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An anisotropic multilevel preconditioner for solving the Helmholtz equation with unequal directional sampling intervals

文献类型：期刊论文

作者Yuan, Yu-Xin3; Li, A-Man3; Hu, Ting3; Liu, Hong3
刊名GEOPHYSICS
出版日期2020-11-01
卷号85期号:6页码:T293-T300
ISSN号0016-8033
DOI10.1190/geo2019-0330.1
英文摘要An efficient finite-difference method for solving the isotropic Helmholtz equation relies on a discretization scheme and an appropriate solver. Accordingly, we have adopted an average derivative optimal scheme that has two advantages: (1) it can be applied to unequal directional sampling intervals and (2) it requires less than four grid points of sampling per wavelength. Direct methods are not of interest for industry-sized problems due to the high memory requirements; Krylov subspace methods such as the biconjugate gradient stabilized method and the flexible generalized minimal residual method that combine a multigrid-based preconditioner are better alternatives. However, standard geometric multigrid algorithms fail to converge when there exist unequal directional sampling intervals; this is called anisotropic grids in terms of the multigrid. We first review our previous research on 2D anisotropic grids: the semicoarsening strategy, line-wise relaxation operator, and matrix-dependent interpolation were used to modify the standard V-cycle multigrid algorithms, resulting in convergence. Although directly extending to the 3D case by substituting line relaxation for plane relaxation deteriorates the convergence rate considerably, we then find that a multilevel generalized minimal residual preconditioner-combined semicoarsening strategy is more suitable for anisotropic grids and the convergence rate is faster in the 2D and 3D cases. The results of the numerical experiments indicate that the standard geometric multigrid does not work for anisotropic grids, whereas our method demonstrates a faster convergence rate than the previous method.
WOS关键词MULTIGRID-BASED PRECONDITIONER ; DERIVATIVE OPTIMAL SCHEME ; FINITE-DIFFERENCE METHODS ; SCALAR WAVE-EQUATION ; ELEMENT-METHOD ; SWEEPING PRECONDITIONER ; FREQUENCY-SPACE ; DIRECT SOLVER ; PROPAGATION
资助项目National Natural Science Foundation of China[41630319] ; National Key R&D Program of China[2018YFF01013503]
WOS研究方向Geochemistry & Geophysics
语种英语
WOS记录号WOS:000618326800047
出版者SOC EXPLORATION GEOPHYSICISTS
资助机构National Natural Science Foundation of China ; National Natural Science Foundation of China ; National Key R&D Program of China ; National Key R&D Program of China ; National Natural Science Foundation of China ; National Natural Science Foundation of China ; National Key R&D Program of China ; National Key R&D Program of China ; National Natural Science Foundation of China ; National Natural Science Foundation of China ; National Key R&D Program of China ; National Key R&D Program of China ; National Natural Science Foundation of China ; National Natural Science Foundation of China ; National Key R&D Program of China ; National Key R&D Program of China
源URL[http://ir.iggcas.ac.cn/handle/132A11/100061]  
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Yuan, Yu-Xin
作者单位1.Chinese Acad Sci, Inst Earth Sci, Beijing 100029, Peoples R China
2.Univ Chinese Acad Sci, Beijing 100049, Peoples R China
3.Chinese Acad Sci, Inst Geol & Geophys, Key Lab Petr Resources Res, Beijing 100029, Peoples R China
推荐引用方式
GB/T 7714		 Yuan, Yu-Xin,Li, A-Man,Hu, Ting,et al. An anisotropic multilevel preconditioner for solving the Helmholtz equation with unequal directional sampling intervals[J]. GEOPHYSICS,2020,85(6):T293-T300.
APA Yuan, Yu-Xin,Li, A-Man,Hu, Ting,&Liu, Hong.(2020).An anisotropic multilevel preconditioner for solving the Helmholtz equation with unequal directional sampling intervals.GEOPHYSICS,85(6),T293-T300.
MLA Yuan, Yu-Xin,et al."An anisotropic multilevel preconditioner for solving the Helmholtz equation with unequal directional sampling intervals".GEOPHYSICS 85.6(2020):T293-T300.

入库方式： OAI收割

来源：地质与地球物理研究所

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