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Performance assessment of energy-preserving, adaptive time-step variational integrators

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dc.contributor.authorSharma, Harshen
dc.contributor.authorBorggaard, Jeffrey T.en
dc.contributor.authorPatil, Mayureshen
dc.contributor.authorWoolsey, Craig A.en
dc.date.accessioned2023-12-21T20:25:18Zen
dc.date.available2023-12-21T20:25:18Zen
dc.date.issued2022-11en
dc.description.abstractA fixed time-step variational integrator cannot preserve momentum, energy, and symplectic form simultaneously for nonintegrable systems. This barrier can be overcome by treating time as a discrete dynamic variable and deriving adaptive time-step variational integrators that conserve the energy in addition to being symplectic and momentum-preserving. Their utility, however, is still an open question due to the numerical difficulties associated with solving the discrete governing equations. In this work, we investigate the numerical performance of energy-preserving, adaptive time-step variational integrators. First, we compare the time adaptation and energy performance of the energy-preserving adaptive algorithm with the adaptive variational integrator for Kepler's two-body problem. Second, we apply tools from Lagrangian backward error analysis to investigate numerical stability of the energy-preserving adaptive algorithm. Finally, we consider a simple mechanical system example to illustrate the backward stability of this energy-preserving, adaptive time-step variational integrator.en
dc.description.versionSubmitted versionen
dc.format.extent17 page(s)en
dc.format.mimetypeapplication/pdfen
dc.identifierARTN 106646 (Article number)en
dc.identifier.doihttps://doi.org/10.1016/j.cnsns.2022.106646en
dc.identifier.eissn1878-7274en
dc.identifier.issn1007-5704en
dc.identifier.orcidWoolsey, Craig [0000-0003-3483-7135]en
dc.identifier.orcidBorggaard, Jeffrey [0000-0002-4023-7841]en
dc.identifier.urihttps://hdl.handle.net/10919/117260en
dc.identifier.volume114en
dc.language.isoenen
dc.publisherElsevieren
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectEnergy-preserving integratorsen
dc.subjectVariational integratorsen
dc.subjectAdaptive time-step integratorsen
dc.subjectBackward stabilityen
dc.titlePerformance assessment of energy-preserving, adaptive time-step variational integratorsen
dc.title.serialCommunications in Nonlinear Science and Numerical Simulationen
dc.typeArticle - Refereeden
dc.type.dcmitypeTexten
dc.type.otherArticleen
dc.type.otherJournalen
pubs.organisational-group/Virginia Techen
pubs.organisational-group/Virginia Tech/Scienceen
pubs.organisational-group/Virginia Tech/Science/Mathematicsen
pubs.organisational-group/Virginia Tech/Engineeringen
pubs.organisational-group/Virginia Tech/Engineering/Aerospace and Ocean Engineeringen
pubs.organisational-group/Virginia Tech/All T&R Facultyen
pubs.organisational-group/Virginia Tech/Engineering/COE T&R Facultyen
pubs.organisational-group/Virginia Tech/Science/COS T&R Facultyen

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