Open Access

ARTICLE

Applicability of the Boundary Particle Method

F.Z. Wang ^1,2,3

1 College of Mathematics, Huaibei Normal University, No. 100 Dongshan Road, Huaibei, Anhui 235000, China
2 Corresponding to: wangfuzhang@hhu.edu.cn
3 Department of Engineering Mechanics, Hohai University, No.1 XiKang Road, Nanjing, Jiangsu 210098, China

Computer Modeling in Engineering & Sciences 2011, 80(3&4), 201-218. https://doi.org/10.3970/cmes.2011.080.201

Abstract

In this paper, we consider the boundary particle method (BPM) which is excellent in solving inhomogeneous partial differential equations in terms of solution accuracy and simplicity. In order to investigate the applicability of the BPM, we examine the relationship between its solution accuracy and the effective condition number. We show that the effective condition number, which estimates system stability with the right-hand side vector taken into account, is inversely proportional to the root mean square error in the numerical approximation. Moreover, for noisy-boundary cases, we find that the BPM can not yield reasonable results, for more noise added to the right-hand side vector, by using Gaussian elimination. Thus, to solve effectively the discrete ill-conditioned coefficient matrix, we adopt three regularization techniques under two different regularization parameter choices. Numerical results indicate that the generalized cross-validation choice rule for the damped singular value decomposition regularization strategy performs the best.

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Keywords

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