Open Access

ARTICLE

Potential Problems by Singular Boundary Method Satisfying Moment Condition

Wen Chen^1,2, Zhuojia Fu¹, Xing Wei¹

1 Center for Numerical Simulation Software in Engineering and Sciences, Department of Engineering Mechanics, College of Civil Engineering, Hohai University, Nanjing, Jiangsu, P.R.China
2 Corresponding author. E-mail: chenwen@hhu.edu.cn. Department of Engineering Mechanics, Hohai University, Xikang Road #1, Nanjing City, Jiangsu Province, 210098, P.R.China

Computer Modeling in Engineering & Sciences 2009, 54(1), 65-86. https://doi.org/10.3970/cmes.2009.054.065

Abstract

This study investigates the singular boundary method (SBM), a novel boundary-type meshless method, in the numerical solution of potential problems. Our finding is that the SBM can not obtain the correct solution in some tested cases, in particular, in the cases whose solution includes a constant term. To remedy this drawback, this paper presents an improved SBM formulation which is a linear sum of the fundamental solution adding in a constant term. It is stressed that this SBM approximation with the additional constant term has to satisfy the so-called moment condition in order to guarantees the uniqueness of the solution. The efficiency and accuracy of the present SBM scheme are demonstrated through detailed comparisons with the exact solution, the method of fundamental solutions and the regularized meshless method.

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Keywords

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