# 臺灣博碩士論文加值系統

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 本篇論文首先介紹「多區域時域有限差分法」的構想，其藉由「柯西荷夫積分公式」與「時域有限差分法」於各子區域的使用來進行問題的解析。藉此我們得以免除某些「時域有限差分法」的問題，諸如具備細微結構問題區域的網格分割限制，以及各子區域間空白區域的額外的記憶體耗費等。然而，取而代之，點對點的積分運算卻留下另一待解決的難題。也因此，本篇論文引入「時域平面波展開法」的架構，其基於Whittaker-type的平面波展開式的概念，得以將時域的場函數以各方向行進平面波來展開。我們可以發現，相較於使用「柯西荷夫積分公式」直接計算所耗費的O(NtNs^2)計算量，使用二階層的「時域平面波展開法」加強計算的方法，將僅需要O(NtNs^1.5logNs)計算量。
 The thesis, first, introduces the concept of multi-region FDTD scheme based on the combination of using Kirchhoff Integral Formula and FDTD method in each sub-region. By this approach, some problems of FDTD method, such as the strict on the grid for total problem domain with some fine structure and the additional memory cost of white space between each sub-region, can be avoided. However, another difficulty about the heavy burden on computational requirement appears because of calculating the integral formula contribution from each point to point. Therefore, the plane wave time domain algorithm (PWTD), relying on a Whittaker-type expansion of transient fields in terms of propagating plane wave, is presented. Opposed to O(NtNs^2) cost by calculating Kirchhoff Integral Formula directly, it is shown that, the algorithm enhanced by two-level PWTD, only requires O(NtNs^1.5logNs) computational resource.
 摘 要................................................Ⅰ Abstract...................................................Ⅱ 目 錄................................................Ⅲ 第一章 緒論............................................... 1 1-1 研究動機............................................... 1 1-2 文獻回顧............................................... 2 1-3 章節概述............................................... 3 第二章 多區域時域有限差分法與時域平面波展開法之基本理論.... 4 2-1 簡介................................................... 4 2-2 多區域時域有限差分法之基本理論......................... 5 2-2.1 等效原理及積分公式................................. 5 2-2.2 全域積分吸收邊界................................... 9 2-2.3 多區域時域有限差分法.............................. 10 2-2.4 使用「柯西荷夫積分公式」的實現觀點................ 14 2-3 時域平面波展開法...................................... 18 2-3.1 時域平面波的展開型式.............................. 18 2-3.2 三階段的時域平面波展開法.......................... 21 2-3.3 「柯西荷夫積分公式」的平面波展開式................ 26 2-3.4 「時域平面波展開法」的實現觀點.................... 29 第三章 實現與程式化的過程................................. 36 3-1 簡介.................................................. 36 3-2 柯西荷夫積分公式的實現與程式化觀點.................... 36 3-2.1封閉面存取場值的考量............................... 36 3-2.2多維動態陣列的使用................................. 39 3-2.3 時間延遲項的內插處理.............................. 42 3-2.4 「柯西荷夫積分公式」直接計算的程式架構............ 43 3-3 時域平面波展開法的實現及程式化觀點................... 49 3-3.1準備工作........................................... 49 3-3.2 三階段的實現...................................... 52 第四章 模擬的結果與分析................................... 59 4-1 簡介.................................................. 59 4-2 「柯西荷夫積分公式」直接計算的結果.................... 59 4-3 「柯西荷夫積分公式」直接計算的複雜度分析.............. 65 4-4「時域平面波展開法」加強「柯西荷夫積分公式」........... 65 4-4.1 單一觀察點、高斯脈衝激發源........................ 66 4-4.2 單一觀察點、多重餘弦激發源........................ 72 4-4.3 平面觀察點的結果（準確性測試）.................... 77 4-4.4 單一段「分段訊號」之場源的計算結果................ 85 4-4.5 改善「第一階段」後的計算結果...................... 88 4-5 以「時域平面波展開法」加強計算的複雜度分析............ 91 4-6 整理與討論............................................ 94 第五章 結論.............................................. 98 參 考 文 獻.............................................. 101
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 1 使用「多區域時域有限差分法」模擬電磁輻射與散射 2 使用[多區域時域有限差分法]模擬相鄰區域間之電磁輻射與散射 3 運用兩階層時域平面波展開法實現多區域時域有限差分法之計算

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