The University of Southampton
University of Southampton Institutional Repository

Solving an eigenvalue problem on a periodic domain using a radial basis function finite differences scheme

Solving an eigenvalue problem on a periodic domain using a radial basis function finite differences scheme
Solving an eigenvalue problem on a periodic domain using a radial basis function finite differences scheme
Local radial basis functions (RBFs) are becoming increasingly popular as an alternative to global RBFs, as the latter suffer from ill-conditioning. In this paper, a local meshless method based on RBFs in a finite-difference (FD) mode with better conditioned matrices has been developed for solving an eigenvalue problem with a periodic domain. Through numerical experiments, we examine the accuracy of the method as a result of variation in the number and layout of nodes in the domain and the effects of shape parameter, using various globally supported RBFs. The presented scheme has been validated on two different types of nodal arrangement, namely uniform and non-uniform node distributions. The results obtained from the method are found to be in good agreement with the benchmark analytical solutions. In addition, a higher-order RBF-FD scheme (which uses ideas from Hermite interpolation) is then proposed for solving the eigenvalue problem with a periodic domain. Tests show that both accuracy and convergence order can be improved dramatically by using higher-order RBF-FD formulae, which converge at a rate of O(h8.5) compared to the standard-order method which converges as O(h4.3) for uniformly distributed nodes with spacing h.
0955-7997
1594-1601
O'Brien, Neil
7856f2e1-73fc-4cb9-a1f4-9b6c8b9373e7
Djidjeli, K.
94ac4002-4170-495b-a443-74fde3b92998
Cox, Simon J.
0e62aaed-24ad-4a74-b996-f606e40e5c55
O'Brien, Neil
7856f2e1-73fc-4cb9-a1f4-9b6c8b9373e7
Djidjeli, K.
94ac4002-4170-495b-a443-74fde3b92998
Cox, Simon J.
0e62aaed-24ad-4a74-b996-f606e40e5c55

O'Brien, Neil, Djidjeli, K. and Cox, Simon J. (2013) Solving an eigenvalue problem on a periodic domain using a radial basis function finite differences scheme. Engineering Analysis with Boundary Elements, 37 (12), 1594-1601. (doi:10.1016/j.enganabound.2013.08.018).

Record type: Article

Abstract

Local radial basis functions (RBFs) are becoming increasingly popular as an alternative to global RBFs, as the latter suffer from ill-conditioning. In this paper, a local meshless method based on RBFs in a finite-difference (FD) mode with better conditioned matrices has been developed for solving an eigenvalue problem with a periodic domain. Through numerical experiments, we examine the accuracy of the method as a result of variation in the number and layout of nodes in the domain and the effects of shape parameter, using various globally supported RBFs. The presented scheme has been validated on two different types of nodal arrangement, namely uniform and non-uniform node distributions. The results obtained from the method are found to be in good agreement with the benchmark analytical solutions. In addition, a higher-order RBF-FD scheme (which uses ideas from Hermite interpolation) is then proposed for solving the eigenvalue problem with a periodic domain. Tests show that both accuracy and convergence order can be improved dramatically by using higher-order RBF-FD formulae, which converge at a rate of O(h8.5) compared to the standard-order method which converges as O(h4.3) for uniformly distributed nodes with spacing h.

Text
1-s2.0-S095579971300177X-main.pdf - Version of Record
Restricted to Repository staff only
Request a copy

More information

Published date: December 2013
Organisations: Computational Engineering & Design Group

Identifiers

Local EPrints ID: 359236
URI: http://eprints.soton.ac.uk/id/eprint/359236
ISSN: 0955-7997
PURE UUID: e615251a-7b02-466d-89f3-0415ff810631

Catalogue record

Date deposited: 24 Oct 2013 10:32
Last modified: 14 Mar 2024 15:18

Export record

Altmetrics

Contributors

Author: Neil O'Brien
Author: K. Djidjeli
Author: Simon J. Cox

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of http://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×