有限元-边界积分法在微波无源器件中的应用

发布时间：2018-01-16 08:10

本文关键词：有限元-边界积分法在微波无源器件中的应用　出处：《电子科技大学》2015年硕士论文　论文类型：学位论文

【摘要】：为了更快速、更精确地解决计算电磁学中的各类问题,不同的数值仿真方法一直是研究的重点。在众多的数值方法中,有限元法广泛用于解决辐射、散射及谐振腔等问题。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,从而增加了计算量。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:首先对有限元法进行分析,并通过对谐振腔本征模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本征解。并通过与谐振腔的解析解进行比较,计算误差大小,进而凸显有限元法在计算此类问题时的优势。然后,采用矢量有限元法分析激励波导的不连续性问题,在边界处添加一阶吸收边界条件,并计算波导结构的S参数。在结果的验证阶段,引入HFSS仿真软件与波导云图进行比较,进而为接下来证明有限元-边界积分方法具有更高的精度做好基础。最后,通过对有限元-边界积分方法一般性公式进行推导,进而求解激励波导的S参数。将腔体开口处用一个虚构面隔开,在虚构面内部应用有限元法进行分析,在虚构面外部应用边界积分法进行处理,这通过场的连续性将两个方程组进行耦合求解。在得到S参数之后与通过只通过有限元法得到的S参数进行比较,得出有限元-边界积分法更加精确的结论。
[Abstract]:In order to solve all kinds of problems in computational electromagnetics more quickly and accurately, different numerical simulation methods have been the focus of research. Among many numerical methods, finite element method is widely used to solve radiation. 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. Although the boundary integral method can directly analyze the target problem on the basis of the integral equation, it is necessary to generate a full rank matrix in the end, which requires high memory and computation of the computer. These two numerical simulation methods can not be applied to large size electromagnetic problems. The finite element boundary integration method is developed. By introducing a fictitious boundary, this method can be applied to the actual electromagnetic problems. The boundary surface is divided, and the finite element method is applied to the interior of the boundary. The boundary integral method is applied outside the boundary and coupled according to the continuity of the field. The finite-boundary integration method has a great advantage in dealing with large infinite domain problems. Therefore, it is necessary to study and apply it. The main work of this paper is as follows: firstly, the finite element method is analyzed. Through the analysis of the eigenmode of the resonator, the finite element method is deeply understood. In this process, the boundary condition is imposed by adding interpolation function through discrete mesh. The final eigensolution is obtained by sparse storage of matrix and solution of matrix, and the error is calculated by comparing it with the analytical solution of resonator. Then, the vector finite element method is used to analyze the discontinuity of the excited waveguide, and the first-order absorbing boundary condition is added to the boundary. The S-parameter of the waveguide structure is calculated. In the stage of verification of the results, the HFSS simulation software is introduced to compare with the waveguide cloud image. Then it is proved that the finite-boundary integral method has higher accuracy. Finally, the general formula of the finite-boundary integral method is deduced. Then the S-parameter of the excited waveguide is solved. The cavity opening is separated by a fictitious surface, the finite element method is applied in the imaginary plane, and the boundary integral method is applied to deal with the external surface. In this paper, the coupled solution of the two equations is carried out by the continuity of the field. After the S-parameter is obtained and compared with the S-parameter obtained by the finite element method only, the finite-boundary integration method is obtained to obtain a more accurate conclusion.
【学位授予单位】：电子科技大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：TN61

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