列天线以及波导宽边缝隙天线阵。通过对比以上三种天线阵元和天线阵列的辐射方向图，可以很明显地发现阵列天线较之阵元单元能获得更好的增益及方向性。
关键词 计算电磁学 有限元区域分解 阵列天线 辐射特性
毕业论文设计说明书（论文）外文摘要
Title Analyzing the radiation pattern of antenna array by
Finite Element Domain Decomposition Method
Abstract
As an efficient numerical method, Finite Element Method stands out in a variety of numerical methods with its powerful fitting of various electromagnetic structure and superiority in analyzing complex medium electromagnetic problems. However, If the area has large size, such as the antenna array referred in the paper, the quantity of the unknowns will dramatically increase, resulting in a sharp increase in memory consumption and slow down in solving equations. In order to solve this problem, the Domain Decomposition Method was introduced in the paper, which has the "pide and conquer" mentality. The Domain Decomposition Method will break down the target area into a number of non-overlapping sub-regions to solve, and then re-join them together by impose a particular boundary condition to the surface of the sub-region. This method overcomes the shortcomings of the Finite Element Method in dealing with large-scale problems due to excessive memory consumption.
This paper firstly described the basic theory of the Finite Element Domain Decomposition Method. Then use Finite Element Domain Decomposition Method to analyze periodic Microstrip antenna array, rectangular waveguide array and broadside waveguide slot array. By comparing these three antenna unit’s radiation pattern with array’s, it is obvious that the array get better gain and directivity.
Keywords Computational electromagnetics Finite Elemen Domain Decomposition antenna array radiation pattern
目 次
1 绪论 1
1.1 研究背景 1
1.2 研究历史和现状 2
1.3 本文的内容安排 3
2 有限元区域分解法分析天线阵列的辐射特性 4
2.1 引言 4
2.2 有限元区域分解法基本原理 4
2.3 有限元区域分解法分析具有周期结构的微带阵列天线 6
2.5 本章小结 8
3 微带阵列天线特性分析 9
3.1 概述 9
3.2 设计指标和天线几何结构参数计算 9
3.3 微带天线阵元 11
3.4 微带天线阵列 17