A state space error estimate for pod-deim nonlinear model reduction

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dc.contributorVirginia Techen
dc.contributor.authorChaturantabut, Saifonen
dc.contributor.authorSorensen, D. C.en
dc.contributor.departmentMathematicsen
dc.date.accessed2014-05-27en
dc.date.accessioned2014-05-28T18:35:06Zen
dc.date.available2014-05-28T18:35:06Zen
dc.date.issued2012en
dc.description.abstractThis paper derives state space error bounds for the solutions of reduced systems constructed using proper orthogonal decomposition (POD) together with the discrete empirical interpolation method (DEIM) recently developed for nonlinear dynamical systems [SIAM J. Sci. Comput., 32 (2010), pp. 2737-2764]. The resulting error estimates are shown to be proportional to the sums of the singular values corresponding to neglected POD basis vectors both in Galerkin projection of the reduced system and in the DEIM approximation of the nonlinear term. The analysis is particularly relevant to ODE systems arising from spatial discretizations of parabolic PDEs. The derivation clearly identifies where the parabolicity is crucial. It also explains how the DEIM approximation error involving the nonlinear term comes into play.en
dc.description.sponsorshipNSF CCF-1017401en
dc.description.sponsorshipAFOSRF FA9550-09-1-0225en
dc.format.mimetypeapplication/pdfen
dc.identifier.citationChaturantabut, S.; Sorensen, D. C., "A state space error estimate for pod-deim nonlinear model reduction," SIAM J. Numer. Anal., 50(1), 46-63, (2012). DOI: 10.1137/110822724en
dc.identifier.doihttps://doi.org/10.1137/110822724en
dc.identifier.issn0036-1429en
dc.identifier.urihttp://hdl.handle.net/10919/48148en
dc.identifier.urlhttp://epubs.siam.org/doi/abs/10.1137/110822724en
dc.language.isoenen
dc.publisherSiam Publicationsen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectnonlinear model reductionen
dc.subjectproper orthogonal decompositionen
dc.subjectempiricalen
dc.subjectinterpolation methodsen
dc.subjectnonlinear partial differential equationsen
dc.subjectproper orthogonal decompositionen
dc.subjectpartial-differential-equationsen
dc.subjectempirical interpolation methoden
dc.subjectreduced-order modelsen
dc.subjectdynamical-systemsen
dc.subjectboundsen
dc.subjectadaptivityen
dc.subjectoperatorsen
dc.subjectmathematics, applieden
dc.titleA state space error estimate for pod-deim nonlinear model reductionen
dc.title.serialSiam Journal on Numerical Analysisen
dc.typeArticle - Refereeden
dc.type.dcmitypeTexten

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