Reduced order modelling of nonlinear cross-diffusion systems

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dc.authoridMulayim, Gulden/0000-0001-8952-7658
dc.authoridUzunca, Murat/0000-0001-5262-063X
dc.contributor.authorKarasozen, Bulent
dc.contributor.authorMulayim, Gulden
dc.contributor.authorUzunca, Murat
dc.contributor.authorYildiz, Suleyman
dc.date.accessioned2025-03-23T19:42:10Z
dc.date.available2025-03-23T19:42:10Z
dc.date.issued2021
dc.departmentSinop Üniversitesi
dc.description.abstractIn this work, we present reduced-order models (ROMs) for a nonlinear cross-diffusion problem from population dynamics, the Shigesada-Kawasaki-Teramoto (SKT) equation with Lotka-Volterra kinetics. The formation of the patterns of the SKT equation consists of a fast transient phase and a long stationary phase. Reduced order solutions are computed by separating the time into two time-intervals. In numerical experiments, we show for one- and two-dimensional SKT equations with pattern formation, the reduced-order solutions obtained in the time-windowed form, i.e., principal decomposition framework, are more accurate than the global proper orthogonal decomposition solutions obtained in the whole time interval. The finite-difference discretization of the SKT equation in space results in a system of linear-quadratic ordinary differential equations. The ROMs have the same linear-quadratic structure as the full order model. Using the linear-quadratic structure of the ROMs, the computation of the reduced-order solutions is further accelerated by the use of proper orthogonal decomposition in a tensorial framework so that the computations in the reduced system are independent of the full-order solutions. Furthermore, the prediction capabilities of the ROMs are illustrated for one- and two-dimensional patterns. Finally, we show that the entropy is decreasing by the reduced solutions, which is important for the global existence of solutions to the nonlinear cross-diffusion equations such as the SKT equation. (C) 2021 Elsevier Inc. All rights reserved.
dc.identifier.doi10.1016/j.amc.2021.126058
dc.identifier.issn0096-3003
dc.identifier.issn1873-5649
dc.identifier.scopus2-s2.0-85101303620
dc.identifier.scopusqualityQ1
dc.identifier.urihttps://doi.org/10.1016/j.amc.2021.126058
dc.identifier.urihttps://hdl.handle.net/11486/6717
dc.identifier.volume401
dc.identifier.wosWOS:000627400800007
dc.identifier.wosqualityQ1
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherElsevier Science Inc
dc.relation.ispartofApplied Mathematics and Computation
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/openAccess
dc.snmzKA_WOS_20250323
dc.subjectPattern formation
dc.subjectFinite differences
dc.subjectEntropy
dc.subjectProper orthogonal decomposition
dc.subjectPrincipal interval decomposition
dc.subjectTensor algebra
dc.titleReduced order modelling of nonlinear cross-diffusion systems
dc.typeArticle

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