KMS Of Academy of mathematics and systems sciences, CAS
LOCAL MULTILEVEL METHODS FOR SECOND-ORDER ELLIPTIC PROBLEMS WITH HIGHLY DISCONTINUOUS COEFFICIENTS | |
其他题名 | Local Multilevel Methods for Second-Order Elliptic Problems with Highly Discontinuous Coefficients |
Chen Huangxin1; Xu Xuejun2; Zheng Weiying2 | |
2012 | |
发表期刊 | JOURNAL OF COMPUTATIONAL MATHEMATICS |
ISSN | 0254-9409 |
卷号 | 30期号:3页码:223-248 |
摘要 | 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. |
其他摘要 | 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. |
关键词 | 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 |
收录类别 | CSCD |
语种 | 英语 |
资助项目 | [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记录号 | CSCD:4564407 |
引用统计 | |
文献类型 | 期刊论文 |
条目标识符 | http://ir.amss.ac.cn/handle/2S8OKBNM/57391 |
专题 | 中国科学院数学与系统科学研究院 |
作者单位 | 1.厦门大学 2.中国科学院数学与系统科学研究院 |
推荐引用方式 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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