臺灣博碩士論文加值系統

本論文重點在開發一個功能完整、使用簡易的波導模擬程式。主要利用有限元素法（Finite Element Method），與Delaunay三角化法（Delaunay Triangulation）來解決此一問題，以求得不規則形狀之波導的電磁物理特性。
此程式可分為兩個獨立的子程式，一為求解區域的分割、網格的產生（Delaunay三角化法）；二為矩陣的求解、場型的計算（有限元素法）。
第一部份將討論有限元素法。如何利用有限元素法來求解問題的過程，以及求解任意形狀之波導結構的方法。
第二部份則討論網格的分割方法，即本程式所使用的Delaunay三角化法。利用自訂格式的結構輸入方式，再一個區域接一個區域的，首先產生網點（node），再切割產生網格（mesh）。
第三部份則探討本程式的結果與理論值的比較。

This thesis is focused on developing a waveguide simulation software with full functionality and ease of operation. FEM ( Finite Element Method ) and Delaunay triangulation method are used in the program in order to solve the eletromagnetic problem of waveguides with arbitrary shapes.
The program consists of two individual sub-programs. One is to divide the area into small pieces, i.e., meshing by Delaunay triangulation. The other is to solve the gobal matrix and get the field pattens using FEM.
The thesis states with a brief introduction to the FEM theory. We will address the solution steps of FEM in dealing with waveguides with arbitrary shapes. Then, we applied the Delaunay triangulation in the automatic mesh generation. In the input design, a simple but general enough format is tailored to define the waveguides with arbitrary shapes. The mesh division is accomplished by adding nodes followed by the Delaunay triangulations region by region. In the output design, the field patterns of the guided modes are demonstrated graphically.
Finally, the program has been applied to some examples and the results are verified with the theoretical one, if available.

第一章　簡介 9
§1.1動機與目的 9
§1.2文獻回顧 9
§1.3章節概述 10
第二章 波導與有限元素法 11
§2.1波導模態 11
§2.2有限元素法 13
第三章 模擬區域的分割 19
§3.1網點的產生 21
§3.2網格的產生 29
§3.3程式實作及演算法 31
第四章 模擬結果 40
§4.1矩形波導 40
§4.2不規則形狀波導 45
第五章 結論 49
附錄A 程式架構與流程 50
程式架構 50
程式流程 55
附錄B 程式操作之說明 56
輸入介面 56
執行模擬 58
輸出介面 58
參考文獻 61

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