The quasi-optimal radial basis function collocation method: a technical note

DOI10.1155/2021/6694369zbMath1477.65256OpenAlexW3202227828MaRDI QIDQ2052102

Yanyan Li

Publication date: 25 November 2021

Published in: Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1155/2021/6694369

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Numerical radial basis function approximation (65D12)

Cites Work

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• Multiquadrics - a scattered data approximation scheme with applications to computational fluid-dynamics. I: Surface approximations and partial derivative estimates
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• Stable computation of multiquadric interpolants for all values of the shape parameter
• An algorithm for selecting a good value for the parameter \(c\) in radial basis function interpolation
• The Kansa RBF method with auxiliary boundary centres for fourth order boundary value problems
• The sample solution approach for determination of the optimal shape parameter in the multiquadric function of the Kansa method
• Analysis on the method of fundamental solutions for biharmonic equations
• A meshless collocation method for band structure simulation of nanoscale phononic crystals based on nonlocal elasticity theory
• The conical radial basis function for partial differential equations
• An accurate and stable RBF method for solving partial differential equations
• A local radial basis function collocation method for band structure computation of phononic crystals with scatterers of arbitrary geometry
• A novel RBF collocation method using fictitious centres
• Combinations of the method of fundamental solutions for general inverse source identification problems
• Investigation of regularized techniques for boundary knot method
• Meshless Collocation Method for Inverse Source Identification Problems

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