Parareal algorithms with local time-integrators for time-fractional differential equations

doi:10.1016/j.jcp.2017.12.029

	Parareal algorithms with local time-integrators for time-fractional differential equations
	Wu, Shu-Lin 1; Zhou, Tao2
	2018-04-01
发表期刊	JOURNAL OF COMPUTATIONAL PHYSICS
ISSN	0021-9991
卷号	358 页码:135-149
摘要	It 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.
关键词	Parareal Time-fractional differential equations Local time-integrators
DOI	10.1016/j.jcp.2017.12.029
语种	英语
资助项目	NSFC[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研究方向	Computer Science ; Physics
WOS类目	Computer Science, Interdisciplinary Applications ; Physics, Mathematical
WOS记录号	WOS:000427395300008
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/29840
专题	计算数学与科学工程计算研究所
通讯作者	Zhou, Tao
作者单位	1.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
推荐引用方式 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.