NUMERICAL INVESTIGATION OF ENSEMBLE METHODS WITH BLOCK ITERATIVE SOLVERS FOR EVOLUTION PROBLEMS

doi:10.3934/dcdsb.2020132

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	NUMERICAL INVESTIGATION OF ENSEMBLE METHODS WITH BLOCK ITERATIVE SOLVERS FOR EVOLUTION PROBLEMS
	Ju, Lili 1; Leng, Wei 2; Wang, Zhu 1; Yuan, Shuai 1
	2020-12-01
发表期刊	DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B
ISSN	1531-3492
卷号	25 期号:12 页码:4905-4923
摘要	The ensemble method has been developed for accelerating a sequence of numerical simulations of evolution problems. Its main idea is, by manipulating the time stepping and grouping discrete problems, to make all members in the same group share a common coefficient matrix. Thus, at each time step, instead of solving a sequence of linear systems each of which contains only one right-hand-side vector, the ensemble method simultaneously solves a single linear system with multiple right-hand-side vectors for each group. Such a system could be solved efficiently by using direct linear solvers when the problems are of small scale, as the same LU factorization would work for the entire group members. However, for large-scale problems, iterative linear solvers often have to be used and then this appealing advantage becomes not obvious. In this paper we systematically investigate numerical performance of the ensemble method with block iterative solvers for two typical evolution problems: the heat equation and the incompressible Navier-Stokes equations. In particular, the block conjugate gradient (CG) solver is considered for the former and the block generalized minimal residual (GMRES) solver for the latter. Our numerical results demonstrate the effectiveness and efficiency of the ensemble method when working together with these block iterative solvers.
关键词	Ensemble method ensemble-based time stepping block CG block GMRES iterative linear solver
DOI	10.3934/dcdsb.2020132
收录类别	SCI
语种	英语
资助项目	U.S. National Science Foundation[DMS-1913073] ; U.S. National Science Foundation[DMS-1818438] ; U.S. Department of Energy[DE-SC0016540] ; U.S. Department of Energy[DE-SC0020270] ; National Key Research and Development Program of China[2016YFB0201304] ; National Natural Science Foundation of China[91430215] ; National Natural Science Foundation of China[91530323] ; National Natural Science Foundation of China[11501553] ; National Natural Science Foundation of China[11771440] ; State Key Laboratory of Scientific and Engineering Computing (LSEC) ; National Center for Mathematics and Interdisciplinary Sciences of Chinese Academy of Sciences (NCMIS) ; Office of the Vice President for Research at the University of South Carolina through an ASPIRE grant
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000581913800020
出版者	AMER INST MATHEMATICAL SCIENCES-AIMS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/52392
专题	中国科学院数学与系统科学研究院
通讯作者	Wang, Zhu
作者单位	1.Univ South Carolina, Dept Math, Columbia, SC 29208 USA 2.Chinese Acad Sci, State Key Lab Sci & Engn Comp, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Ju, Lili,Leng, Wei,Wang, Zhu,et al. NUMERICAL INVESTIGATION OF ENSEMBLE METHODS WITH BLOCK ITERATIVE SOLVERS FOR EVOLUTION PROBLEMS[J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B,2020,25(12):4905-4923.
APA	Ju, Lili,Leng, Wei,Wang, Zhu,&Yuan, Shuai.(2020).NUMERICAL INVESTIGATION OF ENSEMBLE METHODS WITH BLOCK ITERATIVE SOLVERS FOR EVOLUTION PROBLEMS.DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B,25(12),4905-4923.
MLA	Ju, Lili,et al."NUMERICAL INVESTIGATION OF ENSEMBLE METHODS WITH BLOCK ITERATIVE SOLVERS FOR EVOLUTION PROBLEMS".DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B 25.12(2020):4905-4923.