A matrix triangularization algorithm for the polynomial point interpolation method

被引:44
作者
Liu, GR [1 ]
Gu, YT [1 ]
机构
[1] Natl Univ Singapore, Dept Mech Engn, Ctr ACES, Singapore 119260, Singapore
关键词
computational mechanics; meshless method; meshfree method; polynomial interpolation; interpolation function;
D O I
10.1016/S0045-7825(03)00266-4
中图分类号
T [工业技术];
学科分类号
08 ;
摘要
A novel matrix triangularization algorithm (MTA) is proposed to overcome the singularity problem in the point interpolation method (PIM) using the polynomial basis, and to ensure stable and reliable construction of PIM shape functions. The present algorithm is validated using several examples, and implemented in the local point interpolation method (LPIM) that is a truly meshfree method based on a local weak form. Numerical examples demonstrate that LPIM using the present MTA are very easy to implement, and very robust for solving problems of computational mechanics. It is shown that PIM with the present MTA is very effective in constructing shape functions. Most importantly, PIM shape functions possess Kronecker delta function properties. Parameters that influence the performance of them are studied in detail. The convergence and efficiency of them are thoroughly investigated. (C) 2003 Elsevier Science B.V. All rights reserved.
引用
收藏
页码:2269 / 2295
页数:27
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