Efficient approximation of Sparse Jacobians for time-implicit reduced order models

dc.contributor.authorStefanescu, Razvanen
dc.contributor.authorSandu, Adrianen
dc.contributor.departmentComputer Scienceen
dc.date.accessioned2017-03-06T18:34:57Zen
dc.date.available2017-03-06T18:34:57Zen
dc.date.issued2017-01-20en
dc.description.abstractThis paper introduces a sparse matrix discrete interpolation method to effectively compute matrix approximations in the reduced order modeling framework. The sparse algorithm developed herein relies on the discrete empirical interpolation method and uses only samples of the nonzero entries of the matrix series. The proposed approach can approximate very large matrices, unlike the current matrix discrete empirical interpolation method which is limited by its large computational memory requirements. The empirical interpolation indexes obtained by the sparse algorithm slightly differ from the ones computed by the matrix discrete empirical interpolation method as a consequence of the singular vectors round-off errors introduced by the economy or full singular value decomposition (SVD) algorithms when applied to the full matrix snapshots. When appropriately padded with zeros the economy SVD factorization of the nonzero elements of the snapshots matrix is a valid economy SVD for the full snapshots matrix. Numerical experiments are performed with the 1D Burgers and 2D Shallow Water Equations test problems where the quadratic reduced nonlinearities are computed via tensorial calculus. The sparse matrix approximation strategy is compared against five existing methods for computing reduced Jacobians: a) matrix discrete empirical interpolation method, b) discrete empirical interpolation method, c) tensorial calculus, d) full Jacobian projection onto the reduced basis subspace, and e) directional derivatives of the model along the reduced basis functions. The sparse matrix method outperforms all other algorithms. The use of traditional matrix discrete empirical interpolation method is not possible for very large instances due to its excessive memory requirements.en
dc.description.versionPublished versionen
dc.format.extent175 - 204 (30) page(s)en
dc.format.mimetypeapplication/pdfen
dc.identifier.doihttps://doi.org/10.1002/fld.4260en
dc.identifier.issn0271-2091en
dc.identifier.issue2en
dc.identifier.urihttp://hdl.handle.net/10919/75268en
dc.identifier.volume83en
dc.language.isoenen
dc.publisherWiley-Blackwellen
dc.relation.urihttp://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000390568700004&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.subjectPODen
dc.subjectDEIMen
dc.subjectimplicit reduced order modelingen
dc.subjectshallow water equationsen
dc.subjectfinite differenceen
dc.subjectPROPER ORTHOGONAL DECOMPOSITIONen
dc.subjectSHALLOW-WATER EQUATIONSen
dc.subjectPARTIAL-DIFFERENTIAL-EQUATIONSen
dc.subjectVARIATIONAL DATA ASSIMILATIONen
dc.subjectDISCRETE EMPIRICAL INTERPOLATIONen
dc.subjectPOSTERIORI ERROR ESTIMATIONen
dc.subjectNONLINEAR MODELen
dc.subjectCOHERENT STRUCTURESen
dc.subjectPARTIAL-REALIZATIONen
dc.subjectLYAPUNOV EQUATIONSen
dc.titleEfficient approximation of Sparse Jacobians for time-implicit reduced order modelsen
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

Files

Original bundle
Now showing 1 - 1 of 1
Loading...
Thumbnail Image
Name:
1409.5506v3.pdf
Size:
924.78 KB
Format:
Adobe Portable Document Format
Description:
Submitted Version
License bundle
Now showing 1 - 1 of 1
Name:
VTUL_Distribution_License_2016_05_09.pdf
Size:
18.09 KB
Format:
Adobe Portable Document Format
Description: