A TWO-LEVEL PRECONDITIONED HELMHOLTZ-JACOBI-DAVIDSON METHOD FOR THE MAXWELL EIGENVALUE PROBLEM

doi:10.1090/mcom/3702

	A TWO-LEVEL PRECONDITIONED HELMHOLTZ-JACOBI-DAVIDSON METHOD FOR THE MAXWELL EIGENVALUE PROBLEM
	Liang, Qigang 1; Xu, Xuejun1,2
	2022-03-01
发表期刊	MATHEMATICS OF COMPUTATION
ISSN	0025-5718
卷号	91 期号:334 页码:623-657
摘要	In this paper, based on a domain decomposition method, we propose an efficient two-level preconditioned Helmholtz-Jacobi-Davidson (PHJD) method for solving the algebraic eigenvalue problem resulting from the edge element approximation of the Maxwell eigenvalue problem. In order to eliminate the components in orthogonal complement space of the eigenvalue, we shall solve a parallel preconditioned system and a Helmholtz projection system together in fine space. After one coarse space correction in each iteration and minimizing the Rayleigh quotient in a small dimensional Davidson space, we finally get the error reduction of this two-level PHJD method as gamma = c(H)(1 - C delta(2)/H-2), where C is a constant independent of the mesh size h and the diameter of subdomains H, delta is the overlapping size among the subdomains, and c(H) decreasing monotonically to 1 as H -> 0, which means the greater the number of subdomains, the better the convergence rate. Numerical results supporting our theory are given.
关键词	Maxwell eigenvalue problem edge element Helmholtz projection Jacobi-Davidson method domain decomposition
DOI	10.1090/mcom/3702
收录类别	SCI
语种	英语
资助项目	National Natural Science Foundation of China[12071350] ; National Natural Science Foundation of China[11871272] ; Shanghai Municipal Science and Technology Major Project[2021SHZDZX0100] ; Science and Technology Commission of Shanghai Municipality
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000771358600004
出版者	AMER MATHEMATICAL SOC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/60191
专题	计算数学与科学工程计算研究所
通讯作者	Xu, Xuejun
作者单位	1.Tongji Univ, Sch Math Sci, Shanghai 200092, Peoples R China 2.Chinese Acad Sci, Inst Computat Math, AMSS, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Liang, Qigang,Xu, Xuejun. A TWO-LEVEL PRECONDITIONED HELMHOLTZ-JACOBI-DAVIDSON METHOD FOR THE MAXWELL EIGENVALUE PROBLEM[J]. MATHEMATICS OF COMPUTATION,2022,91(334):623-657.
APA	Liang, Qigang,&Xu, Xuejun.(2022).A TWO-LEVEL PRECONDITIONED HELMHOLTZ-JACOBI-DAVIDSON METHOD FOR THE MAXWELL EIGENVALUE PROBLEM.MATHEMATICS OF COMPUTATION,91(334),623-657.
MLA	Liang, Qigang,et al."A TWO-LEVEL PRECONDITIONED HELMHOLTZ-JACOBI-DAVIDSON METHOD FOR THE MAXWELL EIGENVALUE PROBLEM".MATHEMATICS OF COMPUTATION 91.334(2022):623-657.