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Please use this identifier to cite or link to this item: http://ntour.ntou.edu.tw:8080/ir/handle/987654321/24467

Title: NUMERICAL INSTABILITY OF THE DIRECT TREFFTZ METHOD FOR LAPLACE PROBLEMS IN A 2D FINITE DOMAIN
Authors: W. Yeih;R. F. Liu;J. R. Chang;S. R. Kuo
Contributors: NTOU:Department of Systems Engineering and Naval Architecture
國立臺灣海洋大學:系統工程暨造船學系
Keywords: direct Trefftz method;regular formulation;Laplace’s equation;L-curve concept;Tikhonov’s regularization method
Date: 2007
Issue Date: 2011-10-20T08:12:25Z
Publisher: International Journal of Applied Mathematics and Mechanics
Abstract: abstract:This paper proposes a direct Trefftz boundary-type method to solve the Laplace problems in a two-dimensional finite domain. It is found that the ill-posed nature, i.e., the numerical
instability, exists in the solver due to the regular formulation of the Trefftz method The Riemann-Lebesgue lemma is adopted to explain the inherent ill-posed nature. In order to deal with the numerical instability, the Tikhonov’s regularization method and the L-curve concept are suggested to overcome such a difficulty. In particular, how to choose an appropriate set of basis functions when the origin is placed inside or outside the finite domain is critically evaluated along with this scope. Based on the argument, it is further explained that for a multiply connected domain of genus 1, to place the origin inside the hole is the only selection in the numerical sense. Several numerical examples are demonstrated to show the validity of the proposed approach.
Relation: 2(1), pp.41-66
URI: http://ntour.ntou.edu.tw/handle/987654321/24467
Appears in Collections:[系統工程暨造船學系] 期刊論文
[河海工程學系] 期刊論文

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