Iterative optimization method for determining optimal shape parameter in RBF-FD method

DOI10.1016/j.aml.2023.108736OpenAlexW4378975499MaRDI QIDQ6170051

Shihui Ying, Jie Hou, Ying Li

Publication date: 15 August 2023

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aml.2023.108736

zbMATH Keywords

local errorradial basis functionshape parameterRBF-FD method

Mathematics Subject Classification ID

Numerical approximation and computational geometry (primarily algorithms) (65Dxx) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65Mxx) Numerical methods for partial differential equations, boundary value problems (65Nxx)

Cites Work

• Stable calculation of Gaussian-based RBF-FD stencils
• Multiquadrics - a scattered data approximation scheme with applications to computational fluid-dynamics. I: Surface approximations and partial derivative estimates
• RBF-FD formulas and convergence properties
• Optimal constant shape parameter for multiquadric based RBF-FD method
• On the optimal shape parameter for Gaussian radial basis function finite difference approximation of the Poisson equation
• Multiquadrics -- a scattered data approximation scheme with applications to computational fluid-dynamics. II: Solutions to parabolic, hyperbolic and elliptic partial differential equations
• Semi-discretized numerical solution for time fractional convection-diffusion equation by RBF-FD
• Local radial basis function-finite difference based algorithms for singularly perturbed Burgers' model
• A stabilized radial basis-finite difference (RBF-FD) method with hybrid kernels
• Taylor Expansion of exp(∑ ∞ k = 0 a k z k ) and Some Applications
• A review of numerical methods for nonlinear partial differential equations

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