A Meshless Local Petrov-Galerkin Shepard and Least-Squares Method Based on Duo Nodal Supports | Zendy

Xiaoying Zhuang | Zendy; Yongchang Cai | Zendy

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A Meshless Local Petrov-Galerkin Shepard and Least-Squares Method Based on Duo Nodal Supports

Author(s) -

Xiaoying Zhuang,

Yongchang Cai

Publication year - 2014

Publication title -

mathematical problems in engineering

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.262

H-Index - 62

eISSN - 1026-7077

pISSN - 1024-123X

DOI - 10.1155/2014/806142

Subject(s) - kronecker delta , petrov–galerkin method , moving least squares , interpolation (computer graphics) , regularized meshless method , partition of unity , meshfree methods , robustness (evolution) , basis function , partition (number theory) , mathematics , galerkin method , harmonic function , singular boundary method , mathematical analysis , physics , finite element method , classical mechanics , chemistry , combinatorics , quantum mechanics , motion (physics) , biochemistry , boundary element method , gene , thermodynamics

The meshless Shepard and least-squares (MSLS) interpolation is a newly developed partition of unity- (PU-) based method which removes the difficulties with many other meshless methods such as the lack of the Kronecker delta property. The MSLS interpolation is efficient to compute and retain compatibility for any basis function used. In this paper, we extend the MSLS interpolation to the local Petrov-Galerkin weak form and adopt the duo nodal support domain. In the new formulation, there is no need for employing singular weight functions as is required in the original MSLS and also no need for background mesh for integration. Numerical examples demonstrate the effectiveness and robustness of the present method

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