Skip to main content

Research Repository

Advanced Search

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

Zhuang, X.; Zhu, H.; Augarde, C.E.

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


Authors

X. Zhuang

H. Zhu



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.

Citation

Zhuang, X., Zhu, H., & Augarde, C. (2014). An improved meshless Shepard and least squares method possessing the delta property and requiring no singular weight function. Computational Mechanics, 53(2), 343-357. https://doi.org/10.1007/s00466-013-0912-1

Journal Article Type Article
Acceptance Date Aug 12, 2013
Online Publication Date Sep 5, 2013
Publication Date Feb 1, 2014
Deposit Date Sep 3, 2013
Publicly Available Date Oct 6, 2014
Journal Computational Mechanics
Print ISSN 0178-7675
Electronic ISSN 1432-0924
Publisher Springer
Peer Reviewed Peer Reviewed
Volume 53
Issue 2
Pages 343-357
DOI https://doi.org/10.1007/s00466-013-0912-1
Keywords Meshless, Shepard shape function, Partition of unity, Delta property, Compatibility.

Files






You might also like



Downloadable Citations