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Optimal constant shape parameter for multiquadric based RBF-FD method

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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.authorKindelan Segura, Manuel
dc.contributor.funderComunidad de Madrides
dc.contributor.funderMinisterio de Ciencia e Innovación (España)es
dc.date.accessioned2022-12-02T10:14:00Z
dc.date.available2022-12-02T10:14:00Z
dc.date.issued2011-08-10
dc.description.abstractRadial basis functions (RBFs) have become a popular method for interpolation and solution of partial differential equations (PDEs). Many types of RBFs used in these problems contain a shape parameter, and there is much experimental evidence showing that accuracy strongly depends on the value of this shape parameter. In this paper, we focus on PDE problems solved with a multiquadric based RBF finite difference (RBF-FD) method. We propose an efficient algorithm to compute the optimal value of the shape parameter that minimizes the approximation error. The algorithm is based on analytical approximations to the local RBF-FD error derived in [1]. We show through several examples in 1D and 2D, both with structured and unstructured nodes, that very accurate solutions (compared to finite differences) can be achieved using the optimal value of the constant shape parameter.en
dc.description.sponsorshipThis work has been supported by Spanish MICINN grants FIS2010-18473, CSD2010-00011 and by Madrid Autonomous Region grant S2009-1597.en
dc.format.extent16
dc.identifier.bibliographicCitationBayona, V., Moscoso, M. & Kindelan, M. (2011). Optimal constant shape parameter for multiquadric based RBF-FD method. Journal of Computational Physics, 230(19), 7384-7399.en
dc.identifier.doihttps://doi.org/10.1016/j.jcp.2011.06.005
dc.identifier.issn0021-9991
dc.identifier.publicationfirstpage7384
dc.identifier.publicationissue19
dc.identifier.publicationlastpage7399
dc.identifier.publicationtitleJournal of Computational Physicsen
dc.identifier.publicationvolume230
dc.identifier.urihttps://hdl.handle.net/10016/36145
dc.identifier.uxxiAR/0000009380
dc.language.isoeng
dc.publisherElsevieren
dc.relation.projectIDGobierno de España. FIS2010-18473es
dc.relation.projectIDGobierno de España. CSD2010-00011es
dc.relation.projectIDComunidad de Madrid. S2009-1597es
dc.rights© 2011 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.otherMultiquadricen
dc.subject.otherMesh-freeen
dc.subject.otherShape parameteen
dc.titleOptimal constant shape parameter for multiquadric based RBF-FD methoden
dc.typeresearch article*
dc.type.hasVersionAM*
dspace.entity.typePublication
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