Structure-preserving reduced-order modeling of Korteweg-de Vries equation

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dc.authoridUzunca, Murat/0000-0001-5262-063X
dc.contributor.authorUzunca, Murat
dc.contributor.authorKarasozen, Bulent
dc.contributor.authorYildiz, Suleyman
dc.date.accessioned2025-03-23T19:40:56Z
dc.date.available2025-03-23T19:40:56Z
dc.date.issued2021
dc.departmentSinop Üniversitesi
dc.description.abstractComputationally efficient, structure-preserving reduced-order methods are developed for the Korteweg-de Vries (KdV) equations in Hamiltonian form. The semi-discretization in space by finite differences is based on the Hamiltonian structure. The resulting skew-gradient system of ordinary differential equations (ODES) is integrated with the linearly implicit Kahan's method, which preserves the Hamiltonian approximately. We have shown, using proper orthogonal decomposition (POD), the Hamiltonian structure of the full-order model (EOM) is preserved by the reduced-order model (ROM). The reduced model has the same linear-quadratic structure as the FOM. The quadratic nonlinear terms of the KdV equations are evaluated efficiently by the use of tensorial framework, clearly separating the offline-online cost of the FOMs and ROMs. The accuracy of the reduced solutions, preservation of the conserved quantities, and computational speed-up gained by ROMs are demonstrated for the one-dimensional single and coupled KdV equations, and two-dimensional Zakharov-Kuznetsov equation with soliton solutions. (C) 2021 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.
dc.identifier.doi10.1016/j.matcom.2021.03.042
dc.identifier.endpage211
dc.identifier.issn0378-4754
dc.identifier.issn1872-7166
dc.identifier.scopus2-s2.0-85104447301
dc.identifier.scopusqualityQ1
dc.identifier.startpage193
dc.identifier.urihttps://doi.org/10.1016/j.matcom.2021.03.042
dc.identifier.urihttps://hdl.handle.net/11486/6460
dc.identifier.volume188
dc.identifier.wosWOS:000658341000011
dc.identifier.wosqualityQ1
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherElsevier
dc.relation.ispartofMathematics and Computers in Simulation
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/openAccess
dc.snmzKA_WOS_20250323
dc.subjectHamiltonian systems
dc.subjectSolitary waves
dc.subjectKahan's method
dc.subjectEnergy preservation
dc.subjectModel order reduction
dc.subjectTensor algebra
dc.titleStructure-preserving reduced-order modeling of Korteweg-de Vries equation
dc.typeArticle

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