Open Access

ARTICLE

Boundary Knot Method: An Overview and Some Novel Approaches

J.Y. Zhang¹, F.Z. Wang^2,3
1 Department of Engineering Mechanics, Hohai University, No.1 XiKang Road, Nanjing, Jiangsu 210098, China
2 College of Mathematics, Huaibei Normal University, No. 100 Dongshan Road, Huaibei, Anhui 235000, China
3 Corresponding to: wfz1984@chnu.edu.cn

Computer Modeling in Engineering & Sciences 2012, 88(2), 141-154. https://doi.org/10.3970/cmes.2012.088.141

Abstract

The boundary knot method (BKM) is a kind of boundary-type meshless method, only boundary points are needed in the solution process. Since the BKM is mathematically simple and easy to implement, it is superior in dealing with Helmholtz problems with high wavenumbers and high dimensional problems. In this paper, we give an overview of the traditional BKM with collocation approach and provide three novel approaches for the BKM, as far as they are relevant for the other boundary-type techniques. The promising research directions are expected from an improved BKM aspect.

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Keywords

Collocation, least-square, Galerkin, variational, Helmholtz equation, non-singular general solution.

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