矢量有限元方法在电磁场开域问题中的应用

【作者】 梁兵；

【导师】 刘濮鲲；

【作者基本信息】 电子科技大学 ， 物理电子学， 2008， 硕士

【摘要】 近年以来,有限元方法不断发展成为计算电磁学的主要方法之一,由于它对复杂的结构和非均匀介质问题有很强的描述能力,有限元方法的运用研究也越来越多,对比较棘手的开区域问题也取得了不小的进展。科学家提出了几种用虚拟边界截断无限空间的方法并将它用来处理实际问题并取得了理想的结果,本文将讨论这几种方法的实现问题。本文首先讨论了矢量有限元方法通用的程序编写技巧,包括如何将由有限元剖分软件生成的节点信息转化成棱边信息,如何实现对棱边的排序,编号,如何集成系数矩阵,如何强加边界条件,以及求解。然后分析了电磁场开区域问题的求解方法,包括吸收边界条件方法,理想匹配层方法,有限元边界积分方法的原理及推导过程。在吸收边界条件下探讨了入射角与反射系数的关系和参数选取对计算效率和精度的影响,计算并仿真了导电薄平板对入射波的散射。在理想匹配层方法中探讨了匹配层参数结构设置跟电磁波反射的关系,参数大小对计算精度的影响,根据理论分别求解并仿真了三维不连续性波导中加载介质柱和导体柱时的S参数。2004年,美国国防部决定将一种还处在试验阶段的新式非致命性武器部署到伊拉克,以对巴格达的联合作战指挥所附近的安全区域实施保护。这种新式武器被称为主动拒止技术武器,主要用于控制人群,其优点是:对人的攻击无声无息,是“自原子弹研制成功以来最具革命性的新式武器”。美国空军于2001年3月对外公布了这种武器。该武器系统的特别之处在于采用了平板抛物天线技术,平板抛物天线由正交偶极子散射阵列组成。然后本文讨论了这一天线的一个单元,用有限元边界积分方法讨论了平面十字形缝隙天线的电场幅度值以及相位,计算了它的散射特性并进行了验证。最后,文章总结了本文的主要工作,并提出了作者本人对于有限元方法,乃至计算电磁学可能的几个发展方向。随着计算电磁学方法的发展,人类将能够轻松的处理各种电磁场边值问题。作者非常希望能够有人在这方面继续努力对祖国国防和人类文明做出重大的贡献。更多还原

【Abstract】 In recent years, the finite element method continuously develop to one of the main methods of computational electromagnetism, as it has a very strong ability to describe complicated structure and inhomogeneous media the problem. The applications of the finite element method become more and more, the thornier open regional issues also made a lot of progress. Scientists use several virtual borders to truncate unlimited space and to dealing with actual problems, have achieved satisfactory results; this paper will discuss several ways of achieving this issue.Firstly, this paper discussed a common programming writing skill of the vector finite element method. On basis of using the third party software automatically to produce grid, this paper discuss how to compiles the interconnected routine from the grid point information to edges information, how to integrate coefficient matrix, how to impose the boundary condition in detail. Then it analyze the solutions of opened regional problems of electromagnetic field, including absorbing boundary conditions, perfect matched layer method, finite element boundary integral method . In absorbing boundary conditions, discuss relationship between the angle of incidence and reflection coefficients, the relationship between parameters selected and the computational efficiency and accuracy of calculation. Compute and simulate scattering field of thin plate conductivity. In a perfect matched layer method, discuss the relationship between structure and the reflection, and the relationship between parameter and accuracy of calculation. According to this theory, simulate and calculate the S-parameters of the three-dimensional discontinuous waveguide with the medium-loaded and conductor-loaded column. 2004, the United States Department of Defense decided to deploy a still in the testing stage of new non-lethal weapons to Iraq, so that they can protect the joint army from attacking by local force. This new weapon mainly used for crowd control, its advantages is: the attack on the quiet, "Since the successful development of the atomic bomb has been the most revolutionary new weapons." The United States Air Force in March 2001 released such weapons. The distinguishing characteristic of the weapons systems is using flat-panel parabolic antenna technology; the flat-panel parabolic antenna array is consisted of orthogonal dipole. Then this paper discussed a unit of the antenna .by using finite element method, discuss the magnitude and phase of electric field on the slot and it was verified.更多还原