Partitioned exponential methods for coupled multiphysics systems

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dc.contributor.authorNarayanamurthi, Maheshen
dc.contributor.authorSandu, Adrianen
dc.date.accessioned2022-02-27T04:14:46Zen
dc.date.available2022-02-27T04:14:46Zen
dc.date.issued2021-03-01en
dc.date.updated2022-02-27T04:14:44Zen
dc.description.abstractMultiphysics problems involving two or more coupled physical phenomena are ubiquitous in science and engineering. This work develops a new partitioned exponential approach for the time integration of multiphysics problems. After a possible semi-discretization in space, the class of problems under consideration is modeled by a system of ordinary differential equations where the right-hand side is a summation of two component functions, each corresponding to a given set of physical processes. The partitioned-exponential methods proposed herein evolve each component of the system via an exponential integrator, and information between partitions is exchanged via coupling terms. The traditional approach to constructing exponential methods, based on the variation-of-constants formula, is not directly applicable to partitioned systems. Rather, our approach to developing new partitioned-exponential families is based on a general-structure additive formulation of the schemes. Two method formulations are considered, one based on a linear-nonlinear splitting of the right hand component functions, and another based on approximate Jacobians. The paper develops classical (non-stiff) order conditions theory for partitioned exponential schemes based on particular families of T-trees and B-series theory. Several practical methods of third order are constructed that extend the Rosenbrock-type and EPIRK families of exponential integrators. Several implementation optimizations specific to the application of these methods to reaction-diffusion systems are also discussed. Numerical experiments reveal that the new partitioned-exponential methods can perform better than traditional unpartitioned exponential methods on some problems.en
dc.description.notesFixed a definition and other minor typos. Results remain unchangeden
dc.description.versionAccepted versionen
dc.format.extentPages 178-207en
dc.format.extent30 page(s)en
dc.format.mimetypeapplication/pdfen
dc.identifier.doihttps://doi.org/10.1016/j.apnum.2020.10.020en
dc.identifier.eissn1873-5460en
dc.identifier.issn0168-9274en
dc.identifier.orcidSandu, Adrian [0000-0002-5380-0103]en
dc.identifier.urihttp://hdl.handle.net/10919/108900en
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:000613718300014&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=930d57c9ac61a043676db62af60056c1en
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectMathematics, Applieden
dc.subjectMathematicsen
dc.subjectMultiphysics systemsen
dc.subjectExponential time integrationen
dc.subjectButcher seriesen
dc.subjectPartitioned methodsen
dc.subjectmath.NAen
dc.subjectcs.CEen
dc.subjectcs.NAen
dc.subject65L05, 65L04, 65F60, 65M22, 65Y05en
dc.subject0102 Applied Mathematicsen
dc.subject0103 Numerical and Computational Mathematicsen
dc.subject0802 Computation Theory and Mathematicsen
dc.subjectNumerical & Computational Mathematicsen
dc.titlePartitioned exponential methods for coupled multiphysics systemsen
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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