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A substructuring preconditioner with vertex-related interface solvers for elliptic-type equations in three dimensions
Hu, Qiya1,2; Hu, Shaoliang1,2
2019-06-01
Source PublicationADVANCES IN COMPUTATIONAL MATHEMATICS
ISSN1019-7168
Volume45Issue:3Pages:1129-1161
AbstractIn this paper, we propose a variant of the substructuring preconditioner for solving three-dimensional elliptic-type equations with strongly discontinuous coefficients. In the proposed preconditioner, we use the simplest coarse solver associated with the finite element space induced by the coarse partition and construct inexact interface solvers based on overlapping domain decomposition with small overlaps. This new preconditioner has an important merit: its construction and efficiency do not depend on the concrete form of the considered elliptic-type equations. We apply the proposed preconditioner to solve the linear elasticity problems and Maxwell's equations in three dimensions. Numerical results show that the convergence rate of PCG method with the preconditioner is nearly optimal, and also robust with respect to the (possibly large) jumps of the coefficients in the considered equations.
KeywordDomain decomposition Substructuring preconditioner Linear elasticity problems Maxwell's equations PCG iteration Convergence rate
DOI10.1007/s10444-018-9648-y
Language英语
Funding ProjectNatural Science Foundation of China[G11571352]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000469315500001
PublisherSPRINGER
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/34882
Collection计算数学与科学工程计算研究所
Corresponding AuthorHu, Qiya; Hu, Shaoliang
Affiliation1.Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing 100190, Peoples R China
2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
Recommended Citation
GB/T 7714
Hu, Qiya,Hu, Shaoliang. A substructuring preconditioner with vertex-related interface solvers for elliptic-type equations in three dimensions[J]. ADVANCES IN COMPUTATIONAL MATHEMATICS,2019,45(3):1129-1161.
APA Hu, Qiya,&Hu, Shaoliang.(2019).A substructuring preconditioner with vertex-related interface solvers for elliptic-type equations in three dimensions.ADVANCES IN COMPUTATIONAL MATHEMATICS,45(3),1129-1161.
MLA Hu, Qiya,et al."A substructuring preconditioner with vertex-related interface solvers for elliptic-type equations in three dimensions".ADVANCES IN COMPUTATIONAL MATHEMATICS 45.3(2019):1129-1161.
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