Fast parareal iterations for fractional diffusion equations

doi:10.1016/j.jcp.2016.10.046

	Fast parareal iterations for fractional diffusion equations
	Wu, Shu-Lin 1; Zhou, Tao2
	2017-01-15
发表期刊	JOURNAL OF COMPUTATIONAL PHYSICS
ISSN	0021-9991
卷号	329 页码:210-226
摘要	Numerical methods for fractional PDEs is a hot topic recently. This work is concerned with the parareal algorithm for system of ODEs u'(t) + Au(t) = f that arising from semi-discretizations of time-dependent fractional diffusion equations with nonsymmetric Riemann-Liouville fractional derivatives. The spatial semi-discretization of this kind of fractional derivatives often results in a coefficient matrix A with spectrum sigma(A) satisfying sigma(A)subset of S(eta) := {lambda is an element of C : R(lambda) >=eta, F(lambda) is an element of R}, where eta > 0 is a measure of dissipativity of the differential equations. To accelerate the parareal algorithm, we propose a scaled model u'(t) + 1/alpha Au(t) = f (with alpha > 0) to serve the coarse grid correction, which is an important component of our parareal algorithm. Given eta and alpha, we derive a sharp bound of the convergence factor of the parareal iterations. Moreover, by minimizing such a bound we get optimized scaling factor alpha(opt). It is shown that, compared to alpha =1 (i.e., the classical implementation pattern of the coarse grid correction), the optimized scaling factor significantly improves the convergence rate. Numerical examples are presented to support the theoretical finding. (C) 2016 Elsevier Inc. All rights reserved.
关键词	Parareal algorithm Fractional PDEs Convergence analysis Parameter optimization
DOI	10.1016/j.jcp.2016.10.046
语种	英语
资助项目	NSFC[11301362] ; NSFC[61573010] ; Project of China Postdoctoral Science Foundation[2015M580777] ; Project of China Postdoctoral Science Foundation[2016T90841] ; NSF of Technology & Education of Sichuan Province[2014JQ0035] ; NSF of Technology & Education of Sichuan Province[15ZA0220] ; NSF of SUSE[2015LX01] ; National Natural Science Foundation of China[91530118] ; National Natural Science Foundation of China[11571351]
WOS研究方向	Computer Science ; Physics
WOS类目	Computer Science, Interdisciplinary Applications ; Physics, Mathematical
WOS记录号	WOS:000390511500010
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/24391
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. Fast parareal iterations for fractional diffusion equations[J]. JOURNAL OF COMPUTATIONAL PHYSICS,2017,329:210-226.
APA	Wu, Shu-Lin,&Zhou, Tao.(2017).Fast parareal iterations for fractional diffusion equations.JOURNAL OF COMPUTATIONAL PHYSICS,329,210-226.
MLA	Wu, Shu-Lin,et al."Fast parareal iterations for fractional diffusion equations".JOURNAL OF COMPUTATIONAL PHYSICS 329(2017):210-226.