An insight into RBF-FD approximations augmented with polynomials

Bayona Revilla, Víctor

Publication:
An insight into RBF-FD approximations augmented with polynomials

dc.affiliation.dpto	UC3M. Departamento de Matemáticas	es
dc.affiliation.grupoinv	UC3M. Grupo de Investigación: Métodos Numéricos y Aplicaciones	es
dc.contributor.author	Bayona Revilla, Víctor
dc.contributor.funder	Ministerio de Ciencia e Innovación (España)	es
dc.date.accessioned	2021-02-16T13:05:48Z
dc.date.available	2021-05-01T23:00:07Z
dc.date.issued	2019-05-01
dc.description.abstract	Radial basis function-generated finite differences (RBF-FD) based on the combination of polyharmonic splines (PHS) with high degree polynomials have recently emerged as a powerful and robust numerical approach for the local interpolation and derivative approximation of functions over scattered node layouts. Among the key features, (i) high orders of accuracy can be achieved without the need of selecting a shape parameter or the issues related to numerical ill-conditioning, and (ii) the harmful edge effects associated to the use of high order polynomials (better known as Runge's phenomenon) can be overcome by simply increasing the stencil size for a fixed polynomial degree. The present study complements our previous results, providing an analytical insight into RBF-FD approximations augmented with polynomials. It is based on a closed-form expression for the interpolant, which reveals the mechanisms underlying these features, including the role of polynomials and RBFs in the interpolant, the approximation error, and the behavior of the cardinal functions near boundaries. Numerical examples are included for illustration.	en
dc.format.extent	17
dc.identifier.bibliographicCitation	Bayona, V. (2019). An insight into RBF-FD approximations augmented with polynomials. Computers & Mathematics with Applications, 77(9), 2337–2353	en
dc.identifier.doi	https://doi.org/10.1016/j.camwa.2018.12.029
dc.identifier.issn	0898-1221
dc.identifier.publicationfirstpage	2337
dc.identifier.publicationissue	9
dc.identifier.publicationlastpage	2353
dc.identifier.publicationtitle	Computers & Mathematics with Applications	en
dc.identifier.publicationvolume	77
dc.identifier.uri	https://hdl.handle.net/10016/31939
dc.identifier.uxxi	AR/0000022547
dc.language.iso	eng
dc.publisher	Elsevier
dc.relation.projectID	Gobierno de España. FIS2016-77892-R
dc.rights	© 2019 Elsevier
dc.rights	Atribución-NoComercial-SinDerivadas 3.0 España
dc.rights.accessRights	open access
dc.rights.uri	http://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subject.eciencia	Matemáticas	es
dc.subject.other	RBF	en
dc.subject.other	RBF-FD	en
dc.subject.other	Polynomials	en
dc.subject.other	Interpolation	en
dc.subject.other	Meshfree	en
dc.subject.other	Runge's phenomenon	en
dc.subject.other	Radial basis functions	en
dc.subject.other	Finite-differences	en
dc.subject.other	Interpolation	en
dc.subject.other	Quadrature	en
dc.title	An insight into RBF-FD approximations augmented with polynomials	en
dc.type	research article	*
dc.type.hasVersion	AM	*
dspace.entity.type	Publication