臺灣博碩士論文加值系統

在過去的參考文獻中，已有許多學者運用各種方法分析具圓形核心的波導，可是在大部分的研究結果中，其截止波數的精度大多只到小數點後三位，因此，本文利用簡易的邊界選點法和領域媒親法，分析Dirichlet和Neumann條件之具圓形核心的矩形和橢圓形波導，並針對圓形核心為同心或偏心的情況，探討不同佈點方式所求得之截止波數的收斂性。在邊界選點法的求解過程中，先求得四分之一計算領域的勢函數表示式，然後採用邊界選點法建構聯立方程式求得截止波數。在領域媒親法的求解過程中，先引入輔助邊界將四分之一計算領域分成兩個子領域，然後求得各子領域的勢函數表示式，接著利用座標轉換公式統一各子領域的座標系統，再配合選點法和連續邊界條件，建構聯立方程式求得截止波數。本文的所有計算結果皆與參考文獻或邊界元素法做比較，以驗證其正確性和可靠性。根據本文數值計算結果顯示：所有計算結果皆與邊界元素法的答案相吻合。使用邊界選點法和直線輔助邊界的領域媒親法求解同心圓形核心的矩形波導時，等間距佈點的收斂性會比等角度好。另外，對於同心圓形核心的橢圓形波導，使用等間距佈點的邊界選點法時，其所求得之截止波數的收斂性至少都有小數點後七位，而最高可達小數點後九位。

In previous studies, many scholars have used a variety of methods to analyze the waveguide with a circular core. However, in most calculated cases, the precision of the cutoff wavenumber was about 3 digits after the decimal point. Therefore, the main purpose of this thesis is to study the rectangular and elliptical waveguides with a circular core. Both the Dirichlet and Neumann boundary conditions are investigated by means of the simple boundary collocation and region-matching method. Concerning about the effects of the arrangement of the collocation points, the convergence of cut-off wavenumbers for the case of a concentric circular core and an eccentric one is discussed. Following the solution procedure of the boundary collocation method, the expression of the potential function for the quarter computational domain is obtained firstly. Placing the collocation points on the boundary to construct the simultaneous equations, the cut-off wavenumbers can then be determined. In region-matching method solution procedure, an auxiliary boundary is introduced to divide the computational domain into two sub-regions, and then the representation of the potential function for each sub-region is derived. Next, the local coordinate systems of each sub-region are unified by utilizing the coordinate transformation formulas. Applying the collocation method and continuity conditions, the cut-off wavenumbers can be gained from a linear algebra equation set. To verify the correctness and reliability of computational results in this thesis, all of them are compared with those of the boundary element method (BEM). It shows that the presented results and those of BEM are in good agreement with each other. When using the boundary collocation method and region-matching method with line auxiliary boundary to solve the rectangular waveguide with a concentric circular core, the convergence for equidistant points would be better than that for equiangular ones. Furthermore, when using the boundary collocation method with equidistant points to solve the elliptical waveguide with a concentric circular core, the desired precision of cut-off wavenumbers after the decimal point can at least converge to 7 digits and up to 9 digits.

中文摘要
英文摘要
目錄
表目錄
圖目錄

第一章 緒論
1 - 1 前言
1 - 2 文獻回顧
1 - 3 研究動機、目的及方法
1 - 4 研究內容與架構

第二章 具圓形核心的矩形波導
2 - 1 Dirichlet條件下圓形核心為同心之情況
2 - 1 - 1 邊界選點法
2 - 1 - 2 領域媒親法
2 - 2 Dirichlet條件的Meinke波導
2 - 3 Dirichlet條件下圓形核心為偏心之情況
2 - 4 Neumann條件下圓形核心為同心之情況
2 - 4 - 1 邊界選點法
2 - 4 - 2 領域媒親法
2 - 5 Neumann條件的Meinke波導
2 - 6 Neumann條件下圓形核心為偏心之情況

第三章 具圓形核心的橢圓形波導
3 - 1 Dirichlet條件下圓形核心為同心之情況
3 - 2 Dirichlet條件下圓形核心為偏心之情況
3 - 3 Neumann條件下圓形核心為同心之情況
3 - 4 Neumann條件下圓形核心為偏心之情況

第四章 數值計算例與討論
4 - 1 具圓形核心的矩形波導
4 - 1 - 1 同心的情況
4 - 1 - 2 Meinke波導
4 - 1 - 3 偏心的情況
4 - 2 具圓形核心的橢圓形波導
4 - 2 - 1 同心的情況
4 - 2 - 2 偏心的情況

第五章 結論

參考文獻

作者簡歷

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