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Convergence analysis on multigrid methods for elliptic problems with large jumps in coefficients
Zheng, Hui1; Wu, Jinbiao2
2015-10-01
Source PublicationIMA JOURNAL OF NUMERICAL ANALYSIS
ISSN0272-4979
Volume35Issue:4Pages:1888-1912
AbstractIn this paper, we investigate the multigrid methods for the linear finite element approximation of elliptic problems with large jumps in coefficients. Some singular functions, which cause the deterioration of the convergence rate, are introduced in our space splitting. According to the space splitting, we construct a modified multigrid method and prove that its uniform convergence is independent of the mesh size and the jumps. As a result, we also prove that the conjugate gradient method with the 'V'-cycle multigrid preconditioner converges uniformly.
Keywordmultigrid method jump coefficient problem discrete harmonic extension nearly singular problem preconditioned conjugate gradient method
DOI10.1093/imanum/dru055
Language英语
Funding ProjectNational Science Foundation of China (NSFC)[10971006] ; National Science Foundation of China (NSFC)[91130011] ; NSFC[91130001] ; NSFC[11421101]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000362826000015
PublisherOXFORD UNIV PRESS
Citation statistics
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/21011
Collection中国科学院数学与系统科学研究院
Affiliation1.Chinese Acad Sci, Inst Computat Math & Sci Engn Comp, Beijing 100080, Peoples R China
2.Peking Univ, Sch Math Sci, HEDPS, CAPT & LMAM, Beijing 100871, Peoples R China
Recommended Citation
GB/T 7714
Zheng, Hui,Wu, Jinbiao. Convergence analysis on multigrid methods for elliptic problems with large jumps in coefficients[J]. IMA JOURNAL OF NUMERICAL ANALYSIS,2015,35(4):1888-1912.
APA Zheng, Hui,&Wu, Jinbiao.(2015).Convergence analysis on multigrid methods for elliptic problems with large jumps in coefficients.IMA JOURNAL OF NUMERICAL ANALYSIS,35(4),1888-1912.
MLA Zheng, Hui,et al."Convergence analysis on multigrid methods for elliptic problems with large jumps in coefficients".IMA JOURNAL OF NUMERICAL ANALYSIS 35.4(2015):1888-1912.
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