RBF Multiscale Collocation for Second Order Elliptic Boundary Value Problems

Handle URI:
http://hdl.handle.net/10754/599450
Title:
RBF Multiscale Collocation for Second Order Elliptic Boundary Value Problems
Authors:
Farrell, Patricio; Wendland, Holger
Abstract:
In this paper, we discuss multiscale radial basis function collocation methods for solving elliptic partial differential equations on bounded domains. The approximate solution is constructed in a multilevel fashion, each level using compactly supported radial basis functions of smaller scale on an increasingly fine mesh. On each level, standard symmetric collocation is employed. A convergence theory is given, which builds on recent theoretical advances for multiscale approximation using compactly supported radial basis functions. We are able to show that the convergence is linear in the number of levels. We also discuss the condition numbers of the arising systems and the effect of simple, diagonal preconditioners, now proving rigorously previous numerical observations. © 2013 Society for Industrial and Applied Mathematics.
Citation:
Farrell P, Wendland H (2013) RBF Multiscale Collocation for Second Order Elliptic Boundary Value Problems. SIAM J Numer Anal 51: 2403–2425. Available: http://dx.doi.org/10.1137/120898383.
Publisher:
Society for Industrial & Applied Mathematics (SIAM)
Journal:
SIAM Journal on Numerical Analysis
KAUST Grant Number:
KUK-C1-013-04
Issue Date:
Jan-2013
DOI:
10.1137/120898383
Type:
Article
ISSN:
0036-1429; 1095-7170
Sponsors:
This work was supported in part by award KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST).
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorFarrell, Patricioen
dc.contributor.authorWendland, Holgeren
dc.date.accessioned2016-02-28T05:51:22Zen
dc.date.available2016-02-28T05:51:22Zen
dc.date.issued2013-01en
dc.identifier.citationFarrell P, Wendland H (2013) RBF Multiscale Collocation for Second Order Elliptic Boundary Value Problems. SIAM J Numer Anal 51: 2403–2425. Available: http://dx.doi.org/10.1137/120898383.en
dc.identifier.issn0036-1429en
dc.identifier.issn1095-7170en
dc.identifier.doi10.1137/120898383en
dc.identifier.urihttp://hdl.handle.net/10754/599450en
dc.description.abstractIn this paper, we discuss multiscale radial basis function collocation methods for solving elliptic partial differential equations on bounded domains. The approximate solution is constructed in a multilevel fashion, each level using compactly supported radial basis functions of smaller scale on an increasingly fine mesh. On each level, standard symmetric collocation is employed. A convergence theory is given, which builds on recent theoretical advances for multiscale approximation using compactly supported radial basis functions. We are able to show that the convergence is linear in the number of levels. We also discuss the condition numbers of the arising systems and the effect of simple, diagonal preconditioners, now proving rigorously previous numerical observations. © 2013 Society for Industrial and Applied Mathematics.en
dc.description.sponsorshipThis work was supported in part by award KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST).en
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)en
dc.subjectMultiscale collocationen
dc.subjectPartial differential equationen
dc.subjectRadial basis functionsen
dc.titleRBF Multiscale Collocation for Second Order Elliptic Boundary Value Problemsen
dc.typeArticleen
dc.identifier.journalSIAM Journal on Numerical Analysisen
dc.contributor.institutionUniversity of Oxford, Oxford, United Kingdomen
dc.contributor.institutionUniversitat Bayreuth, Bayreuth, Germanyen
kaust.grant.numberKUK-C1-013-04en
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