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- W4308986525 abstract "Abstract 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 $$phi (r)=r^m$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:mi>ϕ</mml:mi> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>r</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>=</mml:mo> <mml:msup> <mml:mi>r</mml:mi> <mml:mi>m</mml:mi> </mml:msup> </mml:mrow> </mml:math> 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 $$ell _2$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msub> <mml:mi>ℓ</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:math> -norm on several representative benchmark problems with smooth and non-smooth solutions, using h -adaptive, uniform, and quasi-uniform point-cloud refinement." @default.
- W4308986525 created "2022-11-20" @default.
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- W4308986525 date "2022-11-14" @default.
- W4308986525 modified "2023-09-30" @default.
- W4308986525 title "h-Adaptive radial basis function finite difference method for linear elasticity problems" @default.
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- W4308986525 doi "https://doi.org/10.1007/s00466-022-02249-9" @default.
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