KMS Of Academy of mathematics and systems sciences, CAS
| NUMERICAL INVESTIGATION OF ENSEMBLE METHODS WITH BLOCK ITERATIVE SOLVERS FOR EVOLUTION PROBLEMS | |
| Ju, Lili1; Leng, Wei2; Wang, Zhu1; Yuan, Shuai1 | |
| 2020-12-01 | |
| Source Publication | DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B
 |
| ISSN | 1531-3492 |
| Volume | 25Issue:12Pages:4905-4923 |
| Abstract | 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. |
| Keyword | Ensemble method ensemble-based time stepping block CG block GMRES iterative linear solver |
| DOI | 10.3934/dcdsb.2020132 |
| Indexed By | SCI |
| Language | 英语 |
| Funding Project | 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 Research Area | Mathematics |
| WOS Subject | Mathematics, Applied |
| WOS ID | WOS:000581913800020 |
| Publisher | AMER INST MATHEMATICAL SCIENCES-AIMS |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/52392 |
| Collection | 中国科学院数学与系统科学研究院 |
| Corresponding Author | Wang, Zhu |
| Affiliation | 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 |
| Recommended Citation 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. |
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