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Boundary Layer Effect in Regularized Meshless Method for Laplace Equation

Weiwei Li1, Wen Chen1,2
Center for Numerical Simulation Software in Engineering and Sciences, Department of Engineering Mechanics, College of Mechanics and Materials, Hohai University, Nanjing, Jiangsu, P.R. China.
Corresponding author. E-mail: chenwen@hhu.edu.cn.

Computer Modeling in Engineering & Sciences 2014, 100(5), 347-362. https://doi.org/10.3970/cmes.2014.100.347

Abstract

This paper presents an efficient strategy for the accurate evaluation of near-boundary solutions in the regularized meshless method (RMM), also known as the boundary layer effect associated with the boundary element method. The RMM uses the double layer potentials as its interpolation basis function. When the field point is close to the boundary, the basis function will present nearly strongand hyper-singularities, respectively, for potentials and its derivative. This paper represents the first attempt to apply a nonlinear transformation, based on sinh function, to the accurate evaluation of nearly singular kernels associated with the RMM. The accuracy and efficiency of the proposed strategy are demonstrated through several numerical examples, where the solutions at as close as 1.0E–6 distance to the boundary are accurately evaluated.

Keywords

Regularized meshless method, Double layer potentials, Near singularity, Boundary layer effect, nonlinear transformation.

Cite This Article

Li, W., Chen, W. (2014). Boundary Layer Effect in Regularized Meshless Method for Laplace Equation. CMES-Computer Modeling in Engineering & Sciences, 100(5), 347–362.



This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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