以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

The Local Multiquadric Differential Quadrature Method for Poisson, Helmholtz Eigenvalue and Cavity Flow Problems

郭曜琪(Yao-Chi Kuo)

指導教授 ： 楊德良

國立臺灣大學/工學院/土木工程學研究所/碩士(2006年)

https://doi.org/10.6342/NTU.2006.02619

摘要

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。

關鍵字

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

並列摘要

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.

並列關鍵字

Multiquadric method ； Differential Quadrature method ； local Multiquadric Differential Quadrature method ； domain decomposition technique ； Poisson equation ； Helmholtz eigenvalue problem ； cavity flow problem

參考文獻

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