Publication:
RBF-FD Formulas and Convergence Properties

dc.affiliation.dptoUC3M. Departamento de Matemáticases
dc.affiliation.grupoinvUC3M. Grupo de Investigación: Modelización, Simulación Numérica y Matemática Industriales
dc.contributor.authorBayona Revilla, Víctor
dc.contributor.authorMoscoso, Miguel
dc.contributor.authorCarretero Cerrajero, Manuel
dc.contributor.authorKindelan Segura, Manuel
dc.contributor.funderComunidad de Madrides
dc.contributor.funderMinisterio de Educación, Cultura y Deporte (España)es
dc.date.accessioned2022-12-02T08:51:21Z
dc.date.available2022-12-02T08:51:21Z
dc.date.issued2010-11-01
dc.description.abstractThe local RBF is becoming increasingly popular as an alternative to the global version that suffers from ill-conditioning. In this paper, we study analytically the convergence behavior of the local RBF method as a function of the number of nodes employed in the scheme, the nodal distance, and the shape parameter. We derive exact formulas for the first and second derivatives in one dimension, and for the Laplacian in two dimensions. Using these formulas we compute Taylor expansions for the error. From this analysis, we find that there is an optimal value of the shape parameter for which the error is minimum. This optimal parameter is independent of the nodal distance. Our theoretical results are corroborated by numerical experiments.en
dc.description.sponsorshipThis work has been supported by Spanish MECD Grants FIS2007-62673, FIS2008-04921 and by Madrid Autonomous Region Grant S2009-1597.en
dc.format.extent15
dc.identifier.bibliographicCitationBayona, V., Moscoso, M., Carretero, M. & Kindelan, M. (2010). RBF-FD formulas and convergence properties. Journal of Computational Physics, 229(22), 8281-8295.en
dc.identifier.doihttps://doi.org/10.1016/j.jcp.2010.07.008
dc.identifier.issn0021-9991
dc.identifier.publicationfirstpage8281
dc.identifier.publicationissue22
dc.identifier.publicationlastpage8295
dc.identifier.publicationtitleJournal of Computational Physicsen
dc.identifier.publicationvolume229
dc.identifier.urihttps://hdl.handle.net/10016/36143
dc.identifier.uxxiAR/0000007311
dc.language.isoeng
dc.publisherElsevieren
dc.relation.projectIDGobierno de España. FIS2008-04921-C02-01es
dc.relation.projectIDGobierno de España. FIS2007-62673es
dc.relation.projectIDComunidad de Madrid. S2009-1597es
dc.rights© 2010 Elsevier Inc. All rights reserved.en
dc.rightsAtribución-NoComercial-SinDerivadas 3.0 España*
dc.rights.accessRightsopen accessen
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/3.0/es/*
dc.subject.ecienciaFísicaes
dc.subject.ecienciaInformáticaes
dc.subject.otherRadial basis functionsen
dc.subject.otherMesh-freeen
dc.titleRBF-FD Formulas and Convergence Propertiesen
dc.typeresearch article*
dc.type.hasVersionAM*
dspace.entity.typePublication
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