A collocation mesh-free method based on multiple basis functions

被引：5

作者：

Mohamed, H. A. ^{[1
]}

Bakrey, A. E. ^{[2
]}

Ahmed, S. G. ^{[1
]}

机构：

[1] Zagazig Univ, Fac Engn, Dept Engn Phys & Math, Zagazig, Egypt

[2] Zagazig Univ, Fac Engn, Dept Struct Engn, Zagazig, Egypt

来源：

ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS | 2012年 / 36卷 / 03期

关键词：

Moving least squares; Radial basis function; Linear interpolation; RADIAL BASIS FUNCTIONS; MOVING LEAST-SQUARES; PARTIAL-DIFFERENTIAL-EQUATIONS; FREE GALERKIN METHOD; THIN-PLATE; INTERPOLATION; SURFACES;

D O I：

10.1016/j.enganabound.2011.09.002

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

Two dominant shape functions are used to approximate scattered points in mesh-free methods, e.g. the interpolating radial basis function (RBF) and the approximating moving least squares (MLS). In the present paper, a new shape function is developed as a linear interpolating function of both MLS and RBF. This function inherits the properties of both MLS and RBF and is regularized by a control parameter mu which takes different values in the domain [0,1]. Based on the proposed shape function, the collocation method is applied to solve initial and boundary value problems in one and two dimensions. The present method gives good results and achieves good convergence trends for different values of mu, compared with MLS and RBF individually, for a large number of nodes. (C) 2011 Elsevier Ltd. All rights reserved.

引用

页码：446 / 450

页数：5

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