Open Access

ARTICLE

An investigation on the regularized meshless method for irregular domain problems

Rencheng Song^1,2, Wen Chen^2,3

1 Department of Mathematics, Zhejiang University, Hangzhou, Zhejiang, China
2 Department of Engineering Mechanics, Hohai University, Nanjing, Jiangsu, China
3 Corresponding author. E-mail: chenwen@hhu.edu.cn. Professor, Department of Engineering, Mechanics, Hohai University, Xikang Road #1, Nanjing City, Jiangsu Province, 210098, China

Computer Modeling in Engineering & Sciences 2009, 42(1), 59-70. https://doi.org/10.3970/cmes.2009.042.059

Abstract

The regularized meshless method (RMM) is a novel boundary-type meshless method but by now has mainly been tested successfully to the regular domain problems in reports. This note makes a further investigation on its solution of irregular domain problems. We find that the method fails to produce satisfactory results for some benchmark problems. The reason is due to the inaccurate calculation of the diagonal elements of the numerical discretization matrix in the original RMM, which have strong effect on the resulting solution accuracy. To overcome this severe drawback, this study introduces the weighted diagonal element approach. Our numerical experiments demonstrate the effectiveness and accuracy of the present RMM technique.

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