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Least‐squares collocation meshless method
Author(s) -
Zhang Xiong,
Liu XiaoHu,
Song KangZu,
Lu MingWan
Publication year - 2001
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.200
Subject(s) - regularized meshless method , collocation (remote sensing) , collocation method , moving least squares , orthogonal collocation , singular boundary method , mathematics , least squares function approximation , point (geometry) , meshfree methods , construct (python library) , mathematical optimization , computer science , mathematical analysis , finite element method , geometry , differential equation , ordinary differential equation , engineering , statistics , boundary element method , structural engineering , machine learning , estimator , programming language
A finite point method, least‐squares collocation meshless method, is proposed. Except for the collocation points which are used to construct the trial functions, a number of auxiliary points are also adopted. Unlike the direct collocation method, the equilibrium conditions are satisfied not only at the collocation points but also at the auxiliary points in a least‐squares sense. The moving least‐squares interpolant is used to construct the trial functions. The computational effort required for the present method is in the same order as that required for the direct collocation, while the present method improves the accuracy of solution significantly. The proposed method does not require any mesh so that it is a truly meshless method. Three numerical examples are studied in detail, which show that the proposed method possesses high accuracy with low computational effort. Copyright © 2001 John Wiley & Sons, Ltd.