An improved meshless Shepard and least squares method possessing the delta property and requiring no singular weight function

Authors:
Xiaoying Zhuang;Hehua Zhu;Charles Augarde
Affiliations:
Department of Geotechnical Engineering, Tongji University, Shanghai, China 200092 and School of Civil and Resource Engineering, The University of Western Australia, Crawley, Australia 6009;Department of Geotechnical Engineering, Tongji University, Shanghai, China 200092;School of Engineering and Computing Sciences, Durham University, Durham, UK DH1 3L3
Venue:
Computational Mechanics
Year:
2014

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Abstract

The meshless Shepard and least squares (MSLS) method and the meshless Shepard method are partition of unity based meshless interpolations which eliminate the problems by other meshless methods such as the difficulty in direct imposition of the essential boundary conditions. However, singular weight functions have to be used in both methods to enforce the approximation interpolatory, which leads to the loss of smoothness in approximation and locally oscillatory results. In this paper, an improved MSLS interpolation is developed by using dually defined nodal supports such that no singular weight function is required. The proposed interpolation satisfies the delta property at boundary nodes and the compatibility condition throughout the domain, and is capable of exactly reproducing the basis function. The computational cost of the present interpolation is much lower than the moving least-squares approximation which is probably the most widely used meshless interpolation at present.