KMS Of Academy of mathematics and systems sciences, CAS
Fast parareal iterations for fractional diffusion equations | |
Wu, Shu-Lin1; Zhou, Tao2 | |
2017-01-15 | |
Source Publication | JOURNAL OF COMPUTATIONAL PHYSICS |
ISSN | 0021-9991 |
Volume | 329Pages:210-226 |
Abstract | 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. |
Keyword | Parareal algorithm Fractional PDEs Convergence analysis Parameter optimization |
DOI | 10.1016/j.jcp.2016.10.046 |
Language | 英语 |
Funding Project | 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 Research Area | Computer Science ; Physics |
WOS Subject | Computer Science, Interdisciplinary Applications ; Physics, Mathematical |
WOS ID | WOS:000390511500010 |
Publisher | ACADEMIC PRESS INC ELSEVIER SCIENCE |
Citation statistics | |
Document Type | 期刊论文 |
Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/24391 |
Collection | 计算数学与科学工程计算研究所 |
Corresponding Author | Zhou, Tao |
Affiliation | 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 |
Recommended Citation 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. |
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