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dc.contributor.authorAksoylu, Burak
dc.contributor.authorKaya, Adem
dc.date.accessioned2020-01-15T12:08:43Z
dc.date.available2020-01-15T12:08:43Z
dc.date.issued2018-06en_US
dc.identifier.citationAksoylu, B., and Kaya, A. (2018). Conditioning and error analysis of nonlocal operators with local boundary conditions. Journal of Computational and Applied Mathematics, 335, 1-19. doi:10.1016/j.cam.2017.11.023en_US
dc.identifier.urihttps://doi.org/10.1016/j.cam.2017.11.023
dc.identifier.urihttps://hdl.handle.net/11147/7585
dc.description.abstractWe study the conditioning and error analysis of novel nonlocal operators in 1D with local boundary conditions. These operators are used, for instance, in peridynamics (PD) and nonlocal diffusion. The original PD operator uses nonlocal boundary conditions (BC). The novel operators agree with the original PD operator in the bulk of the domain and simultaneously enforce local periodic, antiperiodic, Neumann, or Dirichlet BC. We prove sharp bounds for their condition numbers in the parameter δ only, the size of nonlocality. We accomplish sharpness both rigorously and numerically. We also present an error analysis in which we use the Nyström method with the trapezoidal rule for discretization. Using the sharp bounds, we prove that the error bound scales like O(h2δ−2) and verify the bound numerically. The conditioning analysis of the original PD operator was studied by Aksoylu and Unlu (2014). For that operator, we had to resort to a discretized form because we did not have access to the eigenvalues of the analytic operator. Due to analytical construction, we now have direct access to the explicit expression of the eigenvalues of the novel operators in terms of δ. This gives us a big advantage in finding sharp bounds for the condition number without going to a discretized form and makes our analysis easily accessible. We prove that the novel operators have ill-conditioning indicated by δ−2 sharp bounds. For the original PD operator, we had proved the similar δ−2 ill-conditioning when the mesh size approaches 0. From the conditioning perspective, we conclude that the modification made to the original PD operator to obtain the novel operators that accommodate local BC is minor. Furthermore, the sharp δ−2 bounds shed light on the role of δ in nonlocal problems.en_US
dc.description.sponsorshipTUBITAK (MFAG 115F473); European Commission Marie Curie Career Integration 293978; United States Department of Energy (DOE) 1120-1120-99en_US
dc.language.isoengen_US
dc.publisherElsevieren_US
dc.relation.isversionof10.1016/j.cam.2017.11.023en_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectCondition numberen_US
dc.subjectError analysisen_US
dc.subjectIntegral operatoren_US
dc.subjectNonlocal diffusionen_US
dc.subjectPeridynamicsen_US
dc.subjectPreconditioningen_US
dc.titleConditioning and error analysis of nonlocal operators with local boundary conditionsen_US
dc.typearticleen_US
dc.contributor.institutionauthorKaya, Adem
dc.relation.journalJournal of Computational and Applied Mathematicsen_US
dc.contributor.departmentIzmir Institute of Technology. Mathematicsen_US
dc.identifier.volume335en_US
dc.identifier.startpage1en_US
dc.identifier.endpage19en_US
dc.identifier.wosWOS:000424722100001
dc.identifier.scopusSCOPUS:2-s2.0-85039751759
dc.relation.tubitakinfo:eu-repo/grantAgreement/TUBITAK/MFAG/115F473
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US


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