KMS Of Academy of mathematics and systems sciences, CAS
ACCELERATION OF THE TWO-LEVEL MGRIT ALGORITHM VIA THE DIAGONALIZATION TECHNIQUE | |
Wu, Shu-Lin1; Zhou, Tao2 | |
2019 | |
Source Publication | SIAM JOURNAL ON SCIENTIFIC COMPUTING |
ISSN | 1064-8275 |
Volume | 41Issue:5Pages:A3421-A3448 |
Abstract | 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. |
Keyword | multigrid-reduction-in-time (MGRIT) algorithm acceleration convergence analysis diagonalization technique parallel coarse-grid-correction |
DOI | 10.1137/18M1207697 |
Indexed By | SCI |
Language | 英语 |
Funding Project | 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 Research Area | Mathematics |
WOS Subject | Mathematics, Applied |
WOS ID | WOS:000493897100029 |
Publisher | SIAM PUBLICATIONS |
Citation statistics | |
Document Type | 期刊论文 |
Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/50733 |
Collection | 中国科学院数学与系统科学研究院 |
Corresponding Author | Wu, Shu-Lin |
Affiliation | 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 |
Recommended Citation 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. |
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