Comparison of POD reduced order strategies for the nonlinear 2D shallow water equations

dc.contributor.authorStefanescu, Razvanen
dc.contributor.authorSandu, Adrianen
dc.contributor.authorNavon, I. M.en
dc.contributor.departmentComputer Scienceen
dc.date.accessioned2017-03-06T18:40:23Zen
dc.date.available2017-03-06T18:40:23Zen
dc.date.issued2014-11-20en
dc.description.abstractThis paper introduces tensorial calculus techniques in the framework of Proper Orthogonal Decomposition (POD) to reduce the computational complexity of the reduced nonlinear terms. The resulting method, named tensorial POD, can be applied to polynomial nonlinearities of any degree p. Such nonlinear terms have an on-line complexity of O(k<sup>p+1</sup>), where k is the dimension of POD basis, and therefore is independent of full space dimension. However it is efficient only for quadratic nonlinear terms since for higher nonlinearities standard POD proves to be less time consuming once the POD basis dimension k is increased. Numerical experiments are carried out with a two dimensional shallow water equation (SWE) test problem to compare the performance of tensorial POD, standard POD, and POD/Discrete Empirical Interpolation Method (DEIM). Numerical results show that tensorial POD decreases by 76× times the computational cost of the on-line stage of standard POD for configurations using more than 300, 000 model variables. The tensorial POD SWE model was only 2 − 8× slower than the POD/DEIM SWE model but the implementation effort is considerably increased. Tensorial calculus was again employed to construct a new algorithm allowing POD/DEIM shallow water equation model to compute its off-line stage faster than the standard and tensorial POD approaches.en
dc.description.versionPublished versionen
dc.format.extent497 - 521 (25) page(s)en
dc.identifier.doihttps://doi.org/10.1002/fld.3946en
dc.identifier.issn0271-2091en
dc.identifier.issue8en
dc.identifier.urihttp://hdl.handle.net/10919/75280en
dc.identifier.volume76en
dc.language.isoenen
dc.publisherWiley-Blackwellen
dc.relation.urihttp://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000342793300002&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=930d57c9ac61a043676db62af60056c1en
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectTechnologyen
dc.subjectComputer Science, Interdisciplinary Applicationsen
dc.subjectMathematics, Interdisciplinary Applicationsen
dc.subjectMechanicsen
dc.subjectPhysics, Fluids & Plasmasen
dc.subjectComputer Scienceen
dc.subjectMathematicsen
dc.subjectPhysicsen
dc.subjecttensorial proper orthogonal decomposition (POD)en
dc.subjectdiscrete empirical interpolation method (DEIM)en
dc.subjectreduced order models (ROMs)en
dc.subjectshallow water equations (SWE)en
dc.subjectfinite difference methodsen
dc.subjectalternating direction implicit methods (ADI)en
dc.subjectPROPER ORTHOGONAL DECOMPOSITIONen
dc.subjectPARTIAL-DIFFERENTIAL-EQUATIONSen
dc.subjectDISCRETE EMPIRICAL INTERPOLATIONen
dc.subjectMODEL-REDUCTIONen
dc.subjectCOHERENT STRUCTURESen
dc.subjectDIFFUSION EQUATIONSen
dc.subjectGALERKIN PROJECTIONen
dc.subjectPARTIAL-REALIZATIONen
dc.subjectLYAPUNOV EQUATIONSen
dc.subjectFLUID-DYNAMICSen
dc.titleComparison of POD reduced order strategies for the nonlinear 2D shallow water equationsen
dc.title.serialInternational Journal For Numerical Methods in Fluidsen
dc.typeArticle - Refereeden
dc.type.dcmitypeTexten
pubs.organisational-group/Virginia Techen
pubs.organisational-group/Virginia Tech/All T&R Facultyen
pubs.organisational-group/Virginia Tech/Engineeringen
pubs.organisational-group/Virginia Tech/Engineering/COE T&R Facultyen
pubs.organisational-group/Virginia Tech/Engineering/Computer Scienceen

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