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.

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.
• Public URL: https://durham-repository.worktribe.com/output/1471129