Applications of Domain Decomposition Method and the Method of Fundamental Solutions for Some Partial Differential Equations with Clustering
Date Issued
2006
Date
2006
Author(s)
Hsieh, Dar-Der
DOI
en-US
Abstract
This thesis mainly describes the combination of the Domain Decomposition Method (DDM) and the Method of Fundamental Solutions (MFS) as a meshless numerical method (DDM-MFS) to solve problems governed by various Partial Differential Equations (PDEs), including Laplace equation, Stokes’ equations, diffusion equation and advection-diffusion equation. The MFS is an efficient meshless method, which its application can be extensively found in the literature. However, the resultant matrix in the MFS will approach to ill-conditioned as computational points increasing, which creates restrictions for development of this method. The DDM-MFS is thus developed in order to solve this problem. Applied the DDM-MFS, problems including the cusp domain problems, the steady Stokes’ flow problems and the time-dependent problems are successfully addressed. It is to be noted that there is a new approach to solve the cusp problems proposed in this thesis, which is to transform the cusp domains in to semi-infinite domains by conformal mapping techniques. Since the DDM is developed as a preparation for parallel computing, the efficiency of parallel computing applied the DDM-MFS is also tested for the problems mentioned above in the thesis.
Subjects
區域分割
基本解法
平行計算
尖角計算域
拉普拉斯方程式
史托克斯方程式
擴散方程式
對流-擴散方程式
domain decomposition
the method of fundamental solutions
parallel computing
cusp domain
Laplace equation
Stokes’ equation
diffusion equation
advection-diffusion equation
Type
thesis
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