KMS Of Academy of mathematics and systems sciences, CAS
| A TWO-LEVEL PRECONDITIONED HELMHOLTZ-JACOBI-DAVIDSON METHOD FOR THE MAXWELL EIGENVALUE PROBLEM | |
Liang, Qigang1; Xu, Xuejun1,2
| |
| 2022-03-01 | |
| Source Publication | MATHEMATICS OF COMPUTATION
 |
| ISSN | 0025-5718 |
| Volume | 91Issue:334Pages:623-657 |
| Abstract | 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. |
| Keyword | Maxwell eigenvalue problem edge element Helmholtz projection Jacobi-Davidson method domain decomposition |
| DOI | 10.1090/mcom/3702 |
| Indexed By | SCI |
| Language | 英语 |
| Funding Project | 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 Research Area | Mathematics |
| WOS Subject | Mathematics, Applied |
| WOS ID | WOS:000771358600004 |
| Publisher | AMER MATHEMATICAL SOC |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/60191 |
| Collection | 计算数学与科学工程计算研究所 |
| Corresponding Author | Xu, Xuejun |
| Affiliation | 1.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. |
| Files in This Item: | There are no files associated with this item. | |||||
Items in the repository are protected by copyright, with all rights reserved, unless otherwise indicated.
Edit Comment