KMS Of Academy of mathematics and systems sciences, CAS
| SUBSTRUCTURING PRECONDITIONERS FOR THE SYSTEMS ARISING FROM PLANE WAVE DISCRETIZATION OF HELMHOLTZ EQUATIONS | |
Hu, Qiya ; Zhang, Haiyang
| |
| 2016 | |
| Source Publication | SIAM JOURNAL ON SCIENTIFIC COMPUTING
 |
| ISSN | 1064-8275 |
| Volume | 38Issue:4Pages:A2232-A2261 |
| Abstract | In this paper we are concerned with the plane wave methods for Helmholtz equations with large wave numbers. We extend the plane wave weighted least-squares (PWLS) method and the plane wave discontinuous Galerkin (PWDG) method to Helmholtz equations in inhomogeneous mediums and with mixed boundary conditions. The main goal of this paper is to construct parallel preconditioners for solving the resulting discrete systems. To this end, we design a kind of substructuring domain decomposition preconditioner for both the two-dimensional case and the three-dimensional case, which is different from the existing substructuring preconditioners. We apply the proposed preconditioner to solve the Helmholtz systems generated by the PWLS method or the PWDG method, and we find that the new preconditioners with practical coarse mesh sizes possess relatively stable convergence, i.e., the iteration counts of the corresponding iterative methods (PCG or preconditioned GMRES) increase slowly when the wave number increases (and the mesh size decreases). |
| Keyword | Helmholtz equation large wave number plane wave discretization nonoverlapping domain decomposition parallel preconditioner iteration counts |
| DOI | 10.1137/151003040 |
| Language | 英语 |
| Funding Project | Natural Science Foundation of China[G11571352] |
| WOS Research Area | Mathematics |
| WOS Subject | Mathematics, Applied |
| WOS ID | WOS:000385283400014 |
| Publisher | SIAM PUBLICATIONS |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/23762 |
| Collection | 计算数学与科学工程计算研究所 |
| Affiliation | Chinese Acad Sci, Acad Math & Syst Sci, LSEC, Inst Computat Math & Sci Engn Comp, Beijing 100190, Peoples R China |
| Recommended Citation GB/T 7714 | Hu, Qiya,Zhang, Haiyang. SUBSTRUCTURING PRECONDITIONERS FOR THE SYSTEMS ARISING FROM PLANE WAVE DISCRETIZATION OF HELMHOLTZ EQUATIONS[J]. SIAM JOURNAL ON SCIENTIFIC COMPUTING,2016,38(4):A2232-A2261. |
| APA | Hu, Qiya,&Zhang, Haiyang.(2016).SUBSTRUCTURING PRECONDITIONERS FOR THE SYSTEMS ARISING FROM PLANE WAVE DISCRETIZATION OF HELMHOLTZ EQUATIONS.SIAM JOURNAL ON SCIENTIFIC COMPUTING,38(4),A2232-A2261. |
| MLA | Hu, Qiya,et al."SUBSTRUCTURING PRECONDITIONERS FOR THE SYSTEMS ARISING FROM PLANE WAVE DISCRETIZATION OF HELMHOLTZ EQUATIONS".SIAM JOURNAL ON SCIENTIFIC COMPUTING 38.4(2016):A2232-A2261. |
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