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Comparison of moving least squares and RBF+poly for interpolation and derivative approximation

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dc.affiliation.dptoUC3M. Departamento de Matemáticases
dc.affiliation.grupoinvUC3M. Grupo de Investigación: Métodos Numéricos y Aplicacioneses
dc.contributor.authorBayona Revilla, Víctor
dc.contributor.funderMinisterio de Economía y Competitividad (España)es
dc.date.accessioned2021-02-18T09:39:31Z
dc.date.available2021-02-18T09:39:31Z
dc.date.issued2019-10-01
dc.description.abstractThe combination of polyharmonic splines (PHS) with high degree polynomials (PHS+poly) has recently opened new opportunities for radial basis function generated finite difference approximations. The PHS+poly formulation, which relies on a polynomial least squares fitting to enforce the local polynomial reproduction property, resembles somehow the so-called moving least squares (MLS) method. Although these two meshfree approaches are increasingly used nowadays, no direct comparison has been done yet. The present study aims to fill this gap, focusing on scattered data interpolation and derivative approximation. We first review the MLS approach and show that under some mild assumptions PHS+poly can be formulated analogously. Based on heuristic perspectives and numerical demonstrations, we then compare their performances in 1-D and 2-D. One key result is that, as previously found for PHS+poly, MLS can also overcome the edge oscillations (Runge's phenomenon) by simply increasing the stencil size for a fixed polynomial degree. This is, however, controlled by a weighted least squares fitting which fails for high polynomial degrees. Overall, PHS+poly is found to perform superior in terms of accuracy and robustnessen
dc.description.sponsorshipThe author would like to thank Bengt Fornberg, who took the time to carefully review this manuscript and make useful comments. This work was supported by Spanish MECD Grant FIS2016-77892-R.en
dc.format.extent30
dc.identifier.bibliographicCitationBayona, V. (2019). Comparison of Moving Least Squares and RBF+poly for Interpolation and Derivative Approximation. Journal of Scientific Computing, 81, pp. 486–512.en
dc.identifier.doihttps://doi.org/10.1007/s10915-019-01028-8
dc.identifier.issn0885-7474
dc.identifier.publicationfirstpage486
dc.identifier.publicationlastpage512
dc.identifier.publicationtitleJournal of Scientific Computingen
dc.identifier.publicationvolume81
dc.identifier.urihttps://hdl.handle.net/10016/31955
dc.identifier.uxxiAR/0000024343
dc.language.isoengen
dc.publisherSpringeren
dc.relation.projectIDGobierno de España. FIS2016-77892-Res
dc.rights© 2019, Springer Science Business Media, LLC, part of Springer Natureen
dc.rights.accessRightsopen access
dc.subject.ecienciaMatemáticases
dc.subject.otherMeshlessen
dc.subject.otherMoving least squaresen
dc.subject.otherRadial basis functionsen
dc.subject.otherRBF-FDen
dc.subject.otherPolyharmonic splinesen
dc.subject.otherPolynomial augmentationen
dc.subject.otherLocal polynomial reproductionen
dc.subject.otherInterpolationen
dc.subject.otherDerivative approximationen
dc.subject.otherRunge’s phenomenonen
dc.titleComparison of moving least squares and RBF+poly for interpolation and derivative approximationen
dc.typeresearch article*
dc.type.hasVersionAM*
dspace.entity.typePublication
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