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http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/27960
標題: | 含超強奇異性無網格法於三維勢能及外域聲學問題之應用 The Application of Hypersingular Meshless Method for 3D Potential and Exterior Acoustic Problems |
作者: | Tzu-Yumg Liu 劉子雍 |
指導教授: | 楊德良(Der-Liang Young) |
關鍵字: | 含超強奇異性無網格法,基本解法,雙層勢能核函數,徑向基底函數,去除奇異性技術,聲學散射,三維, hypersingular meshless method,method of fundamental solutions,double layer potential,radial basis function,desingularized technique,acoustic scattering,3D, |
出版年 : | 2007 |
學位: | 碩士 |
摘要: | 本論文提出一個含超強奇異性無網格法求解三維勢能及外域聲學問題。其解以雙層勢能核函數代替傳統之基本解法所使用之單層勢能核函數來表示,藉由所提出的去除奇異性技術將含奇異與超強奇異性的核函數正規化,源點可直接佈置於實體邊界上,解決了傳統基本解法具爭議性的源點佈置問題。最後在求解勢能與外域聲學散射問題經一系列的各種不同型態的邊界條件之數值例子中,將其數值結果與解析解、基本解法、有限元素法、邊界元素法以及區域微分積分法等數值方法比較後,證明本方法確實可行且精確。 In this thesis, a hypersingular meshless method is developed to solve the potential and exterior acoustic problems in three dimensions for arbitrary shapes. The solutions are represented by a distribution of double layer potentials instead of the single layer potentials as generally used in the conventional method of fundamental solutions. By using the desingularization technique to regularize the singularity and hypersingularity of double layer potentials, the source points can be located on the real boundary to avoid the sensitivity of locating fictitious boundary as used by the conventional method of fundamental solutions, and therefore the diagonal terms of influence matrices are determined. The main difficulty of the coincidence of the source and collocation points thus can be overcome. The numerical evidences of the proposed meshless method demonstrate the accuracy of the solutions after comparing with the results of analytical solution, the method of fundamental solutions, finite element method, boundary element method and local differential quadrature method for the Dirichlet, Neumann and mix-type boundary conditions problems with simple and complicated boundaries. The numerical results have demonstrated the validity and accuracy in solving a number of testing cases for potential and exterior acoustic problems after comparing with analytical solution and other numerical methods. |
URI: | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/27960 |
全文授權: | 有償授權 |
顯示於系所單位: | 土木工程學系 |
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