KMS Of Academy of mathematics and systems sciences, CAS
| A NOVEL LEAST SQUARES METHOD FOR HELMHOLTZ EQUATIONS WITH LARGE WAVE NUMBERS | |
| Hu, Qiya1,2; Song, Rongrong1,2 | |
| 2020 | |
| Source Publication | SIAM JOURNAL ON NUMERICAL ANALYSIS
 |
| ISSN | 0036-1429 |
| Volume | 58Issue:5Pages:3091-3123 |
| Abstract | In this paper we are concerned with numerical methods for Helmholtz equations with large wave numbers. We design a least squares method for discretization of the considered Helmholtz equations. In this method, an auxiliary unknown is introduced on the common interface of any two neighboring elements and a quadratic objective functional is defined by the jumps of the traces of the solutions of local Helmholtz equations across all the common interfaces, where the local Helmholtz equations are defined on elements and are imposed Robin-type boundary conditions given by the auxiliary unknowns. A minimization problem with the objective functional is proposed to determine the auxiliary unknowns. The resulting discrete system of the auxiliary unknowns is Hermitian positive definite and so it can be solved by the preconditioned conjugate gradient method. Under some assumptions we show that the generated approximate solutions possess almost the same L-2 convergence order as the plane wave methods (for the case of constant wave number). Moreover, we construct a substructuring preconditioner for the discrete system of the auxiliary unknowns. Numerical experiments show that the proposed methods are very effective and have little "wave number pollution" for the tested Helmholtz equations with large wave numbers. |
| Keyword | Helmholtz equations inhomogeneous media large wave number auxiliary unknowns least squares error estimates preconditioner |
| DOI | 10.1137/19M1294101 |
| Indexed By | SCI |
| Language | 英语 |
| Funding Project | National Natural Science Foundation of China[G12071469] |
| WOS Research Area | Mathematics |
| WOS Subject | Mathematics, Applied |
| WOS ID | WOS:000584721000027 |
| Publisher | SIAM PUBLICATIONS |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/52508 |
| Collection | 中国科学院数学与系统科学研究院 |
| Corresponding Author | Hu, Qiya |
| Affiliation | 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 |
| Recommended Citation GB/T 7714 | Hu, Qiya,Song, Rongrong. A NOVEL LEAST SQUARES METHOD FOR HELMHOLTZ EQUATIONS WITH LARGE WAVE NUMBERS[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS,2020,58(5):3091-3123. |
| APA | Hu, Qiya,&Song, Rongrong.(2020).A NOVEL LEAST SQUARES METHOD FOR HELMHOLTZ EQUATIONS WITH LARGE WAVE NUMBERS.SIAM JOURNAL ON NUMERICAL ANALYSIS,58(5),3091-3123. |
| MLA | Hu, Qiya,et al."A NOVEL LEAST SQUARES METHOD FOR HELMHOLTZ EQUATIONS WITH LARGE WAVE NUMBERS".SIAM JOURNAL ON NUMERICAL ANALYSIS 58.5(2020):3091-3123. |
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