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Please use this identifier to cite or link to this item: http://ntour.ntou.edu.tw:8080/ir/handle/987654321/24288

Title: Image solutions for boundary value problems without sources
Authors: Jeng-Tzong Chen;Hung-Chih Shieh;Ying-Te Lee;Jia-Wei Lee
Contributors: NTOU:Department of Harbor and River Engineering
國立臺灣海洋大學:河海工程學系
Keywords: Image method;Boundary value problem;Bipolar coordinates;Method of fundamental solution
Date: 2010-05-01
Issue Date: 2011-10-20T08:11:06Z
Publisher: Applied Mathematics and Computation
Abstract: abstract:In this paper, we employ the image method to solve boundary value problems in domains containing circular or spherical shaped boundaries free of sources. two and threeD problems as well as symmetric and anti-symmetric cases are considered. By treating the image method as a special case of method of fundamental solutions, only at most four unknown strengths, distributed at the center, two locations of frozen images and one free constant, need to be determined. Besides, the optimal locations of sources are determined. For the symmetric and anti-symmetric cases, only two coefficients are required to match the two boundary conditions. The convergence rate versus number of image group is numerically performed. The differences of the image solutions between 2D and 3D problems are addressed. It is found that the 2D solution in terms of the bipolar coordinates is mathematically equivalent to that of the simplest MFS with only two sources and one free constant. Finally, several examples are demonstrated to see the validity of the image method for boundary value problems.
Relation: 216(5), pp.1453–1468
URI: http://ntour.ntou.edu.tw/handle/987654321/24288
Appears in Collections:[河海工程學系] 期刊論文

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