Please use this identifier to cite or link to this item:
https://hdl.handle.net/20.500.11851/1652
Full metadata record
DC Field | Value | Language |
---|---|---|
dc.contributor.author | Aksoylu, Burak | - |
dc.contributor.author | Ünlü, Zuhal | - |
dc.date.accessioned | 2019-07-04T14:19:40Z | |
dc.date.available | 2019-07-04T14:19:40Z | |
dc.date.issued | 2014-03 | |
dc.identifier.citation | Aksoylu, B., & Unlu, Z. (2014). Conditioning analysis of nonlocal integral operators in fractional Sobolev spaces. SIAM Journal on Numerical Analysis, 52(2), 653-677. | en_US |
dc.identifier.issn | 0036-1429 | |
dc.identifier.uri | https://doi.org/10.1137/13092407X | - |
dc.identifier.uri | https://hdl.handle.net/20.500.11851/1652 | - |
dc.description.abstract | We study the conditioning of nonlocal integral operators with singular and integrable kernels in fractional Sobolev spaces. These operators are used, for instance, in peridynamics formulation and nonlocal diffusion. In one dimension (1D), we present sharp quantification of the extremal eigenvalues in all three parameters: size of nonlocality, mesh size, and regularity of the fractional Sobolev space. We accomplish sharpness both rigorously and numerically. For the minimal eigenvalue, we obtain sharpness analytically by using a nonlocal characterization of Sobolev spaces. We verify this estimate by exploiting the Toeplitz property of the stiffness matrix. However, the analytical approach fails to give sharp quantification of the maximal eigenvalue. Hence, in 1D, we take an algebraic approach by directly working with the stiffness matrix entries, which have complicated expressions due to all three parameters. We systematically characterize the nonzero entries and dramatically simplify their expressions by using convenient algebra. We establish the zero row sum property of the stiffness matrix and negativity of the off-diagonal entries. Eventually, we arrive at sharpness through the use of the Gerschgorin circle theorem. | en_US |
dc.language.iso | en | en_US |
dc.publisher | Society for Industrial and Applied Mathematics Publications | en_US |
dc.relation.ispartof | SIAM Journal on Numerical Analysis | en_US |
dc.rights | info:eu-repo/semantics/closedAccess | en_US |
dc.subject | Condition number | en_US |
dc.subject | Nonlocal operators | en_US |
dc.subject | Peridynamics | en_US |
dc.subject | Nonlocal diffusion | en_US |
dc.subject | Toeplitz matrix | en_US |
dc.subject | The Gerschgorin circle theorem | en_US |
dc.subject | Preconditioning | en_US |
dc.title | Conditioning analysis of nonlocal integral operators in fractional Sobolev spaces | en_US |
dc.type | Article | en_US |
dc.department | Faculties, Faculty of Science and Literature, Department of Mathematics | en_US |
dc.department | Fakülteler, Fen Edebiyat Fakültesi, Matematik Bölümü | tr_TR |
dc.identifier.volume | 52 | |
dc.identifier.issue | 2 | |
dc.identifier.startpage | 653 | |
dc.identifier.endpage | 677 | |
dc.relation.tubitak | info:eu-repo/grantAgreement/TÜBİTAK/TBAG/112T240 | en_US |
dc.relation.tubitak | info:eu-repo/grantAgreement/TÜBİTAK/MAG/112M891 | en_US |
dc.relation.ec | European Union Marie Curie Career Integration [293978] | en_US |
dc.authorid | 0000-0002-7244-3340 | - |
dc.identifier.wos | WOS:000335818000004 | en_US |
dc.identifier.scopus | 2-s2.0-84902581457 | en_US |
dc.institutionauthor | Aksoylu, Burak | - |
dc.identifier.doi | 10.1137/13092407X | - |
dc.authorwosid | C-4948-2016 | - |
dc.authorscopusid | 23979376500 | - |
dc.relation.publicationcategory | Makale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı | en_US |
dc.relation.international | National Science Foundation DMS [1016190] | en_US |
dc.identifier.scopusquality | Q1 | - |
item.cerifentitytype | Publications | - |
item.openairecristype | http://purl.org/coar/resource_type/c_18cf | - |
item.grantfulltext | none | - |
item.fulltext | No Fulltext | - |
item.languageiso639-1 | en | - |
item.openairetype | Article | - |
Appears in Collections: | Matematik Bölümü / Department of Mathematics Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection |
CORE Recommender
SCOPUSTM
Citations
29
checked on Sep 7, 2024
WEB OF SCIENCETM
Citations
30
checked on Sep 7, 2024
Page view(s)
28
checked on Sep 9, 2024
Google ScholarTM
Check
Altmetric
Items in GCRIS Repository are protected by copyright, with all rights reserved, unless otherwise indicated.