Open Access

ARTICLE

Effective Condition Number for Boundary Knot Method

F.Z. Wang¹, L. Ling², W. Chen^1,3

1 Center for Numerical Simulation Software in Engineering and Sciences, Department of Engineer-ing Mechanics, Hohai University, No.1 XiKang Road, Nanjing, Jiangsu 210098, China
2 Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong, China. Email: lling@hkbu.edu.hk

3 Corresponding to:

Computers, Materials & Continua 2009, 12(1), 57-70. https://doi.org/10.3970/cmc.2009.012.057

Abstract

This study makes the first attempt to apply the effective condition number (ECN) to the stability analysis of the boundary knot method (BKM). We find that the ECN is a superior criterion over the traditional condition number. The main difference between ECN and the traditional condition numbers is in that the ECN takes into account the right hand side vector to estimates system stability. Numerical results show that the ECN is roughly inversely proportional to the numerical accuracy. Meanwhile, using the effective condition number as an indicator, one can fine-tune the user-defined parameters (without the knowledge of exact solution) to ensure high numerical accuracy from the BKM.

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Keywords

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