A multigrid-based preconditioner for solving the Helmholtz equation with average-derivative optimal scheme
文献类型：期刊论文
| 作者 | Yuan YuXin1,2,3,4; Li AMan1,2,3,4; Hu Ting1,2,3,4; Guo Peng5; Liu Hong1,2,3,4 |
| 刊名 | CHINESE JOURNAL OF GEOPHYSICS-CHINESE EDITION
 |
| 出版日期 | 2019-07-01 |
| 卷号 | 62期号:7页码:2660-2670 |
| 关键词 | Multigrid Anisotropic problem Helmholtz equation Average-derivative optimal scheme |
| ISSN号 | 0001-5733 |
| DOI | 10.6038/cjg2019M0265 |
| 英文摘要 | An efficient finite-difference method for solving Helmholtz equation depends on two points: one is discrete scheme, the other is efficient algorithm. In this paper, we adopt the average-derivative scheme, which owns three advantages : Firstly, it can be applied to unequal directional sampling intervals for Helmholtz equation. Secondly, the scheme is pointwise consistent with Helmholtz equation in a perfect matched layer. And thirdly, it requires less than 4 grid points sampling per wavelength. To solve the discrete Helmholtz equation, which is extremely large and indefinite, direct methods cannot resolve well, and the Krylov subspace iterative methods, such as Bi-CGSTAB and GMRES combining a multigrid-based preconditioner, are good choices. However, the standard multigrid algorithm fails to converge when it encounters unequal directional sampling intervals, which is called anisotropy in multigrid. We analyze the most important three parts of standard multigrid : full weighting restriction operator, point relaxation methods and bilinear interpolation operator, and then we replace them with semi-coarsening, line relaxation and operator-dependent interpolation to make it convergent in anisotropic problems. Consequently, we obtain a satisfactory convergence speed for low and moderate frequency iterative problems in heterogeneous media. |
| WOS关键词 | FINITE-DIFFERENCE ; OPTIMAL 9-POINT ; WAVE-EQUATION ; DEFLATION |
| WOS研究方向 | Geochemistry & Geophysics |
| 语种 | 英语 |
| WOS记录号 | WOS:000474879800023 |
| 出版者 | SCIENCE PRESS |
| 源URL | [http://ir.iggcas.ac.cn/handle/132A11/92670]  |
| 专题 | 地质与地球物理研究所_中国科学院油气资源研究重点实验室 |
| 通讯作者 | Liu Hong |
| 作者单位 | 1.Chinese Acad Sci, Inst Geol & Geophys, Beijing 100029, Peoples R China 2.Chinese Acad Sci, Inst Earth Sci, Beijing 100029, Peoples R China 3.Chinese Acad Sci, Key Lab Petr Resources Res, Inst Geol & Geophys, Beijing 100029, Peoples R China 4.Univ Chinese Acad Sci, Beijing 100049, Peoples R China 5.Tianjin Univ, State Key Lab Hydraul Engn Simulat & Safety, Tianjin 300072, Peoples R China |
| 推荐引用方式 GB/T 7714 | Yuan YuXin,Li AMan,Hu Ting,et al. A multigrid-based preconditioner for solving the Helmholtz equation with average-derivative optimal scheme[J]. CHINESE JOURNAL OF GEOPHYSICS-CHINESE EDITION,2019,62(7):2660-2670. |
| APA | Yuan YuXin,Li AMan,Hu Ting,Guo Peng,&Liu Hong.(2019).A multigrid-based preconditioner for solving the Helmholtz equation with average-derivative optimal scheme.CHINESE JOURNAL OF GEOPHYSICS-CHINESE EDITION,62(7),2660-2670. |
| MLA | Yuan YuXin,et al."A multigrid-based preconditioner for solving the Helmholtz equation with average-derivative optimal scheme".CHINESE JOURNAL OF GEOPHYSICS-CHINESE EDITION 62.7(2019):2660-2670. |
入库方式： OAI收割
来源：地质与地球物理研究所
浏览0
下载0
收藏0
其他版本
除非特别说明，本系统中所有内容都受版权保护，并保留所有权利。