Symplectic GARK methods for Hamiltonian systems

dc.contributor.authorGuenther, Michaelen
dc.contributor.authorSandu, Adrianen
dc.contributor.authorZanna, Antonellaen
dc.date.accessioned2022-02-27T04:12:55Zen
dc.date.available2022-02-27T04:12:55Zen
dc.date.issued2021-03-06en
dc.date.updated2022-02-27T04:12:53Zen
dc.description.abstractGeneralized Additive Runge-Kutta schemes have shown to be a suitable tool for solving ordinary differential equations with additively partitioned right-hand sides. This work generalizes these GARK schemes to symplectic GARK schemes for additively partitioned Hamiltonian systems. In a general setting, we derive conditions for symplecticeness, as well as symmetry and time-reversibility. We show how symplectic and symmetric schemes can be constructed based on schemes which are only symplectic. Special attention is given to the special case of partitioned schemes for Hamiltonians split into multiple potential and kinetic energies. Finally we show how symplectic GARK schemes can use efficiently different time scales and evaluation costs for different potentials by using different order for these parts.en
dc.description.versionSubmitted versionen
dc.format.mimetypeapplication/pdfen
dc.identifier.orcidSandu, Adrian [0000-0002-5380-0103]en
dc.identifier.urihttp://hdl.handle.net/10919/108898en
dc.identifier.volumeabs/2103.04110en
dc.language.isoenen
dc.relation.urihttp://arxiv.org/abs/2103.04110v1en
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectmath.NAen
dc.subjectcs.NAen
dc.subject65L05, 65L06, 65L07, 65L020en
dc.titleSymplectic GARK methods for Hamiltonian systemsen
dc.title.serialCoRRen
dc.typeArticleen
dc.type.dcmitypeTexten
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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