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Parareal algorithms with local time-integrators for time-fractional differential equations
Wu, Shu-Lin1; Zhou, Tao2
AbstractIt is challenge work to design parareal algorithms for time-fractional differential equations due to the historical effect of the fractional operator. A direct extension of the classical parareal methodto such equations will lead to unbalance computational time in each process. In this work, we present an efficient parareal iteration scheme to overcome this issue, by adopting two recently developed local time-integrators for time fractional operators. In both approaches, one introduces auxiliary variables to localized the fractional operator. To this end, we propose a new strategy to perform the coarse grid correction so that the auxiliary variables and the solution variable are corrected separately in a mixed pattern. It is shown that the proposed parareal algorithm admits robust rate of convergence. Numerical examples are presented to support our conclusions. (C) 2017 Elsevier Inc. All rights reserved.
KeywordParareal Time-fractional differential equations Local time-integrators
Funding ProjectNSFC[11301362] ; NSFC[61573010] ; NSFC[11688101] ; NSFC[91630312] ; NSFC[91630203] ; NSFC[11571351] ; NSFC[11731006] ; NSF of Technology & Education of Sichuan Province[2014JQ0035] ; NSF of Technology & Education of Sichuan Province[15ZA0220] ; NSF of SUSE[2015LX01] ; science challenge project[TZ2016001] ; NCMIS ; youth innovation promotion association (CAS) ; [2015M580777] ; [2016T90841]
WOS Research AreaComputer Science ; Physics
WOS SubjectComputer Science, Interdisciplinary Applications ; Physics, Mathematical
WOS IDWOS:000427395300008
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Document Type期刊论文
Corresponding AuthorZhou, Tao
Affiliation1.Sichuan Univ Sci & Engn, Sch Sci, Zigong, Sichuan, Peoples R China
2.Chinese Acad Sci, AMSS, Inst Computat Math & Sci Engn Comp, LSEC, Beijing, Peoples R China
Recommended Citation
GB/T 7714
Wu, Shu-Lin,Zhou, Tao. Parareal algorithms with local time-integrators for time-fractional differential equations[J]. JOURNAL OF COMPUTATIONAL PHYSICS,2018,358:135-149.
APA Wu, Shu-Lin,&Zhou, Tao.(2018).Parareal algorithms with local time-integrators for time-fractional differential equations.JOURNAL OF COMPUTATIONAL PHYSICS,358,135-149.
MLA Wu, Shu-Lin,et al."Parareal algorithms with local time-integrators for time-fractional differential equations".JOURNAL OF COMPUTATIONAL PHYSICS 358(2018):135-149.
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