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研究生:黃玠肇
研究生(外文):jie-zhao Huang
論文名稱:探討在時域有限差分法中低網格色散之計算方法與不同完全吸收層之效果
論文名稱(外文):On the Low Grid-Dispersion Algorithm in Finite Difference Time Domain Method and Various Perfectly Matched Layer Schemes
指導教授:林俊華林俊華引用關係
指導教授(外文):J.H. Lin
學位類別:碩士
校院名稱:國立海洋大學
系所名稱:電機工程學系
學門:工程學門
學類:電資工程學類
論文種類:學術論文
論文出版年:2002
畢業學年度:90
語文別:中文
論文頁數:77
中文關鍵詞:時域有限差分法完全吸收層網格色散
外文關鍵詞:Finite Difference Time Domain MethodPMLGrid-Dispersion
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時域有限差分法是一種在電磁傳播、電磁散射與電磁輻射方面有效的計算方法之一。在利用時域有限差分法模擬開放空間中分析電磁問題時,是需要人為的吸收邊界。
我們介紹兩種不同的完全吸收層。第一種吸收層的損耗介質稱為單軸向異向性損耗介質。第二種吸收層的損耗介質稱為單軸向複數頻率平移式損耗介質。這兩種完全吸收層在吸收層中都有顯著吸收效果,其吸收效果是等效於Berenger的吸收層。
使用時域有限差分法來模擬電磁現象時,演算法的穩定與網格色散是我們必需注重的條件。我們提出等向性有限差分法,一方面為了減少網格散誤差對模擬結果的影響,另一方則可增加時間間距以減少計算時間。
於本文中,我們首先介紹兩種完全吸收的技術,其次說明幾種減低網格色散誤差的方法,並比較這些方法之間的優缺點。

The Finite-Difference Time-Domain Method is one of most powerful computational methods in propagation, scattering, and radiation and to solve the electromagnetic problem in open space by FDTD, it requires the artificial absorbing boundary.
Two kinds of the different PMLs as absorbing boundaries are introduced here. One is the Uniaxial anisotropic lossy medium and the other is the Uniaxial complex frequency shifted (CFS) loss medium. Both of the PMLs have nice performace among various kinds of absorbing boundaries, and in absorption characteistics are equivalent to the Berenger’s PML.
Using FDTD method to simulate and observe the electromagnetic phenomena in open space, it is very important to satisfy stability condition and to reduce the dispersion error. we introduce the isotropic finite-difference time-domain method (IFDTD) to improve the numerical dispersion problem and to increase the time step.
The first part of the thesis introduces two PML techniques. The second part is focused on several schemes in reducing numerical grid-dispersion error, and comparisons among these schemes.

第一章 緒論
1-1. 研究的動機與目的…………………………………… 1
1-2. 文獻回顧……………………………………………… 2
1-3. 章節概要……………………………………………… 3
第二章 各項時域有限差分法之理論分析…………………………… 4
2-1. 簡介…………………………………………………… 4
2-2. 使用有限差分法之基本理論 …………………………4
2-2.1. 有限差分法的架構………………………………….4
2-2.2. 時域有限差分演算法……………………………….7
2-2.3. Yee’s演算法之網格色散與穩定性分析………….10
2-2.4. 激發元之選取 ……………………………………12
2-3. 不同完全吸收層之基本理論…………………………13
2-3.1. 簡介…………………………………………………13
2-3.2. 單軸向異向性損耗介質之吸收層技術……………13
2-3.3. 一般式的吸收層電磁場計算方法………………16
2-3.4. 吸收層的介質定義…………………………………20
2-3.5. 單軸向複數頻率平移式吸收層之介紹……………21
2-3.6. 實現單軸向複數頻率平移式吸收層之技術………23
2-4. 網格色散誤差之基本理論…………………………25
2-4.1.簡介…………………………………………………25
2-4.2.不同網格之色散分析……………………………25
2-4.3.有效減低網格色散之方法……………………………28
2-4.4.最佳化網格色散的方法……………………………38
第三章 吸收層與網格色散之程式化探討……………………49
3-1. 簡介………………………………………………………49
3-2. 三維吸收層程式化過程之問題探討…………………49
3-3. 低網格色散程式化過程………………………………53
第四章 模擬結果與分析……………………………………………54
4-1. 簡介……………………………………………………54
4-2. 三維一般性完全吸收層的特性測試…………………54
4-2.1.反射係數R(0)特性測試……………………………54
4-2.2.導電率分佈特性測試………………………………56
4-2.3.吸收效果與層數特性測試…………………………57
4-2.4.單軸向複數頻率平移式吸收層之吸收特性測試..58
4-3.三種低網格色散方法之比較………………………….60
4-4. 結果與討論……………………………………………62
第五章 結論……………………………………………………….72
附錄…………………………………………………………………..76
文獻參考………………………………………………………………74

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