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Zbl 1098.74741
Wang, J. G.; Liu, G. R.
A point interpolation meshless method based on radial basis functions. (English)
[J] Int. J. Numer. Methods Eng. 54, No. 11, 1623-1648 (2002). ISSN 0029-5981

Summary: 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.

MSC 2000:: *74S30 Other numerical methods
74K20 Plates
74L10 Soil and rock mechanics

Keywords: meshless method; point interpolation; radial basis function; singularity; stress analysis

Cited in: Zbl 1065.74074

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