EFFICIENT MULTILEVEL PRECONDITIONERS FOR THREE-DIMENSIONAL PLANE WAVE HELMHOLTZ SYSTEMS WITH LARGE WAVE NUMBERS
文献类型：期刊论文
| 作者 | Hu, Qiya1,2 ; Li, Xuan3
|
| 刊名 | MULTISCALE MODELING & SIMULATION
 |
| 出版日期 | 2017 |
| 卷号 | 15期号:3页码:1242-1266 |
| 关键词 | Helmholtz equation large wave numbers plane wave methods overlapping domain decomposition multilevel preconditioners 3-level smoothers |
| ISSN号 | 1540-3459 |
| DOI | 10.1137/16M1084791 |
| 英文摘要 | In this paper we are concerned with solvers for the systems arising from the plane wave discretizations of three dimensional Helmholtz equations with large wave numbers. For simplicity, we consider only the plane wave weighted least squares (PWLS) method for Helmholtz equations. The main goal of this paper is to construct efficient multilevel 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 overlapping domain decompositions. Then, corresponding to the space decomposition, we construct two additive multilevel preconditioners with smoothers for the underlying Helmholtz systems. In these preconditioners, each subproblem to be solved has a very small number of degrees of freedom, which just equals the number of the plane wave basis functions on one element. Moreover, the preconditioners possess the optimal computational complexity per iteration. We apply the proposed multilevel preconditioners with a constant coarse mesh size to solve the systems generated by the PWLS discretization for three dimensional Helmholtz equations, and we find that the new preconditioners possess nearly stable convergence, i.e., the iteration counts of the preconditioned CG methods with the preconditioners increase very slowly when the wave number increases (and the fine mesh size decreases). |
| 资助项目 | Natural Science Foundation of China[G11571352] |
| WOS研究方向 | Mathematics ; Physics |
| 语种 | 英语 |
| WOS记录号 | WOS:000412162400007 |
| 出版者 | SIAM PUBLICATIONS |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/26679]  |
| 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 Aveune, Nanjing 210012, Jiangsu, Peoples R China |
| 推荐引用方式 GB/T 7714 | Hu, Qiya,Li, Xuan. EFFICIENT MULTILEVEL PRECONDITIONERS FOR THREE-DIMENSIONAL PLANE WAVE HELMHOLTZ SYSTEMS WITH LARGE WAVE NUMBERS[J]. MULTISCALE MODELING & SIMULATION,2017,15(3):1242-1266. |
| APA | Hu, Qiya,&Li, Xuan.(2017).EFFICIENT MULTILEVEL PRECONDITIONERS FOR THREE-DIMENSIONAL PLANE WAVE HELMHOLTZ SYSTEMS WITH LARGE WAVE NUMBERS.MULTISCALE MODELING & SIMULATION,15(3),1242-1266. |
| MLA | Hu, Qiya,et al."EFFICIENT MULTILEVEL PRECONDITIONERS FOR THREE-DIMENSIONAL PLANE WAVE HELMHOLTZ SYSTEMS WITH LARGE WAVE NUMBERS".MULTISCALE MODELING & SIMULATION 15.3(2017):1242-1266. |
入库方式： OAI收割
来源：数学与系统科学研究院
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