Spatially Partitioned Embedded Runge--Kutta Methods

Handle URI:
http://hdl.handle.net/10754/333579
Title:
Spatially Partitioned Embedded Runge--Kutta Methods
Authors:
Ketcheson, David I. ( 0000-0002-1212-126X ) ; MacDonald, Colin B.; Ruuth, Steven J.
Abstract:
We study spatially partitioned embedded Runge--Kutta (SPERK) schemes for partial differential equations (PDEs), in which each of the component schemes is applied over a different part of the spatial domain. Such methods may be convenient for problems in which the smoothness of the solution or the magnitudes of the PDE coefficients vary strongly in space. We focus on embedded partitioned methods as they offer greater efficiency and avoid the order reduction that may occur in nonembedded schemes. We demonstrate that the lack of conservation in partitioned schemes can lead to nonphysical effects and propose conservative additive schemes based on partitioning the fluxes rather than the ordinary differential equations. A variety of SPERK schemes are presented, including an embedded pair suitable for the time evolution of fifth-order weighted nonoscillatory spatial discretizations. Numerical experiments are provided to support the theory.
KAUST Department:
Numerical Mathematics Group; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Citation:
Spatially Partitioned Embedded Runge--Kutta Methods 2013, 51 (5):2887 SIAM Journal on Numerical Analysis
Publisher:
Society for Industrial and Applied Mathematics
Journal:
SIAM Journal on Numerical Analysis
Issue Date:
30-Oct-2013
DOI:
10.1137/130906258
Type:
Article
ISSN:
0036-1429; 1095-7170
Additional Links:
http://epubs.siam.org/doi/abs/10.1137/130906258; http://arxiv.org/abs/1301.4006
Appears in Collections:
Articles; Numerical Mathematics Group; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorKetcheson, David I.en
dc.contributor.authorMacDonald, Colin B.en
dc.contributor.authorRuuth, Steven J.en
dc.date.accessioned2014-11-03T16:18:03Z-
dc.date.available2014-11-03T16:18:03Z-
dc.date.issued2013-10-30en
dc.identifier.citationSpatially Partitioned Embedded Runge--Kutta Methods 2013, 51 (5):2887 SIAM Journal on Numerical Analysisen
dc.identifier.issn0036-1429en
dc.identifier.issn1095-7170en
dc.identifier.doi10.1137/130906258en
dc.identifier.urihttp://hdl.handle.net/10754/333579en
dc.description.abstractWe study spatially partitioned embedded Runge--Kutta (SPERK) schemes for partial differential equations (PDEs), in which each of the component schemes is applied over a different part of the spatial domain. Such methods may be convenient for problems in which the smoothness of the solution or the magnitudes of the PDE coefficients vary strongly in space. We focus on embedded partitioned methods as they offer greater efficiency and avoid the order reduction that may occur in nonembedded schemes. We demonstrate that the lack of conservation in partitioned schemes can lead to nonphysical effects and propose conservative additive schemes based on partitioning the fluxes rather than the ordinary differential equations. A variety of SPERK schemes are presented, including an embedded pair suitable for the time evolution of fifth-order weighted nonoscillatory spatial discretizations. Numerical experiments are provided to support the theory.en
dc.language.isoenen
dc.publisherSociety for Industrial and Applied Mathematicsen
dc.relation.urlhttp://epubs.siam.org/doi/abs/10.1137/130906258en
dc.relation.urlhttp://arxiv.org/abs/1301.4006en
dc.rightsArchived with thanks to SIAM Journal on Numerical Analysisen
dc.subjectembedded Runge–Kutta methodsen
dc.subjectspatially partitioned methodsen
dc.subjectconservation lawsen
dc.subjectmethod of linesen
dc.titleSpatially Partitioned Embedded Runge--Kutta Methodsen
dc.typeArticleen
dc.contributor.departmentNumerical Mathematics Groupen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journalSIAM Journal on Numerical Analysisen
dc.eprint.versionPublisher's Version/PDFen
dc.contributor.institutionMathematical Institute, University of Oxford, OX1 3LB, UKen
dc.contributor.institutionDepartment of Mathematics, Simon Fraser University, Burnaby, British Columbia V5A 1S6, Canadaen
dc.contributor.affiliationKing Abdullah University of Science and Technology (KAUST)en
dc.identifier.arxividarXiv:1301.4006en
kaust.authorKetcheson, David I.en
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