A substructuring preconditioner with vertex-related interface solvers for elliptic-type equations in three dimensions

doi:10.1007/s10444-018-9648-y

	A substructuring preconditioner with vertex-related interface solvers for elliptic-type equations in three dimensions
	Hu, Qiya1,2 ; Hu, Shaoliang 1,2
	2019-06-01
发表期刊	ADVANCES IN COMPUTATIONAL MATHEMATICS
ISSN	1019-7168
卷号	45 期号:3 页码:1129-1161
摘要	In 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.
关键词	Domain decomposition Substructuring preconditioner Linear elasticity problems Maxwell's equations PCG iteration Convergence rate
DOI	10.1007/s10444-018-9648-y
语种	英语
资助项目	Natural Science Foundation of China[G11571352]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000469315500001
出版者	SPRINGER
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/34882
专题	计算数学与科学工程计算研究所
通讯作者	Hu, Qiya; Hu, Shaoliang
作者单位	1.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
推荐引用方式 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.