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A new higher-order RBF-FD scheme with optimal variable shape parameter for partial differential equation

Radial basis functions (RBFs) with multiquadric (MQ) kernel have been commonly used to solve partial differential equation (PDE). The MQ kernel contains a user-defined shape parameter (ε), and the solution accuracy is strongly dependent on the value of this ε. In this study, the MQ-based RBF finite...

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Main Authors: Ng, Y.L., Ng, K.C., Sheu, T.W.H.
Format: Article
Language:English
Published: 2020
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spelling my.uniten.dspace-130292020-08-18T05:25:47Z A new higher-order RBF-FD scheme with optimal variable shape parameter for partial differential equation Ng, Y.L. Ng, K.C. Sheu, T.W.H. Radial basis functions (RBFs) with multiquadric (MQ) kernel have been commonly used to solve partial differential equation (PDE). The MQ kernel contains a user-defined shape parameter (ε), and the solution accuracy is strongly dependent on the value of this ε. In this study, the MQ-based RBF finite difference (RBF-FD) method is derived in a polynomial form. The optimal value of ε is computed such that the leading error term of the RBF-FD scheme is eliminated to improve the solution accuracy and to accelerate the rate of convergence. The optimal ε is computed by using finite difference (FD) and combined compact differencing (CCD) schemes. From the analyses, the optimal ε is found to vary throughout the domain. Therefore, by using the localized shape parameter, the computed PDE solution accuracy is higher as compared to the RBF-FD scheme which employs a constant value of ε. In general, the solution obtained by using the ε computed from CCD scheme is more accurate, but at a higher computational cost. Nevertheless, the cost-effectiveness study shows that when the number of iterative prediction of ε is limited to two, the present RBF-FD with ε by CCD scheme is as effective as the one using FD scheme. © 2019, © 2019 Taylor & Francis Group, LLC. 2020-02-03T03:29:54Z 2020-02-03T03:29:54Z 2019-05 Article 10.1080/10407790.2019.1627811 en Numerical Heat Transfer, Part B: Fundamentals
institution Universiti Tenaga Nasional
building UNITEN Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Tenaga Nasional
content_source UNITEN Institutional Repository
url_provider http://dspace.uniten.edu.my/
language English
description Radial basis functions (RBFs) with multiquadric (MQ) kernel have been commonly used to solve partial differential equation (PDE). The MQ kernel contains a user-defined shape parameter (ε), and the solution accuracy is strongly dependent on the value of this ε. In this study, the MQ-based RBF finite difference (RBF-FD) method is derived in a polynomial form. The optimal value of ε is computed such that the leading error term of the RBF-FD scheme is eliminated to improve the solution accuracy and to accelerate the rate of convergence. The optimal ε is computed by using finite difference (FD) and combined compact differencing (CCD) schemes. From the analyses, the optimal ε is found to vary throughout the domain. Therefore, by using the localized shape parameter, the computed PDE solution accuracy is higher as compared to the RBF-FD scheme which employs a constant value of ε. In general, the solution obtained by using the ε computed from CCD scheme is more accurate, but at a higher computational cost. Nevertheless, the cost-effectiveness study shows that when the number of iterative prediction of ε is limited to two, the present RBF-FD with ε by CCD scheme is as effective as the one using FD scheme. © 2019, © 2019 Taylor & Francis Group, LLC.
format Article
author Ng, Y.L.
Ng, K.C.
Sheu, T.W.H.
spellingShingle Ng, Y.L.
Ng, K.C.
Sheu, T.W.H.
A new higher-order RBF-FD scheme with optimal variable shape parameter for partial differential equation
author_facet Ng, Y.L.
Ng, K.C.
Sheu, T.W.H.
author_sort Ng, Y.L.
title A new higher-order RBF-FD scheme with optimal variable shape parameter for partial differential equation
title_short A new higher-order RBF-FD scheme with optimal variable shape parameter for partial differential equation
title_full A new higher-order RBF-FD scheme with optimal variable shape parameter for partial differential equation
title_fullStr A new higher-order RBF-FD scheme with optimal variable shape parameter for partial differential equation
title_full_unstemmed A new higher-order RBF-FD scheme with optimal variable shape parameter for partial differential equation
title_sort new higher-order rbf-fd scheme with optimal variable shape parameter for partial differential equation
publishDate 2020
_version_ 1678595888025436160
score 13.211869

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