Please use this identifier to cite or link to this item: https://hdl.handle.net/11147/8903
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dc.contributor.authorAksoylu, Burak-
dc.contributor.authorKaya, Adem-
dc.date.accessioned2020-07-18T08:34:06Z-
dc.date.available2020-07-18T08:34:06Z-
dc.date.issued2019-
dc.identifier.issn1070-5325-
dc.identifier.issn1099-1506-
dc.identifier.urihttps://doi.org/10.1002/nla.2267-
dc.identifier.urihttps://hdl.handle.net/11147/8903-
dc.description.abstractWe study smoothers for the multigrid method of the second kind arising from Fredholm integral equations. Our model problems use nonlocal governing operators that enforce local boundary conditions. For discretization, we utilize the Nystrom method with the trapezoidal rule. We find the eigenvalues of matrices associated to periodic, antiperiodic, and Dirichlet problems in terms of the nonlocality parameter and mesh size. Knowing explicitly the spectrum of the matrices enables us to analyze the behavior of smoothers. Although spectral analyses exist for finding effective smoothers for 1D elliptic model problems, to the best of our knowledge, a guiding spectral analysis is not available for smoothers of a multigrid of the second kind. We fill this gap in the literature. The Picard iteration has been the default smoother for a multigrid of the second kind. Jacobi-like methods have not been considered as viable options. We propose two strategies. The first one focuses on the most oscillatory mode and aims to damp it effectively. For this choice, we show that weighted-Jacobi relaxation is equivalent to the Picard iteration. The second strategy focuses on the set of oscillatory modes and aims to damp them as quickly as possible, simultaneously. Although the Picard iteration is an effective smoother for model nonlocal problems under consideration, we show that it is possible to find better than ones using the second strategy. We also shed some light on internal mechanism of the Picard iteration and provide an example where the Picard iteration cannot be used as a smoother.en_US
dc.language.isoenen_US
dc.publisherJohn Wiley and Sons Inc.en_US
dc.relation.ispartofNumerical Linear Algebra With Applicationsen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectLocal boundary conditionen_US
dc.subjectMultigrid of the second kinden_US
dc.subjectNonlocal operatoren_US
dc.subjectSmootheren_US
dc.subjectPicard iterationen_US
dc.titleOn smoothers for multigrid of the second kinden_US
dc.typeArticleen_US
dc.institutionauthorKaya, Adem-
dc.departmentİzmir Institute of Technology. Mathematicsen_US
dc.identifier.volume26en_US
dc.identifier.issue6en_US
dc.identifier.wosWOS:000496150100002en_US
dc.identifier.scopus2-s2.0-85074111622en_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.identifier.doi10.1002/nla.2267-
dc.relation.doi10.1002/nla.2267en_US
dc.coverage.doi10.1002/nla.2267en_US
dc.identifier.wosqualityQ1-
dc.identifier.scopusqualityQ1-
item.languageiso639-1en-
item.fulltextWith Fulltext-
item.cerifentitytypePublications-
item.openairecristypehttp://purl.org/coar/resource_type/c_18cf-
item.grantfulltextopen-
item.openairetypeArticle-
Appears in Collections:Mathematics / Matematik
Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection
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