Gaussian RBF-FD weights and its corresponding local truncation errors

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Show simple item record Bayona Revilla, Víctor Moscoso, Miguel Kindelan Segura, Manuel 2023-01-20T13:39:47Z 2023-01-20T13:39:47Z 2012-09
dc.identifier.bibliographicCitation Bayona, V., Moscoso, M., & Kindelan, M. (2012). Gaussian RBF-FD weights and its corresponding local truncation errors. Engineering Analysis with Boundary Elements, 36(9), 1361-1369.
dc.identifier.issn 0955-7997
dc.description.abstract In this work we derive analytical expressions for the weights of Gaussian RBF-FD and Gaussian RBF-HFD formulas for some differential operators. These weights are used to derive analytical expressions for the leading order approximations to the local truncation error in powers of the inter-node distance h and the shape parameter є. We show that for each differential operator, there is a range of values of the shape parameter for which RBF-FD formulas and RBF-HFD formulas are significantly more accurate than the corresponding standard FD formulas. In fact, very often there is an optimal value of the shape parameter є+ for which the local error is zero to leading order. This value can be easily computed from the analytical expressions for the leading order approximations to the local error. Contrary to what is generally believed, this value is, to leading order, independent of the internodal distance and only dependent on the value of the function and its derivatives at the node.
dc.description.sponsorship This work has been supported by Spanish MICINN Grants FIS2010-18473, CSD2010-00011 and by Madrid Autonomous Region Grant S2009-1597. M.K. acknowledges Fundacion Caja Madrid for its financial support.
dc.format.extent 9
dc.language.iso eng
dc.publisher Elsevier
dc.rights © 2012 Elsevier Ltd. All rights reserved.
dc.rights Atribución-NoComercial-SinDerivadas 3.0 España
dc.subject.other Radial basis functions
dc.subject.other Multiquadric
dc.subject.other RBF-FD
dc.subject.other Shape parameter
dc.title Gaussian RBF-FD weights and its corresponding local truncation errors
dc.type article
dc.subject.eciencia Matemáticas
dc.rights.accessRights openAccess
dc.relation.projectID Gobierno de España. FIS2010-18473
dc.relation.projectID Gobierno de España. CSD2010-00011
dc.relation.projectID Comunidad de Madrid. S2009-1597
dc.type.version acceptedVersion
dc.identifier.publicationfirstpage 1361
dc.identifier.publicationissue 9
dc.identifier.publicationlastpage 1369
dc.identifier.publicationtitle Engineering Analysis with Boundary Elements
dc.identifier.publicationvolume 36
dc.identifier.uxxi AR/0000010019
dc.contributor.funder Comunidad de Madrid
dc.contributor.funder Ministerio de Ciencia e Innovación (España)
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