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Please use this identifier to cite or link to this item: http://ntour.ntou.edu.tw:8080/ir/handle/987654321/52230

Title: Localized method of fundamental solutions for solving two-dimensional Laplace and biharmonic equations
Authors: Fan, C.M.
Huang, Y.K.
Chen, C.S
Kuo, S.R.
Contributors: 國立臺灣海洋大學:河海工程學系
Keywords: Localized method of fundamental solutions
Laplace equation
Biharmonic equation
Meshless method
Complicated domain
Date: 2019
Issue Date: 2019-06-13T05:57:15Z
Publisher: Engineering Analysis with Boundary Elements
Abstract: Abstract: The localized method of fundamental solutions (LMFS) is proposed in this paper for solving two-dimensional boundary value problems, governed by Laplace and biharmonic equations, in complicated domains. Traditionally, the method of fundamental solutions (MFS) is a global method and the resultant matrix is dense and ill-conditioned. In this paper, it is the first time that the LMFS, the localized version of the MFS, is proposed. In the LMFS, the solutions at every interior node are expressed as linear combinations of solutions at some nearby nodes, while the numerical procedures of MFS are implemented within every local subdomain. The satisfactions of governing equation at interior nodes and boundary conditions at boundary nodes can yield a sparse system of linear algebraic equations, so the numerical solutions can be efficiently acquired by solving the resultant sparse system. Six numerical examples are given to demonstrate the effectiveness of the proposed LMFS.
Relation: 101 pp.188-197
URI: http://ntour.ntou.edu.tw:8080/ir/handle/987654321/52230
Appears in Collections:[河海工程學系] 期刊論文

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