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.
1594-1601
O'Brien, Neil
7856f2e1-73fc-4cb9-a1f4-9b6c8b9373e7
Djidjeli, K.
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Cox, Simon J.
0e62aaed-24ad-4a74-b996-f606e40e5c55
December 2013
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), .
(doi:10.1016/j.enganabound.2013.08.018).
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.
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Published date: December 2013
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Computational Engineering & Design Group
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Local EPrints ID: 359236
URI: http://eprints.soton.ac.uk/id/eprint/359236
ISSN: 0955-7997
PURE UUID: e615251a-7b02-466d-89f3-0415ff810631
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Date deposited: 24 Oct 2013 10:32
Last modified: 14 Mar 2024 15:18
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Neil O'Brien
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