Multirate linearly-implicit GARK schemes

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dc.contributor.authorGuenther, Michaelen
dc.contributor.authorSandu, Adrianen
dc.date.accessioned2022-02-27T04:01:57Zen
dc.date.available2022-02-27T04:01:57Zen
dc.date.issued2021-12-28en
dc.date.updated2022-02-27T04:01:55Zen
dc.description.abstractMany complex applications require the solution of initial-value problems where some components change fast, while others vary slowly. Multirate schemes apply different step sizes to resolve different components of the system, according to their dynamics, in order to achieve increased computational efficiency. The stiff components of the system, fast or slow, are best discretized with implicit base methods in order to ensure numerical stability. To this end, linearly implicit methods are particularly attractive as they solve only linear systems of equations at each step. This paper develops the Multirate GARK-ROS/ROW (MR-GARK-ROS/ROW) framework for linearly-implicit multirate time integration. The order conditions theory considers both exact and approximative Jacobians. The effectiveness of implicit multirate methods depends on the coupling between the slow and fast computations; an array of efficient coupling strategies and the resulting numerical schemes are analyzed. Multirate infinitesimal step linearly-implicit methods, that allow arbitrarily small micro-steps and offer extreme computational flexibility, are constructed. The new unifying framework includes existing multirate Rosenbrock(-W) methods as particular cases, and opens the possibility to develop new classes of highly effective linearly implicit multirate integrators.en
dc.description.versionAccepted versionen
dc.format.extent33 page(s)en
dc.format.mimetypeapplication/pdfen
dc.identifier.doihttps://doi.org/10.1007/s10543-021-00898-5en
dc.identifier.eissn1572-9125en
dc.identifier.issn0006-3835en
dc.identifier.orcidSandu, Adrian [0000-0002-5380-0103]en
dc.identifier.urihttp://hdl.handle.net/10919/108890en
dc.language.isoenen
dc.publisherSpringeren
dc.relation.urihttp://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000735337100001&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=930d57c9ac61a043676db62af60056c1en
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectComputer Science, Software Engineeringen
dc.subjectMathematics, Applieden
dc.subjectComputer Scienceen
dc.subjectMathematicsen
dc.subjectMultirate integrationen
dc.subjectGeneralized Additive Runge-Kutta (GARK) schemesen
dc.subjectLinear implicitnessen
dc.subjectGARK ROSen
dc.subjectROW methodsen
dc.subjectStabilityen
dc.subjectRUNGE-KUTTA SCHEMESen
dc.subjectDIFFERENTIAL-EQUATIONSen
dc.subjectNUMERICAL-SOLUTIONen
dc.subjectINTEGRATIONen
dc.subjectSTABILITYen
dc.subjectSYSTEMSen
dc.subject0102 Applied Mathematicsen
dc.subject0103 Numerical and Computational Mathematicsen
dc.subjectNumerical & Computational Mathematicsen
dc.titleMultirate linearly-implicit GARK schemesen
dc.title.serialBIT Numerical Mathematicsen
dc.typeArticleen
dc.type.dcmitypeTexten
dc.type.otherArticleen
dc.type.otherEarly Accessen
dc.type.otherJournalen
pubs.organisational-group/Virginia Techen
pubs.organisational-group/Virginia Tech/Engineeringen
pubs.organisational-group/Virginia Tech/Engineering/Computer Scienceen
pubs.organisational-group/Virginia Tech/All T&R Facultyen
pubs.organisational-group/Virginia Tech/Engineering/COE T&R Facultyen

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