KMS Of Academy of mathematics and systems sciences, CAS
NOVEL MULTILEVEL PRECONDITIONERS FOR THE SYSTEMS ARISING FROM PLANE WAVE DISCRETIZATION OF HELMHOLTZ EQUATIONS WITH LARGE WAVE NUMBERS | |
Hu, Qiya1,2; Li, Xuan3 | |
2017 | |
发表期刊 | SIAM JOURNAL ON SCIENTIFIC COMPUTING |
ISSN | 1064-8275 |
卷号 | 39期号:4页码:A1675-A1709 |
摘要 | In this paper we are concerned with fast algorithms for the systems arising from the plane wave discretizations for two-dimensional Helmholtz equations with large wave numbers. We consider the plane wave weighted least squares (PWLS) method and the plane wave discontinuous Galerkin (PWDG) method. The main goal of this paper is to construct multilevel parallel preconditioners for solving the resulting Helmholtz systems. To this end, we first build a multilevel space decomposition for the plane wave discretization space based on a multilevel overlapping domain decomposition method. Then, corresponding to the space decomposition, we construct an additive multilevel preconditioner for the underlying Helmholtz systems. Further, we design both additive and multiplicative multilevel preconditioners with smoothers, which are different from the standard multigrid preconditioners. We apply the proposed multilevel preconditioners with a constant coarsest mesh size to solve two-dimensional Helmholtz systems generated by the PWLS method or PWDG method, and we find that the new preconditioners possess nearly stable convergence; i.e., the iteration counts of the preconditioned iterative methods (PCG or PGMRES) with the preconditioners increase very slowly when the wave number increases (and the fine mesh size decreases). |
关键词 | Helmholtz equation large wave numbers plane wave methods multilevel overlapping domain decomposition multilevel overlapping preconditioner smoothers |
DOI | 10.1137/15M1022963 |
语种 | 英语 |
资助项目 | National Natural Science Foundation of China[G11571352] |
WOS研究方向 | Mathematics |
WOS类目 | Mathematics, Applied |
WOS记录号 | WOS:000408922600030 |
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/26535 |
专题 | 计算数学与科学工程计算研究所 |
通讯作者 | Hu, Qiya |
作者单位 | 1.Chinese Acad Sci, Acad Math & Syst Sci, LSEC, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Beijing, Peoples R China 3.Huawei Technol CO LTD, 101 Software Ave, Nanjing 210012, Jiangsu, Peoples R China |
推荐引用方式 GB/T 7714 | Hu, Qiya,Li, Xuan. NOVEL MULTILEVEL PRECONDITIONERS FOR THE SYSTEMS ARISING FROM PLANE WAVE DISCRETIZATION OF HELMHOLTZ EQUATIONS WITH LARGE WAVE NUMBERS[J]. SIAM JOURNAL ON SCIENTIFIC COMPUTING,2017,39(4):A1675-A1709. |
APA | Hu, Qiya,&Li, Xuan.(2017).NOVEL MULTILEVEL PRECONDITIONERS FOR THE SYSTEMS ARISING FROM PLANE WAVE DISCRETIZATION OF HELMHOLTZ EQUATIONS WITH LARGE WAVE NUMBERS.SIAM JOURNAL ON SCIENTIFIC COMPUTING,39(4),A1675-A1709. |
MLA | Hu, Qiya,et al."NOVEL MULTILEVEL PRECONDITIONERS FOR THE SYSTEMS ARISING FROM PLANE WAVE DISCRETIZATION OF HELMHOLTZ EQUATIONS WITH LARGE WAVE NUMBERS".SIAM JOURNAL ON SCIENTIFIC COMPUTING 39.4(2017):A1675-A1709. |
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