Step Sizes for Strong Stability Preservation with Downwind-Biased Operators

Handle URI:
http://hdl.handle.net/10754/333575
Title:
Step Sizes for Strong Stability Preservation with Downwind-Biased Operators
Authors:
Ketcheson, David I. ( 0000-0002-1212-126X )
Abstract:
Strong stability preserving (SSP) integrators for initial value ODEs preserve temporal monotonicity solution properties in arbitrary norms. All existing SSP methods, including implicit methods, either require small step sizes or achieve only first order accuracy. It is possible to achieve more relaxed step size restrictions in the discretization of hyperbolic PDEs through the use of both upwind- and downwind-biased semidiscretizations. We investigate bounds on the maximum SSP step size for methods that include negative coefficients and downwind-biased semi-discretizations. We prove that the downwind SSP coefficient for linear multistep methods of order greater than one is at most equal to two, while the downwind SSP coefficient for explicit Runge–Kutta methods is at most equal to the number of stages of the method. In contrast, the maximal downwind SSP coefficient for second order Runge–Kutta methods is shown to be unbounded. We present a class of such methods with arbitrarily large SSP coefficient and demonstrate that they achieve second order accuracy for large CFL number.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Numerical Mathematics Group
Citation:
Step Sizes for Strong Stability Preservation with Downwind-Biased Operators 2011, 49 (4):1649 SIAM Journal on Numerical Analysis
Publisher:
Society for Industrial and Applied Mathematics
Journal:
SIAM Journal on Numerical Analysis
Issue Date:
4-Aug-2011
DOI:
10.1137/100818674
Type:
Article
ISSN:
0036-1429; 1095-7170
Additional Links:
http://epubs.siam.org/doi/abs/10.1137/100818674; http://numerics.kaust.edu.sa/papers/dwrk2011/downwind_ssp.html; http://arxiv.org/abs/1105.5798; http://github.com/ketch/downwind_IRK_RR
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.date.accessioned2014-11-03T14:38:09Z-
dc.date.available2014-11-03T14:38:09Z-
dc.date.issued2011-08-04en
dc.identifier.citationStep Sizes for Strong Stability Preservation with Downwind-Biased Operators 2011, 49 (4):1649 SIAM Journal on Numerical Analysisen
dc.identifier.issn0036-1429en
dc.identifier.issn1095-7170en
dc.identifier.doi10.1137/100818674en
dc.identifier.urihttp://hdl.handle.net/10754/333575en
dc.description.abstractStrong stability preserving (SSP) integrators for initial value ODEs preserve temporal monotonicity solution properties in arbitrary norms. All existing SSP methods, including implicit methods, either require small step sizes or achieve only first order accuracy. It is possible to achieve more relaxed step size restrictions in the discretization of hyperbolic PDEs through the use of both upwind- and downwind-biased semidiscretizations. We investigate bounds on the maximum SSP step size for methods that include negative coefficients and downwind-biased semi-discretizations. We prove that the downwind SSP coefficient for linear multistep methods of order greater than one is at most equal to two, while the downwind SSP coefficient for explicit Runge–Kutta methods is at most equal to the number of stages of the method. In contrast, the maximal downwind SSP coefficient for second order Runge–Kutta methods is shown to be unbounded. We present a class of such methods with arbitrarily large SSP coefficient and demonstrate that they achieve second order accuracy for large CFL number.en
dc.language.isoenen
dc.publisherSociety for Industrial and Applied Mathematicsen
dc.relation.urlhttp://epubs.siam.org/doi/abs/10.1137/100818674en
dc.relation.urlhttp://numerics.kaust.edu.sa/papers/dwrk2011/downwind_ssp.htmlen
dc.relation.urlhttp://arxiv.org/abs/1105.5798en
dc.relation.urlhttp://github.com/ketch/downwind_IRK_RRen
dc.rightsArchived with thanks to SIAM Journal on Numerical Analysisen
dc.subjectstrong stability-preservingen
dc.subjectmonotonicityen
dc.subjectRunge–Kutta methodsen
dc.titleStep Sizes for Strong Stability Preservation with Downwind-Biased Operatorsen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.contributor.departmentNumerical Mathematics Groupen
dc.identifier.journalSIAM Journal on Numerical Analysisen
dc.eprint.versionPublisher's Version/PDFen
dc.contributor.affiliationKing Abdullah University of Science and Technology (KAUST)en
dc.identifier.arxividarXiv:1105.5798en
kaust.authorKetcheson, David I.en
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