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研究生:鄭人愷
研究生(外文):Jen-Kai Cheng
論文名稱:快速多極點加速之無奇異性邊界積分方程
論文名稱(外文):Solving Non-singular Boundary Integral Equation with Fast Multipole Method
指導教授:黃維信黃維信引用關係
指導教授(外文):Wei-Shien Hwang
口試委員:許文翰蔡武廷王昭男
口試委員(外文):Wen-Hann SheuWu-Ting TsaiChao-Nan Wang
口試日期:2018-07-03
學位類別:碩士
校院名稱:國立臺灣大學
系所名稱:工程科學及海洋工程學研究所
學門:工程學門
學類:綜合工程學類
論文種類:學術論文
論文出版年:2018
畢業學年度:106
語文別:中文
論文頁數:79
中文關鍵詞:快速多極點法無奇異性邊界積分法勢流理論分層結構
相關次數:
  • 被引用被引用:1
  • 點閱點閱:174
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  • 收藏至我的研究室書目清單書目收藏:0
  本文利用快速多極點法加速之無奇異性邊界積分方程來計算二維的勢流場問題,並且在數值計算中處理奇異點之奇異性。首先假設流場內之流體滿足勢流理論,並且依照算例不同使用梯形積分法或是高斯積分法進行積分,最後使用廣義最小殘量誤差法進行迭代求解。本文將討論快速多極點法操作過程中,泰勒級數展開項數及分層結構中分層的數量對CPU運算時間與均方根誤差之影響。接下來使用快速多極點法分別加速邊界積分法與邊界元素法,利用此二方法計算二維之內、外流場問題,並且比較CPU運算時間以及均方根誤差,本文亦比較快速多極點法加速與未使用對邊界積分法在CPU運算時間上之差異。
  The objective of the present thesis is to solve the non-singular Boundary Integral Equation with the Fast Multipole Method for the 2-D potential problems. Assume the flow field to satisfy the potential theory. Then apply the Trapezoidal rule or Gauss-Legendre rule on integration. In finally, apply the iterative solvers (e.g., GMRES) to solve the equations. CPU time and the Root-mean-square error are discussed for the numbers of Taylor series expansion term and the numbers of the level in the hierarchical structure of the Fast Multipole Method. Compare the CPU time and the Root-mean-square error in combination of the FMM-BIM, FMM-BEM and BIM.
口試委員會審定書 #
致謝 i
摘要 ii
ABSTRACT iii
目錄 iv
圖目錄 vi
第一章 緒論 1
1.1 研究動機及背景 1
1.2 文獻回顧 2
1.3 研究目的與方法 4
第二章 基本理論 5
2.1 基本假設 5
2.2 高斯散度定理及格林定理 5
2.3 邊界積分方程式 7
2.4 快速多極點加速邊界積分法(FMM-BIM) 9
2.4.1 Multipole Expansion和Moment 11
2.4.2 Moment-to-Moment (M2M)轉換 13
2.4.3 Local Expansion和Moment-to-Local (M2L)轉換 14
2.4.4 Local-to-Local (L2L)轉換 16
2.4.5 格林函數法向導數積分核的積分式展開 17
第三章 數值計算方法與結果 19
3.1 快速多極點法加速邊界積分方程之操作流程 20
3.2 奇異點之處理 27
3.2.1 Doublet項積分式之奇異點處理 27
3.2.2 Source項積分式之奇異點處理 28
3.3 無奇異性邊界積分方程式 31
3.3.1 外流場問題 31
3.3.2 內流場問題 34
3.4 數值計算結果 37
3.4.1 外流場問題 37
3.4.2 內流場問題 54
第四章 結論與展望 75
4.1 結論 75
4.2 展望 77
參考文獻 78
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