Reduced order optimal control of the convective FitzHugh-Nagumo equations

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dc.authoridUzunca, Murat/0000-0001-5262-063X
dc.contributor.authorKarasozen, Bulent
dc.contributor.authorUzunca, Murat
dc.contributor.authorKucukseyhan, Tugba
dc.date.accessioned2025-03-23T19:41:54Z
dc.date.available2025-03-23T19:41:54Z
dc.date.issued2020
dc.departmentSinop Üniversitesi
dc.description.abstractIn this paper, we compare three model order reduction methods: the proper orthogonal decomposition (POD), discrete empirical interpolation method (DEIM) and dynamic mode decomposition (DMD) for the optimal control of the convective FitzHugh-Nagumo (FHN) equations. The convective FHN equations consist of the semi-linear activator and the linear inhibitor equations, modeling blood coagulation in moving excitable media. The semilinear activator equation leads to a non-convex optimal control problem (OCP). The most commonly used method in reduced optimal control is POD. We use DEIM and DMD to approximate efficiently the nonlinear terms in reduced order models. We compare the accuracy and computational times of three reduced-order optimal control solutions with the full order discontinuous Galerkin finite element solution of the convection dominated FHN equations with terminal controls. Numerical results show that POD is the most accurate whereas POD-DMD is the fastest. (C) 2019 Elsevier Ltd. All rights reserved.
dc.identifier.doi10.1016/j.camwa.2019.08.009
dc.identifier.endpage995
dc.identifier.issn0898-1221
dc.identifier.issn1873-7668
dc.identifier.issue4
dc.identifier.scopus2-s2.0-85070873703
dc.identifier.scopusqualityQ1
dc.identifier.startpage982
dc.identifier.urihttps://doi.org/10.1016/j.camwa.2019.08.009
dc.identifier.urihttps://hdl.handle.net/11486/6677
dc.identifier.volume79
dc.identifier.wosWOS:000514024500006
dc.identifier.wosqualityQ1
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherPergamon-Elsevier Science Ltd
dc.relation.ispartofComputers & Mathematics With Applications
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/openAccess
dc.snmzKA_WOS_20250323
dc.subjectFitzHugh-Nagumo equation
dc.subjectOptimal control
dc.subjectDiscontinuous Galerkin method
dc.subjectProper orthogonal decomposition
dc.subjectDiscrete empirical interpolation
dc.subjectDynamic mode decomposition
dc.titleReduced order optimal control of the convective FitzHugh-Nagumo equations
dc.typeArticle

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