Block preconditioners for linear systems arising from multiscale collocation with compactly supported RBFs

Handle URI:
http://hdl.handle.net/10754/597686
Title:
Block preconditioners for linear systems arising from multiscale collocation with compactly supported RBFs
Authors:
Farrell, Patricio; Pestana, Jennifer
Abstract:
© 2015John Wiley & Sons, Ltd. Symmetric collocation methods with RBFs allow approximation of the solution of a partial differential equation, even if the right-hand side is only known at scattered data points, without needing to generate a grid. However, the benefit of a guaranteed symmetric positive definite block system comes at a high computational cost. This cost can be alleviated somewhat by considering compactly supported RBFs and a multiscale technique. But the condition number and sparsity will still deteriorate with the number of data points. Therefore, we study certain block diagonal and triangular preconditioners. We investigate ideal preconditioners and determine the spectra of the preconditioned matrices before proposing more practical preconditioners based on a restricted additive Schwarz method with coarse grid correction. Numerical results verify the effectiveness of the preconditioners.
Citation:
Farrell P, Pestana J (2015) Block preconditioners for linear systems arising from multiscale collocation with compactly supported RBFs. Numerical Linear Algebra with Applications 22: 731–747. Available: http://dx.doi.org/10.1002/nla.1984.
Publisher:
Wiley-Blackwell
Journal:
Numerical Linear Algebra with Applications
KAUST Grant Number:
KUK- C1-013-04
Issue Date:
30-Apr-2015
DOI:
10.1002/nla.1984
Type:
Article
ISSN:
1070-5325
Sponsors:
We thank the referees for their helpful comments that improved the paper. This work was supported in part by award KUK- C1-013-04, made by King Abdullah University of Science and Technology (KAUST).
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Full metadata record

DC FieldValue Language
dc.contributor.authorFarrell, Patricioen
dc.contributor.authorPestana, Jenniferen
dc.date.accessioned2016-02-25T12:44:24Zen
dc.date.available2016-02-25T12:44:24Zen
dc.date.issued2015-04-30en
dc.identifier.citationFarrell P, Pestana J (2015) Block preconditioners for linear systems arising from multiscale collocation with compactly supported RBFs. Numerical Linear Algebra with Applications 22: 731–747. Available: http://dx.doi.org/10.1002/nla.1984.en
dc.identifier.issn1070-5325en
dc.identifier.doi10.1002/nla.1984en
dc.identifier.urihttp://hdl.handle.net/10754/597686en
dc.description.abstract© 2015John Wiley & Sons, Ltd. Symmetric collocation methods with RBFs allow approximation of the solution of a partial differential equation, even if the right-hand side is only known at scattered data points, without needing to generate a grid. However, the benefit of a guaranteed symmetric positive definite block system comes at a high computational cost. This cost can be alleviated somewhat by considering compactly supported RBFs and a multiscale technique. But the condition number and sparsity will still deteriorate with the number of data points. Therefore, we study certain block diagonal and triangular preconditioners. We investigate ideal preconditioners and determine the spectra of the preconditioned matrices before proposing more practical preconditioners based on a restricted additive Schwarz method with coarse grid correction. Numerical results verify the effectiveness of the preconditioners.en
dc.description.sponsorshipWe thank the referees for their helpful comments that improved the paper. This work was supported in part by award KUK- C1-013-04, made by King Abdullah University of Science and Technology (KAUST).en
dc.publisherWiley-Blackwellen
dc.subjectAdditive Schwarz methoden
dc.subjectKrylov subspace methodsen
dc.subjectMultiscale collocation, compactly supported RBFsen
dc.subjectPartial differential equationen
dc.subjectPreconditioningen
dc.titleBlock preconditioners for linear systems arising from multiscale collocation with compactly supported RBFsen
dc.typeArticleen
dc.identifier.journalNumerical Linear Algebra with Applicationsen
dc.contributor.institutionMathematical Institute; University of Oxford; Oxford OX2 6GG Englanden
dc.contributor.institutionSchool of Mathematics; The University of Manchester; Manchester M13 9PL Englanden
kaust.grant.numberKUK- C1-013-04en
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