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NOVEL MULTILEVEL PRECONDITIONERS FOR THE SYSTEMS ARISING FROM PLANE WAVE DISCRETIZATION OF HELMHOLTZ EQUATIONS WITH LARGE WAVE NUMBERS
Hu, Qiya1,2; Li, Xuan3
2017
Source PublicationSIAM JOURNAL ON SCIENTIFIC COMPUTING
ISSN1064-8275
Volume39Issue:4Pages:A1675-A1709
AbstractIn 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).
KeywordHelmholtz equation large wave numbers plane wave methods multilevel overlapping domain decomposition multilevel overlapping preconditioner smoothers
DOI10.1137/15M1022963
Language英语
Funding ProjectNational Natural Science Foundation of China[G11571352]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000408922600030
PublisherSIAM PUBLICATIONS
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/26535
Collection计算数学与科学工程计算研究所
Corresponding AuthorHu, Qiya
Affiliation1.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
Recommended Citation
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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