An investigation of radial basis function-finite difference (RBF-FD) method for numerical solution of elliptic partial differential equations
type: Item
instance of: scholarly article
title: An investigation of radial basis function-finite difference (RBF-FD) method for numerical solution of elliptic partial differential equations
zbMATH Open document ID: 1395.65121
author: Suranon Yensiri
author: Ruth J. Skulkhu
published in: Mathematics
publication date: 2018-07-05T00:00:00Z
review text: Summary: The Radial Basis Function (RBF) method has been considered an important meshfree tool for numerical solutions of Partial Differential Equations (PDEs). For various situations, RBF with infinitely differentiable functions can provide accurate results and more flexibility in the geometry of computation domains than traditional methods such as finite difference and finite element methods. However, RBF does not suit large scale problems, and, therefore, a combination of RBF and the finite difference (RBF-FD) method was proposed because of its own strengths not only on feasibility and computational cost, but also on solution accuracy. In this study, we try the RBF-FD method on elliptic PDEs and study the effect of it on such equations with different shape parameters. Most importantly, we study the solution accuracy after additional ghost node strategy, preconditioning strategy, regularization strategy, and floating point arithmetic strategy. We have found more satisfactory accurate solutions in most situations than those from global RBF, except in the preconditioning and regularization strategies.
Mathematics Subject Classification ID: 65N06
Mathematics Subject Classification ID: 65N35
Mathematics Subject Classification ID: 65F22
Mathematics Subject Classification ID: 65F08
zbMATH DE Number: 6898683
zbMATH Keywords: numerical partial differential equations (PDEs)
zbMATH Keywords: radial basis function-finite difference (RBF-FD) method
zbMATH Keywords: ghost node
zbMATH Keywords: preconditioning
zbMATH Keywords: regularization
zbMATH Keywords: floating point arithmetic
describes a project that uses: Matlab
describes a project that uses: Matlab-RBF-Toolbox
MaRDI profile type: Publication
full work available at URL: math5040054
OpenAlex ID: W2766666589
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DOI: 10.3390/MATH5040054
description: scientific article; zbMATH DE number 6898683