Energy preserving model order reduction of the nonlinear Schrodinger equation

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dc.authoridUzunca, Murat/0000-0001-5262-063X
dc.contributor.authorKarasozen, Bulent
dc.contributor.authorUzunca, Murat
dc.date.accessioned2025-03-23T19:44:32Z
dc.date.available2025-03-23T19:44:32Z
dc.date.issued2018
dc.departmentSinop Üniversitesi
dc.description3rd Workshop on Model Reduction of Complex Dynamical Systems (MODRED) -- JAN 11-13, 2017 -- Univ Southern Denmark, Odense, DENMARK
dc.description.abstractAn energy preserving reduced order model is developed for two dimensional nonlinear Schrodinger equation (NLSE) with plane wave solutions and with an external potential. The NLSE is discretized in space by the symmetric interior penalty discontinuous Galerkin (SIPG) method. The resulting system of Hamiltonian ordinary differential equations are integrated in time by the energy preserving average vector field (AVF) method. The mass and energy preserving reduced order model (ROM) is constructed by proper orthogonal decomposition (POD) Galerkin projection. The nonlinearities are computed for the ROM efficiently by discrete empirical interpolation method (DEIM) and dynamic mode decomposition (DMD). Preservation of the semi-discrete energy and mass are shown for the full order model (FOM) and for the ROM which ensures the long term stability of the solutions. Numerical simulations illustrate the preservation of the energy and mass in the reduced order model for the two dimensional NLSE with and without the external potential. The POD-DMD makes a remarkable improvement in computational speed-up over the POD-DEIM. Both methods approximate accurately the FOM, whereas POD-DEIM is more accurate than the POD-DMD.
dc.description.sponsorshipEuropean Model Reduct Network,Univ Southern Denmark, Dept Math & Comp Sci
dc.identifier.doi10.1007/s10444-018-9593-9
dc.identifier.endpage1796
dc.identifier.issn1019-7168
dc.identifier.issn1572-9044
dc.identifier.issue6
dc.identifier.scopus2-s2.0-85041918264
dc.identifier.scopusqualityQ2
dc.identifier.startpage1769
dc.identifier.urihttps://doi.org/10.1007/s10444-018-9593-9
dc.identifier.urihttps://hdl.handle.net/11486/6959
dc.identifier.volume44
dc.identifier.wosWOS:000451251900005
dc.identifier.wosqualityQ1
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherSpringer
dc.relation.ispartofAdvances in Computational Mathematics
dc.relation.publicationcategoryKonferans Öğesi - Uluslararası - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/openAccess
dc.snmzKA_WOS_20250323
dc.subjectNonlinear Schrodinger equation
dc.subjectDiscontinuous Galerkin method
dc.subjectAverage vector field method
dc.subjectProper orthogonal decomposition
dc.subjectDiscrete empirical interpolation method
dc.subjectDynamic mode decomposition
dc.titleEnergy preserving model order reduction of the nonlinear Schrodinger equation
dc.typeConference Object

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