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Optimal shape parameter for the solution of elastostatic problems with the RBF method

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dc.affiliation.dptoUC3M. Departamento de Matemáticases
dc.affiliation.grupoinvUC3M. Grupo de Investigación: Métodos Numéricos y Aplicacioneses
dc.affiliation.institutoUC3M. Instituto Universitario sobre Modelización y Simulación en Fluidodinámica, Nanociencia y Matemática Industrial Gregorio Millán Barbanyes
dc.contributor.authorSimonenko, Stanislav
dc.contributor.authorBayona Revilla, Víctor
dc.contributor.authorKindelan Segura, Manuel
dc.contributor.funderComunidad de Madrides
dc.contributor.funderMinisterio de Economía y Competitividad (España)es
dc.date.accessioned2021-02-18T11:14:01Z
dc.date.available2021-02-18T11:14:01Z
dc.date.issued2014-04-01
dc.description.abstractRadial basis functions (RBFs) have become a popular method for the solution of partial differential equations. In this paper we analyze the applicability of both the global and the local versions of the method for elastostatic problems. We use multiquadrics as RBFs and describe how to select an optimal value of the shape parameter to minimize approximation errors. The selection of the optimal shape parameter is based on analytical approximations to the local error using either the same shape parameter at all nodes or a node-dependent shape parameter. We show through several examples using both equispaced and nonequispaced nodes that significant gains in accuracy result from a proper selection of the shape parameter.en
dc.description.sponsorshipThis work was supported by Spanish MICINN Grants FIS2011-28838 and CSD2010-00011 and by Madrid Autonomous Region Grant S2009-1597. M.K. acknowledges Fundación Caja Madrid for its financial support.en
dc.format.extent15
dc.identifier.bibliographicCitationSimonenko, S., Bayona, V. y Kindelan, M.(2014). Optimal shape parameter for the solution of elastostatic problems with the RBF method. Journal of Engineering Mathematics, 85, 115–129.en
dc.identifier.doihttps://doi.org/10.1007/s10665-013-9636-7
dc.identifier.issn0022-0833
dc.identifier.publicationfirstpage115
dc.identifier.publicationlastpage129
dc.identifier.publicationtitleJournal of Engineering Mathematicsen
dc.identifier.publicationvolume85
dc.identifier.urihttps://hdl.handle.net/10016/31960
dc.identifier.uxxiAR/0000014760
dc.language.isoengen
dc.publisherSpringeren
dc.relation.projectIDComunidad de Madrid. S2009-1597es
dc.relation.projectIDGobierno de España. FIS2011-28838es
dc.relation.projectIDGobierno de España. CSD2010-00011es
dc.rights© 2013 Springer Science Business Media Dordrecht.en
dc.rights.accessRightsopen access
dc.subject.ecienciaMatemáticases
dc.subject.otherMeshlessen
dc.subject.otherRadial basis function (RBF)en
dc.subject.otherRBF–FDen
dc.subject.otherShape parameteren
dc.titleOptimal shape parameter for the solution of elastostatic problems with the RBF methoden
dc.typeresearch article*
dc.type.hasVersionAM*
dspace.entity.typePublication
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