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 |
Appears in Collections: | Publications without fulltext |
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