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  本文關(guān)鍵詞：有限元-邊界積分法在微波無源器件中的應(yīng)用　出處：《電子科技大學》2015年碩士論文　論文類型：學位論文

  更多相關(guān)文章： 有限元法 邊界積分法 諧振腔

【摘要】：為了更快速、更精確地解決計算電磁學中的各類問題,不同的數(shù)值仿真方法一直是研究的重點。在眾多的數(shù)值方法中,有限元法廣泛用于解決輻射、散射及諧振腔等問題。而在實際應(yīng)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(shè)置合適的邊界條件,從而增加了計算量。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(yīng)用到尺寸較大的電磁問題中。為了更好地應(yīng)用這兩種數(shù)值仿真方法,發(fā)展出有限元-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(yīng)用到實際的電磁問題中,以邊界面分割,邊界內(nèi)部應(yīng)用有限元法,邊界外應(yīng)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(yīng)用。本文主要工作分為以下三點:首先對有限元法進行分析,并通過對諧振腔本征模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本征解。并通過與諧振腔的解析解進行比較,計算誤差大小,進而凸顯有限元法在計算此類問題時的優(yōu)勢。然后,采用矢量有限元法分析激勵波導(dǎo)的不連續(xù)性問題,在邊界處添加一階吸收邊界條件,并計算波導(dǎo)結(jié)構(gòu)的S參數(shù)。在結(jié)果的驗證階段,引入HFSS仿真軟件與波導(dǎo)云圖進行比較,進而為接下來證明有限元-邊界積分方法具有更高的精度做好基礎(chǔ)。最后,通過對有限元-邊界積分方法一般性公式進行推導(dǎo),進而求解激勵波導(dǎo)的S參數(shù)。將腔體開口處用一個虛構(gòu)面隔開,在虛構(gòu)面內(nèi)部應(yīng)用有限元法進行分析,在虛構(gòu)面外部應(yīng)用邊界積分法進行處理,這通過場的連續(xù)性將兩個方程組進行耦合求解。在得到S參數(shù)之后與通過只通過有限元法得到的S參數(shù)進行比較,得出有限元-邊界積分法更加精確的結(jié)論。
[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.
【學位授予單位】：電子科技大學
【學位級別】：碩士
【學位授予年份】：2015
【分類號】：TN61

【參考文獻】

相關(guān)碩士學位論文 前1條

1 倪朝旭;復(fù)雜目標電磁散射特性有限元邊界積分方法分析[D];南京理工大學;2013年

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本文編號：1432259