楊德良臺灣大學：土木工程學研究所郭曜琪Kuo, Yao-ChiYao-ChiKuo2007-11-252018-07-092007-11-252018-07-092006http://ntur.lib.ntu.edu.tw//handle/246246/50358在這篇論文中，我們應用區域多元二次微分積分法求解卜易松、赫姆霍茲特徵值與穴室流場問題。無網格數值方法有許多種類﹐本方法是基於區域分解技術並結合多元二次法與微分積分法，也是無網格數值方法的一種。因此，本方法仍保有無網格法不需要建立網格組織的特性。在本論文中，我們使用此方法與傳統多元二次法、理論解析解、以及其他數值方法結果作比較。本論文主要貢獻在於應用此方法在不規則區域以及方法的行為分析。由比較結果可以看出此方法與其他方法的結果相當吻合。因此﹐我們認為此數值方法是一可信賴且有效率的方法。In this thesis, we employ the meshless local Multiquadric Differential Quadrature method (LMQDQ method) to deal with the Poisson, Helmholtz eigenvalue and cavity flow problems. Meshless methods can be classified as lots of categories. The numerical method in this thesis combines the Multiquadric method (MQ method) and the domain decomposition technique in Differential Quadrature (DQ) form. Thus, this method keeps the mesh-free property. We will discuss this method in the thesis and compare the results with those obtained by the conventional MQ method, analytic solutions or numerical solutions made by other methods. The main contribution of the thesis is to employ LMQDQ method to solve irregular domain problem and the behavior analysis of this method. These results indicate that this method is reliable and efficient.Table of contents 摘要 I Abstract II Table of contents III Table caption V Figure caption VI Chapter 1 Introduction 1 1.1 Objective 1 1.2 Outline of the thesis 2 Chapter 2 Literature review and formulation of LMQDQ method 4 2.1 DQ method 4 2.1.1 Advantages and weaknesses of DQ method 9 2.2 Meshless methods, RBFs and MQ method 14 2.2.1 RBFs 14 2.2.2 MQ RBF 16 2.2.3 Weaknesses of RBFs interpolation 17 2.3 Formulation of LMQDQ method 18 Chapter 3 Numerical solutions of Poisson equation using LMQDQ method 21 3.1 Results of Dirichlet boundary condition 21 3.2 Results of Neumann boundary condition 31 Chapter 4 Helmholtz eigenvalue problem 42 4.1 Governing equations and SVD technique 42 4.1.1 Governing equations 42 4.1.2 Singular value decomposition 45 4.2 Square eigenvalue problem 47 4.2.1 Results and comparisons for square TM case 48 4.2.2 Results and comparisons for square TE case 50 4.3 Circular eigenvalue problem 53 4.3.1 Results and comparisons for circular TM case 54 4.3.2 Results and comparisons for circular TE case 57 4.4 Multi-connected domain eigenvalue problem 60 4.5 Peanut-shaped eigenvalue problem 67 Chapter 5 Cavity flow problem 72 5.1 The velocity-vorticity formulation 72 5.2 Steady Stokes cavity problem 74 5.3 Steady Navier-Stokes cavity problem 78 Chapter 6 Conclusion, recommendations and further works 85 6.1 Conclusions 85 6.2 Recommendations and further works 86 References 877761331 bytesapplication/pdfen-US多元二次法微分積分法區域多元二次微分積分法區域分解技術卜易松方程式赫姆霍茲特徵值問題穴室流場問題Multiquadric methodDifferential Quadrature methodlocal Multiquadric Differential Quadrature methoddomain decomposition techniquePoisson equationHelmholtz eigenvalue problemcavity flow problemthesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/50358/1/ntu-95-R92521319-1.pdf