KMS Of Academy of mathematics and systems sciences, CAS
| LOCAL MULTILEVEL METHODS FOR SECOND-ORDER ELLIPTIC PROBLEMS WITH HIGHLY DISCONTINUOUS COEFFICIENTS | |
| Alternative Title | Local Multilevel Methods for Second-Order Elliptic Problems with Highly Discontinuous Coefficients |
| Chen Huangxin1; Xu Xuejun2; Zheng Weiying2 | |
| 2012 | |
| Source Publication | JOURNAL OF COMPUTATIONAL MATHEMATICS
 |
| ISSN | 0254-9409 |
| Volume | 30Issue:3Pages:223-248 |
| Abstract | In this paper, local multiplicative and additive multilevel methods on adaptively refined meshes are considered for second-order elliptic problems with highly discontinuous coefficients. For the multilevel-preconditioned system, we study the distribution of its spectrum by using the abstract Schwarz theory. It is proved that, except for a few small eigenvalues, the spectrum of the preconditioned system is bounded quasi-uniformly with respect to the jumps of the coefficient and the mesh sizes. The convergence rate of multilevel-preconditioned conjugate gradient methods is shown to be quasi-optimal regarding the jumps and the meshes. Numerical experiments are presented to illustrate the theoretical findings. |
| Other Abstract | In this paper, local multiplicative and additive multilevel methods on adaptively refined meshes are considered for second-order elliptic problems with highly discontinuous coefficients. For the multilevel-preconditioned system, we study the distribution of its spectrum by using the abstract Schwarz theory. It is proved that, except for a few small eigenvalues, the spectrum of the preconditioned system is bounded quasi-uniformly with respect to the jumps of the coefficient and the mesh sizes. The convergence rate of multilevel-preconditioned conjugate gradient methods is shown to be quasi-optimal regarding the jumps and the meshes. Numerical experiments are presented to illustrate the theoretical findings. |
| Keyword | BOUNDARY-VALUE-PROBLEMS WEIGHTED L2 PROJECTION FINITE-ELEMENT METHODS MULTIGRID V-CYCLE DOMAIN DECOMPOSITION 3 DIMENSIONS ITERATIVE METHODS ERROR ESTIMATORS SCHWARZ METHODS REFINED MESHES Local multilevel method Adaptive finite element method Preconditioned conjugate gradient method Discontinuous coefficients |
| Indexed By | CSCD |
| Language | 英语 |
| Funding Project | [National Basic Research Program] ; [National Science Foundation of China] ; [China NSF] ; [Funds for Creative Research Groups of China] ; [National Magnetic Confinement Fusion Science Program] |
| CSCD ID | CSCD:4564407 |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/57391 |
| Collection | 中国科学院数学与系统科学研究院 |
| Affiliation | 1.厦门大学 2.中国科学院数学与系统科学研究院 |
| Recommended Citation GB/T 7714 | Chen Huangxin,Xu Xuejun,Zheng Weiying. LOCAL MULTILEVEL METHODS FOR SECOND-ORDER ELLIPTIC PROBLEMS WITH HIGHLY DISCONTINUOUS COEFFICIENTS[J]. JOURNAL OF COMPUTATIONAL MATHEMATICS,2012,30(3):223-248. |
| APA | Chen Huangxin,Xu Xuejun,&Zheng Weiying.(2012).LOCAL MULTILEVEL METHODS FOR SECOND-ORDER ELLIPTIC PROBLEMS WITH HIGHLY DISCONTINUOUS COEFFICIENTS.JOURNAL OF COMPUTATIONAL MATHEMATICS,30(3),223-248. |
| MLA | Chen Huangxin,et al."LOCAL MULTILEVEL METHODS FOR SECOND-ORDER ELLIPTIC PROBLEMS WITH HIGHLY DISCONTINUOUS COEFFICIENTS".JOURNAL OF COMPUTATIONAL MATHEMATICS 30.3(2012):223-248. |
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