A novel algorithm for shape parameter selection in radial basis functions collocation method

Gherlone, Marco; Iurlaro, Luigi; Sciuva, Marco Di

doi:10.1016/j.compstruct.2011.08.001

Cited by 31 publications

(19 citation statements)

References 16 publications

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“…No mathematical theory has been developed yet to determine its optimal value. In most papers, the authors end up choosing this shape parameter by trial and error or some other ad hoc means [16,17].…”

Section: Reconstruction Algorithmmentioning

confidence: 99%

Acoustic tomography system for online monitoring of temperature fields

Yan

Zhou

2017

IET Science, Measurement & Technology

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Section: Reconstruction Algorithmmentioning

confidence: 99%

Acoustic tomography system for online monitoring of temperature fields

Yan

Zhou

2017

IET Science, Measurement & Technology

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“…For highly non-uniform nodal distribution, the resultant ill conditionings in the coefficient matrices dominate the solution causing significant inaccuracies in the values of expansion coefficients(λ). These inaccuracies result in breakdown of solution during subsequent iteration process [14]. Therefore, severe limitations are imposed on the use of non-uniform or random particle distribution within the domain.…”

Section: Type Of Radial Basis Functionmentioning

confidence: 99%

Adaptive Shape Parameter (ASP) Technique for Local Radial Basis Functions (RBFs) and Their Application for Solution of Navier-Stokes Equations

Javed

Djidjeli

2013

21st AIAA Computational Fluid Dynamics Conference

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The concept of adaptive shape parameters (ASP) has been presented for solution of incompressible Navier Strokes equations using mesh-free local Radial Basis Functions (RBF). The aim is to avoid ill-conditioning of coefficient matrices of RBF weights and inaccuracies in RBF interpolation resulting from non-optimized shape of basis functions for the cases where data points (or nodes) are not distributed uniformly throughout the domain. Unlike conventional approaches which assume globally similar values of RBF shape parameters, the presented ASP technique suggests that shape parameter be calculated exclusively for each data point (or node) based on the distribution of data points within its own influence domain. This will ensure interpolation accuracy while still maintaining well-conditioned system of equations for RBF weights. Performance and accuracy of ASP technique has been tested by evaluating derivatives and laplacian of a known function using RBF in Finite difference mode (RBF-FD), with and without the use of adaptivity in shape parameters. Application of adaptive shape parameters (ASP) for solution of incompressible Navier Strokes equations has been presented by solving lid driven cavity flow problem on mesh-free domain using RBF-FD. The results have been compared for fixed and adaptive shape parameters. Improved accuracy has been achieved with the use of ASP in RBF-FD especially at regions where larger gradients of field variables exist.

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“…Using a cross validation technique it is possible to obtain good solutions for the plate in bending problem, even with a reduced number of grid points, for regular and irregular node distributions. Gherlone et al proposed an algorithm that finds an optimal value of the shape parameter through a convergence analysis, inside a user-defined range [16].…”

Section: Introductionmentioning

confidence: 99%