ACCELERATION OF THE TWO-LEVEL MGRIT ALGORITHM VIA THE DIAGONALIZATION TECHNIQUE

doi:10.1137/18M1207697

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	ACCELERATION OF THE TWO-LEVEL MGRIT ALGORITHM VIA THE DIAGONALIZATION TECHNIQUE
	Wu, Shu-Lin 1; Zhou, Tao 2
	2019
发表期刊	SIAM JOURNAL ON SCIENTIFIC COMPUTING
ISSN	1064-8275
卷号	41 期号:5 页码:A3421-A3448
摘要	The multigrid-reduction-in-time (MGRIT) algorithm is an efficient parallel-in-time algorithm for solving dynamic problems. The goal of this paper is to accelerate this algorithm via two strategies. The first strategy is to improve the convergence rate by using the 2nd-order Lobatto IIIC (LIIIC-2) method as the c-propagator, instead of using the backward-Euler method which is the common choice in this field. For a system of linear ODEs with a symmetric positive definite (SPD) coefficient matrix, we show that such a choice reduces the convergence factor of the MGRIT algorithm from 0.1 to 0.02. We prove a robust convergence factor for the MGRIT algorithm, which is independent of the eigenvalues of the coefficient matrix and the ratio J = Delta T/Delta t. The second strategy is to make the coarse-grid-correction (CGC) parallel by using the diagonalization technique. By properly choosing the involved parameter, we show that the new MGRIT algorithm has the same convergence rate as that of the original algorithm. Moreover, we show that within the framework of the parallel CGC the cost of the LIIIC-2 method, which is an implicit two-stage Runge-Kutta method, can be reduced to the same cost of the backward-Euler method. The idea toward this goal is still a suitable application of the diagonalization technique. Numerical experiments for the advection-diffusion equations with uncertain coefficients and the Gray-Scott model are given to support our findings.
关键词	multigrid-reduction-in-time (MGRIT) algorithm acceleration convergence analysis diagonalization technique parallel coarse-grid-correction
DOI	10.1137/18M1207697
收录类别	SCI
语种	英语
资助项目	NSF of China[11771313] ; NSF of China[11822111] ; NSF of China[11688101] ; NSF of China[91630312] ; NSF of China[91630203] ; NSF of China[11571351] ; NSF of China[11731006] ; NSF of Sichuan Province[2018JY0469] ; Science Challenge Project[TZ2018001] ; National Key Basic Research Program[2018YFB0704304] ; NCMIS ; Youth Innovation Promotion Association (CAS)
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000493897100029
出版者	SIAM PUBLICATIONS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/50733
专题	中国科学院数学与系统科学研究院
通讯作者	Wu, Shu-Lin
作者单位	1.Northeast Normal Univ, Sch Math & Stat, Changchun 130024, Jilin, Peoples R China 2.Chinese Acad Sci, AMSS, Inst Computat Math & Sci Engn Comp, LSEC, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Wu, Shu-Lin,Zhou, Tao. ACCELERATION OF THE TWO-LEVEL MGRIT ALGORITHM VIA THE DIAGONALIZATION TECHNIQUE[J]. SIAM JOURNAL ON SCIENTIFIC COMPUTING,2019,41(5):A3421-A3448.
APA	Wu, Shu-Lin,&Zhou, Tao.(2019).ACCELERATION OF THE TWO-LEVEL MGRIT ALGORITHM VIA THE DIAGONALIZATION TECHNIQUE.SIAM JOURNAL ON SCIENTIFIC COMPUTING,41(5),A3421-A3448.
MLA	Wu, Shu-Lin,et al."ACCELERATION OF THE TWO-LEVEL MGRIT ALGORITHM VIA THE DIAGONALIZATION TECHNIQUE".SIAM JOURNAL ON SCIENTIFIC COMPUTING 41.5(2019):A3421-A3448.