Global energy preserving model reduction for multi-symplectic PDEs

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dc.authoridKarasozen, Bulent/0000-0003-1037-5431
dc.authoridUzunca, Murat/0000-0001-5262-063X
dc.contributor.authorUzunca, Murat
dc.contributor.authorKarasozen, Bulent
dc.contributor.authorAydin, Ayhan
dc.date.accessioned2025-03-23T19:42:09Z
dc.date.available2025-03-23T19:42:09Z
dc.date.issued2023
dc.departmentSinop Üniversitesi
dc.description.abstractMany Hamiltonian systems can be recast in multi-symplectic form. We develop a reduced -order model (ROM) for multi-symplectic Hamiltonian partial differential equations (PDEs) that preserves the global energy. The full-order solutions are obtained by finite difference discretization in space and the global energy preserving average vector field (AVF) method. The ROM is constructed in the same way as the full-order model (FOM) applying proper orthogonal decomposition (POD) with the Galerkin projection. The reduced-order system has the same structure as the FOM, and preserves the discrete reduced global energy. Ap-plying the discrete empirical interpolation method (DEIM), the reduced-order solutions are computed efficiently in the online stage. A priori error bound is derived for the DEIM ap-proximation to the nonlinear Hamiltonian. The accuracy and computational efficiency of the ROMs are demonstrated for the Korteweg de Vries (KdV) equation, Zakharov-Kuznetzov (ZK) equation, and nonlinear Schrodinger (NLS) equation in multi-symplectic form. Preser-vation of the reduced energies shows that the reduced-order solutions ensure the long-term stability of the solutions.(c) 2022 Elsevier Inc. All rights reserved.
dc.identifier.doi10.1016/j.amc.2022.127483
dc.identifier.issn0096-3003
dc.identifier.issn1873-5649
dc.identifier.scopus2-s2.0-85136584284
dc.identifier.scopusqualityQ1
dc.identifier.urihttps://doi.org/10.1016/j.amc.2022.127483
dc.identifier.urihttps://hdl.handle.net/11486/6715
dc.identifier.volume436
dc.identifier.wosWOS:000862781400004
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.subjectmodel reduction
dc.subjectproper orthogonal decomposition
dc.subjectdiscrete empirical interpolation method
dc.subjectHamiltonian PDE
dc.subjectmulti-symplecticity
dc.subjectenergy preservation
dc.titleGlobal energy preserving model reduction for multi-symplectic PDEs
dc.typeArticle

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