Publisher DOI: 10.1007/s00466-022-02249-9
Title: h-Adaptive radial basis function finite difference method for linear elasticity problems
Language: English
Authors: Tóth, Balázs 
Düster, Alexander 
Keywords: Adaptivity; Finite differences; Linear elasticity; Polyharmonic splines; Polynomials; Radial basis functions
Issue Date: 2022
Source: Computational Mechanics (in Press, cc by): (2022)
Abstract (english): 
In this research work, the radial basis function finite difference method (RBF-FD) is further developed to solve one- and two-dimensional boundary value problems in linear elasticity. The related differentiation weights are generated by using the extended version of the RBF utilizing a polynomial basis. The type of the RBF is restricted to polyharmonic splines (PHS), i.e., a combination of the odd m-order PHS ϕ(r) = rm with additional polynomials up to degree p will serve as the basis. Furthermore, a new residual-based adaptive point-cloud refinement algorithm will be presented and its numerical performance will be demonstrated. The computational efficiency of the PHS RBF-FD approach is tested by means of the relative errors measured in ℓ2-norm on several representative benchmark problems with smooth and non-smooth solutions, using h-adaptive, uniform, and quasi-uniform point-cloud refinement.
URI: http://hdl.handle.net/11420/14188
ISSN: 0178-7675
Journal: Computational Mechanics 
Institute: Konstruktion und Festigkeit von Schiffen M-10 
Document Type: Article
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