A comparison of high-order explicit Runge–Kutta, extrapolation, and deferred correction methods in serial and parallel

Handle URI:
http://hdl.handle.net/10754/333641
Title:
A comparison of high-order explicit Runge–Kutta, extrapolation, and deferred correction methods in serial and parallel
Authors:
Ketcheson, David I. ( 0000-0002-1212-126X ) ; Waheed, Umair bin ( 0000-0002-5189-0694 )
Abstract:
We compare the three main types of high-order one-step initial value solvers: extrapolation, spectral deferred correction, and embedded Runge–Kutta pairs. We consider orders four through twelve, including both serial and parallel implementations. We cast extrapolation and deferred correction methods as fixed-order Runge–Kutta methods, providing a natural framework for the comparison. The stability and accuracy properties of the methods are analyzed by theoretical measures, and these are compared with the results of numerical tests. In serial, the eighth-order pair of Prince and Dormand (DOP8) is most efficient. But other high-order methods can be more efficient than DOP8 when implemented in parallel. This is demonstrated by comparing a parallelized version of the wellknown ODEX code with the (serial) DOP853 code. For an N-body problem with N = 400, the experimental extrapolation code is as fast as the tuned Runge–Kutta pair at loose tolerances, and is up to two times as fast at tight tolerances.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Numerical Mathematics Group; Physical Sciences and Engineering (PSE) Division
Citation:
A comparison of high-order explicit Runge–Kutta, extrapolation, and deferred correction methods in serial and parallel 2014, 9 (2):175 Communications in Applied Mathematics and Computational Science
Publisher:
Mathematical Sciences Publishers
Journal:
Communications in Applied Mathematics and Computational Science
Issue Date:
13-Jun-2014
DOI:
10.2140/camcos.2014.9.175
Type:
Article
ISSN:
2157-5452; 1559-3940
Additional Links:
http://msp.org/camcos/2014/9-2/p01.xhtml; http://github.com/ketch/high_order_RK_RR/; http://arxiv.org/abs/1305.6165
Appears in Collections:
Articles; Physical Sciences and Engineering (PSE) Division; 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.authorWaheed, Umair binen
dc.date.accessioned2014-11-04T07:19:32Z-
dc.date.available2014-11-04T07:19:32Z-
dc.date.issued2014-06-13en
dc.identifier.citationA comparison of high-order explicit Runge–Kutta, extrapolation, and deferred correction methods in serial and parallel 2014, 9 (2):175 Communications in Applied Mathematics and Computational Scienceen
dc.identifier.issn2157-5452en
dc.identifier.issn1559-3940en
dc.identifier.doi10.2140/camcos.2014.9.175en
dc.identifier.urihttp://hdl.handle.net/10754/333641en
dc.description.abstractWe compare the three main types of high-order one-step initial value solvers: extrapolation, spectral deferred correction, and embedded Runge–Kutta pairs. We consider orders four through twelve, including both serial and parallel implementations. We cast extrapolation and deferred correction methods as fixed-order Runge–Kutta methods, providing a natural framework for the comparison. The stability and accuracy properties of the methods are analyzed by theoretical measures, and these are compared with the results of numerical tests. In serial, the eighth-order pair of Prince and Dormand (DOP8) is most efficient. But other high-order methods can be more efficient than DOP8 when implemented in parallel. This is demonstrated by comparing a parallelized version of the wellknown ODEX code with the (serial) DOP853 code. For an N-body problem with N = 400, the experimental extrapolation code is as fast as the tuned Runge–Kutta pair at loose tolerances, and is up to two times as fast at tight tolerances.en
dc.language.isoenen
dc.publisherMathematical Sciences Publishersen
dc.relation.urlhttp://msp.org/camcos/2014/9-2/p01.xhtmlen
dc.relation.urlhttp://github.com/ketch/high_order_RK_RR/en
dc.relation.urlhttp://arxiv.org/abs/1305.6165en
dc.rightsArchived with thanks to Communications in Applied Mathematics and Computational Scienceen
dc.subjectRunge–Kutta methodsen
dc.subjectextrapolationen
dc.subjectdeferred correctionen
dc.subjectordinary differential equationsen
dc.subjecthigh-order methodsen
dc.subjectparallelen
dc.titleA comparison of high-order explicit Runge–Kutta, extrapolation, and deferred correction methods in serial and parallelen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.contributor.departmentNumerical Mathematics Groupen
dc.contributor.departmentPhysical Sciences and Engineering (PSE) Divisionen
dc.identifier.journalCommunications in Applied Mathematics and Computational Scienceen
dc.eprint.versionPublisher's Version/PDFen
dc.contributor.affiliationKing Abdullah University of Science and Technology (KAUST)en
kaust.authorKetcheson, David I.en
kaust.authorWaheed, Umair binen
All Items in KAUST are protected by copyright, with all rights reserved, unless otherwise indicated.