Linearly Implicit Multistep Methods for Time Integration

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dc.contributor.authorGlandon, Steven R.en
dc.contributor.authorNarayanamurthi, Maheshen
dc.contributor.authorSandu, Adrianen
dc.date.accessioned2023-02-28T14:22:06Zen
dc.date.available2023-02-28T14:22:06Zen
dc.date.issued2022-12en
dc.date.updated2023-02-25T22:40:33Zen
dc.description.abstractTime integration methods for solving initial value problems are an important component of many scientific and engineering simulations. Implicit time integrators are desirable for their stability properties, which significantly relax restrictions on timestep size. However, implicit methods require solutions to one or more systems of nonlinear equations at each timestep, which for large simulations can be prohibitively expensive. This paper introduces a new family of linearly implicit multistep methods (Limm), which only requires the solution of one linear system per timestep. Order conditions and stability theory for these methods are presented, as well as design and implementation considerations. Practical methods of order up to five are developed that have similar error coefficients, but improved stability regions, when compared to the widely used BDF methods. Numerical testing of a self-starting variable stepsize and variable order implementation of the new Limm methods shows measurable performance improvement over a similar BDF implementation.en
dc.description.versionAccepted versionen
dc.format.extentPages A3437-A3462en
dc.format.mimetypeapplication/pdfen
dc.identifier.doihttps://doi.org/10.1137/20M133748Xen
dc.identifier.eissn1095-7197en
dc.identifier.issn1064-8275en
dc.identifier.issue6en
dc.identifier.orcidSandu, Adrian [0000-0002-5380-0103]en
dc.identifier.urihttp://hdl.handle.net/10919/113998en
dc.identifier.volume44en
dc.language.isoenen
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)en
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.titleLinearly Implicit Multistep Methods for Time Integrationen
dc.title.serialSIAM Journal on Scientific Computingen
dc.typeArticle - Refereeden
dc.type.dcmitypeTexten
dc.type.otherJournal Articleen
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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