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A multigrid-based preconditioner for solving the Helmholtz equation with average-derivative optimal scheme
Yuan YuXin1,2,3,4; Li AMan1,2,3,4; Hu Ting1,2,3,4; Guo Peng5; Liu Hong1,2,3,4
2019-07-01
Source PublicationCHINESE JOURNAL OF GEOPHYSICS-CHINESE EDITION
ISSN0001-5733
Volume62Issue:7Pages:2660-2670
AbstractAn 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.
KeywordMultigrid Anisotropic problem Helmholtz equation Average-derivative optimal scheme
DOI10.6038/cjg2019M0265
WOS KeywordFINITE-DIFFERENCE ; OPTIMAL 9-POINT ; WAVE-EQUATION ; DEFLATION
Language英语
WOS Research AreaGeochemistry & Geophysics
WOS SubjectGeochemistry & Geophysics
WOS IDWOS:000474879800023
PublisherSCIENCE PRESS
Citation statistics
Document Type期刊论文
Identifierhttp://ir.iggcas.ac.cn/handle/132A11/92670
Collection油气资源研究院重点实验室
Corresponding AuthorLiu Hong
Affiliation1.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
First Author AffilicationInstitute of Geology and Geophysics, Chinese Academy of Sciences
Corresponding Author AffilicationInstitute of Geology and Geophysics, Chinese Academy of Sciences
Recommended Citation
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.
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