Local RBF Algorithms for Elliptic Boundary Value Problems in Annular Domains

DOI10.4208/cicp.OA-2018-0031zbMath1473.65326OpenAlexW2914129037MaRDI QIDQ5160529

Ching-Shyang Chen, Andreas Karageorghis

Publication date: 29 October 2021

Published in: Communications in Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4208/cicp.oa-2018-0031

zbMATH Keywords

fast Fourier transformsradial basis functionsbiharmonic equationPoisson equationKansa methodmatrix decomposition algorithmsCauchy-Navier equations of elasticity

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Numerical solution of discretized equations for boundary value problems involving PDEs (65N22) Numerical radial basis function approximation (65D12)

Related Items

A meshless collocation method for band structure simulation of nanoscale phononic crystals based on nonlocal elasticity theory ⋮ The local meshless collocation method for numerical simulation of shallow water waves based on generalized equal width (GEW) equation ⋮ Improved RBF Collocation Methods for Fourth Order Boundary Value Problems ⋮ The radial basis function-differential quadrature method for elliptic problems in annular domains

Uses Software

• Matlab
• Stony Brook

Cites Work

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• Superconvergence and recovery type a posteriori error estimation for hybrid stress finite element method
• Recent advances on radial basis function collocation methods
• Matrix decomposition RBF algorithm for solving 3D elliptic problems
• Multiquadric and its shape parameter -- a numerical investigation of error estimate, condition number, and round-off error by arbitrary precision computation
• A new preconditioner for indefinite and asymmetric matrices
• Radial basis function interpolation on irregular domain through conformal transplantation
• Matrix decomposition algorithms for elliptic boundary value problems: A survey
• A localized approach for the method of approximate particular solutions
• On using radial basis functions in a ``finite difference mode with applications to elasticity problems
• Chebyshev-type methods and preconditioning techniques
• A matrix decomposition RBF algorithm: approximation of functions and their derivatives
• A Kansa-radial basis function method for elliptic boundary value problems in annular domains
• Local radial basis function-based differential quadrature method and its application to solve two-dimensional incompressible Navier--Stokes equations
• Local multiquadric approximation for solving boundary value problems
• Circumventing the ill-conditioning problem with multiquadric radial basis functions: Applications to elliptic partial differential equations
• Matrix decomposition algorithms for separable elliptic boundary value problems in two space dimensions
• Multiquadrics -- a scattered data approximation scheme with applications to computational fluid-dynamics. II: Solutions to parabolic, hyperbolic and elliptic partial differential equations
• An algorithm for selecting a good value for the parameter \(c\) in radial basis function interpolation
• On choosing ``optimal shape parameters for RBF approximation
• The method of fundamental solutions for elliptic problems in circular domains with mixed boundary conditions
• Kansa-RBF Algorithms for Elliptic Problems in Axisymmetric Domains
• Solving biharmonic equation using the localized method of approximate particular solutions
• A PRECONDITIONED METHOD FOR THE SOLUTION OF THE ROBBINS PROBLEM FOR THE HELMHOLTZ EQUATION
• A Compact Difference Scheme for the Biharmonic Equation in Planar Irregular Domains
• Radial Basis Functions
• Uniform Convergence Analysis of a Higher Order Hybrid Stress Quadrilateral Finite Element Method for Linear Elasticity Problems