Premium
A point interpolation meshless method based on radial basis functions
Author(s) -
Wang J. G.,
Liu G. R.
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.489
Subject(s) - radial basis function , interpolation (computer graphics) , moving least squares , regularized meshless method , basis function , mathematics , polynomial basis , singularity , singular boundary method , polynomial , polynomial interpolation , meshfree methods , point (geometry) , boundary (topology) , function (biology) , basis (linear algebra) , domain (mathematical analysis) , mathematical analysis , convergence (economics) , computer science , geometry , linear interpolation , boundary element method , finite element method , artificial intelligence , physics , motion (physics) , biology , evolutionary biology , artificial neural network , thermodynamics , economic growth , economics
A point interpolation meshless method is proposed based on combining radial and polynomial basis functions. Involvement of radial basis functions overcomes possible singularity associated with the meshless methods based on only the polynomial basis. This non‐singularity is useful in constructing well‐performed shape functions. Furthermore, the interpolation function obtained passes through all scattered points in an influence domain and thus shape functions are of delta function property. This makes the implementation of essential boundary conditions much easier than the meshless methods based on the moving least‐squares approximation. In addition, the partial derivatives of shape functions are easily obtained, thus improving computational efficiency. Examples on curve/surface fittings and solid mechanics problems show that the accuracy and convergence rate of the present method is high. Copyright © 2002 John Wiley & Sons, Ltd.