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An Improved Formulation of Singular Boundary Method

Published online by Cambridge University Press:  03 June 2015

Wen Chen  and
Yan Gu
Wen Chen*
Affiliation:
College of Harbour, Coastal and Offshore Engineering, Hohai University, No. 1 Xikang Road, Nanjing, Jiangsu 210098, China
Yan Gu*
Affiliation:
College of Harbour, Coastal and Offshore Engineering, Hohai University, No. 1 Xikang Road, Nanjing, Jiangsu 210098, China
*
Corresponding author. URL:http://em.hhu.edu.cn/chenwen/english.html, Email: chenwen@hhu.edu.cn
Email: guyan1913@163.com
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Abstract

This study proposes a new formulation of singular boundary method (SBM) to solve the 2D potential problems, while retaining its original merits being free of integration and mesh, easy-to-program, accurate and mathematically simple without the requirement of a fictitious boundary as in the method of fundamental solutions (MFS). The key idea of the SBM is to introduce the concept of the origin intensity factor to isolate the singularity of fundamental solution so that the source points can be placed directly on the physical boundary. This paper presents a new approach to derive the analytical solution of the origin intensity factor based on the proposed subtracting and adding-back techniques. And the troublesome sample nodes in the ordinary SBM are avoided and the sample solution is also not necessary for the Neumann boundary condition. Three benchmark problems are tested to demonstrate the feasibility and accuracy of the new formulation through detailed comparisons with the boundary element method (BEM), MFS, regularized meshless method (RMM) and boundary distributed source (BDS) method.

Keywords

65N1565N38Singular boundary methodfundamental solutionsingularitydesingularization techniquemeshless
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 4 , Issue 5 , October 2012 , pp. 543 - 558
Copyright
Copyright © Global-Science Press 2012

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