Linearly implicit GARK schemes

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dc.contributor.authorSandu, Adrianen
dc.contributor.authorGuenther, Michaelen
dc.contributor.authorRoberts, Stevenen
dc.date.accessioned2022-02-27T04:16:51Zen
dc.date.available2022-02-27T04:16:51Zen
dc.date.issued2021-03-01en
dc.date.updated2022-02-27T04:16:49Zen
dc.description.abstractSystems driven by multiple physical processes are central to many areas of science and engineering. Time discretization of multiphysics systems is challenging, since different processes have different levels of stiffness and characteristic time scales. The multimethod approach discretizes each physical process with an appropriate numerical method; the methods are coupled appropriately such that the overall solution has the desired accuracy and stability properties. The authors developed the general-structure additive Runge–Kutta (GARK) framework, which constructs multimethods based on Runge–Kutta schemes. This paper constructs the new GARK-ROS/GARK-ROW families of multimethods based on linearly implicit Rosenbrock/Rosenbrock-W schemes. For ordinary differential equation models, we develop a general order condition theory for linearly implicit methods with any number of partitions, using exact or approximate Jacobians. We generalize the order condition theory to two-way partitioned index-1 differential-algebraic equations. Applications of the framework include decoupled linearly implicit, linearly implicit/explicit, and linearly implicit/implicit methods. Practical GARK-ROS and GARK-ROW schemes of order up to four are constructed.en
dc.description.versionPublished versionen
dc.format.extentPages 286-310en
dc.format.extent25 page(s)en
dc.format.mimetypeapplication/pdfen
dc.identifier.doihttps://doi.org/10.1016/j.apnum.2020.11.014en
dc.identifier.eissn1873-5460en
dc.identifier.issn0168-9274en
dc.identifier.orcidSandu, Adrian [0000-0002-5380-0103]en
dc.identifier.urihttp://hdl.handle.net/10919/108902en
dc.identifier.volume161en
dc.language.isoenen
dc.publisherElsevieren
dc.relation.urihttp://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000613718300020&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=930d57c9ac61a043676db62af60056c1en
dc.relation.urihttps://doi.org/10.1016/j.apnum.2020.11.014en
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectMathematics, Applieden
dc.subjectMathematicsen
dc.subjectMultiphysics systemsen
dc.subjectGARK methodsen
dc.subjectLinear implicitnessen
dc.subjectmath.NAen
dc.subjectmath.NAen
dc.subjectcs.NAen
dc.subject65L05, 65L06, 65L07, 65L20en
dc.subject0102 Applied Mathematicsen
dc.subject0103 Numerical and Computational Mathematicsen
dc.subject0802 Computation Theory and Mathematicsen
dc.subjectNumerical & Computational Mathematicsen
dc.titleLinearly implicit GARK schemesen
dc.title.serialApplied Numerical Mathematicsen
dc.typeArticle - Refereeden
dc.type.dcmitypeTexten
dc.type.otherArticleen
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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