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Moving kriging interpolation and element‐free Galerkin method
Author(s) -
Gu Lei
Publication year - 2002
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.553
Subject(s) - kronecker delta , interpolation (computer graphics) , mathematics , galerkin method , finite element method , boundary (topology) , boundary value problem , function (biology) , mathematical analysis , property (philosophy) , convergence (economics) , mathematical optimization , computer science , structural engineering , physics , engineering , computer graphics (images) , epistemology , quantum mechanics , evolutionary biology , economics , biology , economic growth , animation , philosophy
Abstract A new formulation of the element‐free Galerkin (EFG) method is presented in this paper. EFG has been extensively popularized in the literature in recent years due to its flexibility and high convergence rate in solving boundary value problems. However, accurate imposition of essential boundary conditions in the EFG method often presents difficulties because the Kronecker delta property, which is satisfied by finite element shape functions, does not necessarily hold for the EFG shape function. The proposed new formulation of EFG eliminates this shortcoming through the moving kriging (MK) interpolation. Two major properties of the MK interpolation: the Kronecker delta property ( ϕ I ( s J )= δ IJ ) and the consistency property (∑ I n ϕ I ( x )=1 and ∑ I n ϕ I ( x ) x Ii = x i ) are proved. Some preliminary numerical results are given. Copyright © 2002 John Wiley & Sons, Ltd.