On the role of polynomials in RBF-FD approximations: II. numerical solution of elliptic PDEs

Bayona Revilla, Víctor; Flyer, Natasha; Fornberg, Bengt; Barnett, Gregory A.

Publication:
On the role of polynomials in RBF-FD approximations: II. numerical solution of elliptic PDEs

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.author	Flyer, Natasha
dc.contributor.author	Fornberg, Bengt
dc.contributor.author	Barnett, Gregory A.
dc.date.accessioned	2021-02-16T12:11:26Z
dc.date.available	2021-02-16T12:11:26Z
dc.date.issued	2017-03-01
dc.description.abstract	RBF-generated finite differences (RBF-FD) have in the last decade emerged as a very powerful and flexible numerical approach for solving a wide range of PDEs. We find in the present study that combining polyharmonic splines (PHS) with multivariate polynomials offers an outstanding combination of simplicity, accuracy, and geometric flexibility when solving elliptic equations in irregular (or regular) regions. In particular, the drawbacks on accuracy and stability due to Runge's phenomenon are overcome once the RBF stencils exceed a certain size due to an underlying minimization property. Test problems include the classical 2-D driven cavity, and also a 3-D global electric circuit problem with the earth's irregular topography as its bottom boundary. The results we find are fully consistent with previous results for data interpolation.	en
dc.description.sponsorship	The National Center for Atmospheric Research is sponsored by the NSF. Victor Bayona was a post-doctoral fellow funded by the Advanced Study Program at the National Center for Atmospheric Research during the majority of this work.	en
dc.format.extent	17
dc.identifier.bibliographicCitation	Bayona, V., Flyer, N., Fornberg, B., Barnett, G. A. (2017). On the role of polynomials in RBF-FD approximations: II. Numerical solution of elliptic PDEs. Journal of Computational Physics, 332, 257–273.	en
dc.identifier.doi	https://doi.org/10.1016/j.jcp.2016.12.008
dc.identifier.issn	0021-9991
dc.identifier.publicationfirstpage	257
dc.identifier.publicationlastpage	273
dc.identifier.publicationtitle	Journal of Computational Physics	en
dc.identifier.publicationvolume	332
dc.identifier.uri	https://hdl.handle.net/10016/31935
dc.identifier.uxxi	AR/0000022054
dc.language.iso	eng
dc.publisher	Elsevier
dc.rights	© 2017 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	Elliptic Pdes	en
dc.subject.other	RBF-FD	en
dc.subject.other	Polynomials	en
dc.subject.other	Polyharmonic splines	en
dc.subject.other	Runge's phenomenon	en
dc.subject.other	Meshless	en
dc.title	On the role of polynomials in RBF-FD approximations: II. numerical solution of elliptic PDEs	en
dc.type	research article	*
dc.type.hasVersion	AM	*
dspace.entity.type	Publication