Point collocation methods using the fast moving least-square reproducing kernel approximation

被引:83
作者
Kim, DW [1 ]
Kim, Y
机构
[1] Sunmoon Univ, Dept Math, Asan 336708, Chungnam, South Korea
[2] Yonsei Univ, Dept Math, Seoul 120749, South Korea
关键词
moving least-square reproducing kernel; approximate derivatives; point collocation; poisson problem; Stokes problem;
D O I
10.1002/nme.618
中图分类号
T [工业技术];
学科分类号
08 ;
摘要
A pseudo-spectral point collocation meshfree method is proposed. We apply a scheme of approximating derivatives based on the moving least-square reproducing kernel approximations. Using approximated derivatives, we propose a new point collocation method. Unlike other meshfree methods that require direct calculation of derivatives for shape functions, with the proposed scheme, approximated derivatives are obtained in the process of calculating the shape function itself without further cost. Moreover, the scheme does not require the regularity of the window function, which ensures the regularity of shape functions. In this paper, we show the reproducing property and the convergence of interpolation for approximated derivatives of shape functions. As numerical examples of the proposed scheme, Poisson and Stokes problems are considered in various situations including the case of randomly generated node sets. In short, the proposed scheme is efficient and accurate even for complicated geometry such as the flow past a cylinder. Copyright (C) 2003 John Wiley Sons, Ltd.
引用
收藏
页码:1445 / 1464
页数:20
相关论文
共 28 条
[1]  
AHN MY, ANAL MESHFREE METHOD
[2]  
Aluru NR, 2000, INT J NUMER METH ENG, V47, P1083, DOI 10.1002/(SICI)1097-0207(20000228)47:6<1083::AID-NME816>3.0.CO
[3]  
2-N
[4]   A critical assessment of the truly Meshless Local Petrov-Galerkin (MLPG), and Local Boundary Integral Equation (LBIE) methods [J].
Atluri, SN ;
Kim, HG ;
Cho, JY .
COMPUTATIONAL MECHANICS, 1999, 24 (05) :348-372
[5]  
Belytschko T, 1998, INT J NUMER METH ENG, V43, P785, DOI 10.1002/(SICI)1097-0207(19981115)43:5<785::AID-NME420>3.0.CO
[6]  
2-9
[7]  
Choe HJ, 2001, DISCRETE CONT DYN-B, V1, P495
[8]  
CHOE HJ, MESHFREE METHOD NONS
[9]   An h-p adaptive method using clouds [J].
Duarte, CA ;
Oden, JT .
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 1996, 139 (1-4) :237-262
[10]  
Fürst J, 2001, Z ANGEW MATH MECH, V81, P403, DOI 10.1002/1521-4001(200106)81:6<403::AID-ZAMM403>3.0.CO