On optimization of the RBF shape parameter in a grid-free local scheme for convection dominated problems over non-uniform centers

DOI10.1016/j.apm.2013.01.054zbMath1427.65300OpenAlexW2056083784MaRDI QIDQ1789022

Y. V. S. S. Sanyasiraju, Chirala Satyanarayana

Publication date: 9 October 2018

Published in: Applied Mathematical Modelling (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apm.2013.01.054

zbMATH Keywords

convection-diffusionradial basis functionoptimal shape parametergrid-free schememulti-quadric

Mathematics Subject Classification ID

Numerical interpolation (65D05) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70)

Related Items (16)

Approximation of insurance liability contracts using radial basis functions ⋮ A radial basis functions based finite differences method for wave equation with an integral condition ⋮ Upwind strategies for local RBF scheme to solve convection dominated problems ⋮ Improved localized radial basis functions with fitting factor for dominated convection-diffusion differential equations ⋮ Variable shape parameter strategy in local radial basis functions collocation method for solving the 2D nonlinear coupled Burgers' equations ⋮ A hybrid radial basis functions collocation technique to numerically solve fractional advection–diffusion models ⋮ A two-stage adaptive scheme based on RBF collocation for solving elliptic PDEs ⋮ A non-uniform Haar wavelet method for numerically solving two-dimensional convection-dominated equations and two-dimensional near singular elliptic equations ⋮ Analysis on the upwind local radial basis functions method to solve convection dominated problems and it's application for MHD flow ⋮ Consistent, non-oscillatory RBF finite difference solutions to boundary layer problems for any degree on uniform grids ⋮ A numerical scheme for solving a class of logarithmic integral equations arisen from two-dimensional Helmholtz equations using local thin plate splines ⋮ On the search of the shape parameter in radial basis functions using univariate global optimization methods ⋮ Radial basis function interpolation in the limit of increasingly flat basis functions ⋮ Local variably scaled Newton basis functions collocation method for solving Burgers' equation ⋮ An algorithm for choosing a good shape parameter for radial basis functions method with a case study in image processing ⋮ Educating local radial basis functions using the highest gradient of interest in three dimensional geometries

Uses Software

• rbf_qr

Cites Work

• A method for solving partial differential equations via radial basis functions: application to the heat equation
• A not-a-knot meshless method using radial basis functions and predictor-corrector scheme to the numerical solution of improved Boussinesq equation
• Adaptive meshless centres and RBF stencils for Poisson equation
• The near-equivalence of five species of spectrally-accurate radial basis functions (RBFs): Asymptotic approximations to the RBF cardinal functions on a uniform, unbounded grid
• On the optimal shape parameter for Gaussian radial basis function finite difference approximation of the Poisson equation
• On the solution of the non-local parabolic partial differential equations via radial basis functions
• Local radial basis function based gridfree scheme for unsteady incompressible viscous flows
• A numerical method for solution of the two-dimensional sine-Gordon equation using the radial basis functions
• Improved accuracy of multiquadric interpolation using variable shape parameters
• Local radial basis function-based differential quadrature method and its application to solve two-dimensional incompressible Navier--Stokes equations
• Stable computation of multiquadric interpolants for all values of the shape parameter
• Multiquadrics -- a scattered data approximation scheme with applications to computational fluid-dynamics. II: Solutions to parabolic, hyperbolic and elliptic partial differential equations
• Error estimates and condition numbers for radial basis function interpolation
• An algorithm for selecting a good value for the parameter \(c\) in radial basis function interpolation
• Numerical solution of the nonlinear Klein-Gordon equation using radial basis functions
• Determination of a control parameter in a one-dimensional parabolic equation using the method of radial basis functions
• On choosing ``optimal shape parameters for RBF approximation
• A numerical method for two-dimensional Schrödinger equation using collocation and radial basis functions
• The Runge phenomenon and spatially variable shape parameters in RBF interpolation
• Scattered node compact finite difference-type formulas generated from radial basis functions
• A Meshless Method Using Radial Basis Functions for the Numerical Solution of Two-Dimensional Complex Ginzburg-Landau Equation
• Stable Computations with Gaussian Radial Basis Functions
• Numerical experiments on optimal shape parameters for radial basis functions
• Local RBF-FD solutions for steady convection–diffusion problems
• A Stable Algorithm for Flat Radial Basis Functions on a Sphere
• Scattered Data Interpolation: Tests of Some Method
• Discrete Weighted Mean Approximation of a Model Convection-Diffusion Equation
• Formulation and experiments with high‐order compact schemes for nonuniform grids

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