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A TWO-LEVEL PRECONDITIONED HELMHOLTZ-JACOBI-DAVIDSON METHOD FOR THE MAXWELL EIGENVALUE PROBLEM
Liang, Qigang1; Xu, Xuejun1,2
2022-03-01
Source PublicationMATHEMATICS OF COMPUTATION
ISSN0025-5718
Volume91Issue:334Pages:623-657
AbstractIn 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.
KeywordMaxwell eigenvalue problem edge element Helmholtz projection Jacobi-Davidson method domain decomposition
DOI10.1090/mcom/3702
Indexed BySCI
Language英语
Funding ProjectNational 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 Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000771358600004
PublisherAMER MATHEMATICAL SOC
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/60191
Collection计算数学与科学工程计算研究所
Corresponding AuthorXu, Xuejun
Affiliation1.Tongji Univ, Sch Math Sci, Shanghai 200092, Peoples R China
2.Chinese Acad Sci, Inst Computat Math, AMSS, Beijing 100190, Peoples R China
Recommended Citation
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.
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