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h-Adaptive radial basis function finite difference method for linear elasticity problems
Citation Link: https://doi.org/10.15480/882.4954
Publikationstyp
Journal Article
Date Issued
2023-03
Sprache
English
Author(s)
TORE-DOI
Journal
Volume
71
Issue
3
Start Page
433
End Page
452
Citation
Computational Mechanics 71 (3): 433-452 (2023-03)
Publisher DOI
Scopus ID
Publisher
Springer
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.
Subjects
Adaptivity
Finite differences
Linear elasticity
Polyharmonic splines
Polynomials
Radial basis functions
DDC Class
530: Physik
600: Technik
620: Ingenieurwissenschaften
Funding Organisations
Hungarian National Research, Development and Innovation Office (NKFIH)
Publication version
publishedVersion
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s00466-022-02249-9-1.pdf
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3.29 MB
Format
Adobe PDF