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dc.contributor.authorAnderson, Joel
dc.contributor.authorHarrison, Robert J.
dc.contributor.authorSekino, Hideo
dc.contributor.authorSundahl, Bryan
dc.contributor.authorBeylkin, Gregory
dc.contributor.authorFann, George I.
dc.contributor.authorJensen, Stig Rune
dc.contributor.authorSagert, Irina
dc.date.accessioned2020-01-08T12:39:40Z
dc.date.available2020-01-08T12:39:40Z
dc.date.issued2019-07-24
dc.description.abstractWe construct high-order derivative operators for smooth functions represented via discontinuous multiwavelet bases. The need for such operators arises in order to avoid artifacts when computing functionals involving high-order derivatives of solutions of integral equations. Previously high-order derivatives had to be formed by repeated application of a first-derivative operator that, while uniquely defined, has a spectral norm that grows quadratically with polynomial order and, hence, greatly amplifies numerical noise (truncation error) in the multiwavelet computation. The new constructions proceed via least-squares projection onto smooth bases and provide substantially improved numerical properties as well as permitting direct construction of high-order derivatives. We employ either b-splines or bandlimited exponentials as the intermediate smooth basis, with the former maintaining the concept of approximation order while the latter preserves the pure imaginary spectrum of the first-derivative operator and provides more direct control over the bandlimit and accuracy of computation. We demonstrate the properties of these new operators via several numerical tests as well as application to a problem in nuclear physics.en_US
dc.identifier.citationAnderson, Harrison, Sekino, Sundahl, Beylkin, Fann, Jensen SR, Sagert. On derivatives of smooth functions represented in multiwavelet bases. Journal of Computational Physics: X. 2019;4:100033en_US
dc.identifier.cristinIDFRIDAID 1717045
dc.identifier.doi10.1016/j.jcpx.2019.100033
dc.identifier.issn2590-0552
dc.identifier.urihttps://hdl.handle.net/10037/17033
dc.language.isoengen_US
dc.publisherElsevieren_US
dc.relation.journalJournal of Computational Physics: X
dc.relation.projectIDNorges forskningsråd: 262695en_US
dc.relation.projectIDinfo:eu-repo/grantAgreement/RCN/SFF/262695/Norway/Hylleraas Centre for Quantum Molecular Sciences//en_US
dc.rights.accessRightsopenAccessen_US
dc.rights.holderCopyright 2019 The Author(s)en_US
dc.subjectVDP::Mathematics and natural science: 400en_US
dc.subjectVDP::Matematikk og Naturvitenskap: 400en_US
dc.titleOn derivatives of smooth functions represented in multiwavelet basesen_US
dc.type.versionpublishedVersionen_US
dc.typeJournal articleen_US
dc.typeTidsskriftartikkelen_US
dc.typePeer revieweden_US


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