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Title: A matrix triangularization algorithm for the polynomial point interpolation method
Authors: Liu, G.R. 
Gu, Y.T.
Keywords: Computational mechanics
Interpolation function
Meshfree method
Meshless method
Polynomial interpolation
Issue Date: 9-May-2003
Citation: Liu, G.R., Gu, Y.T. (2003-05-09). A matrix triangularization algorithm for the polynomial point interpolation method. Computer Methods in Applied Mechanics and Engineering 192 (19) : 2269-2295. ScholarBank@NUS Repository.
Abstract: 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. © 2003 Elsevier Science B.V. All rights reserved.
Source Title: Computer Methods in Applied Mechanics and Engineering
ISSN: 00457825
DOI: 10.1016/S0045-7825(03)00266-4
Appears in Collections:Staff Publications

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