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Title: A generalized BPX multigrid framework covering nonnested V-cycle methods
Authors: Duan, H.-Y. 
Gao, S.-Q.
Tan, R.C.E. 
Zhang, S.
Keywords: V-cycle nonnested multigrid method
Issue Date: Jan-2007
Source: Duan, H.-Y.,Gao, S.-Q.,Tan, R.C.E.,Zhang, S. (2007-01). A generalized BPX multigrid framework covering nonnested V-cycle methods. Mathematics of Computation 76 (257) : 137-152. ScholarBank@NUS Repository.
Abstract: More than a decade ago, Bramble, Pasciak and Xu developed a framework in analyzing the multigrid methods with nonnested spaces or non-inherited quadratic forms. It was subsequently known as the BPX multigrid framework, which was widely used in the analysis of multigrid and domain decomposition methods. However, the framework has an apparent limit in the analysis of nonnested V-cycle methods, and it produces a variable V-cycle, or nonuniform convergence rate V-cycle methods, or other nonoptimal results in analysis thus far. This paper completes a long-time effort in extending the BPX multigrid framework so that it truly covers the nonnested V-cycle. We will apply the extended BPX framework to the analysis of many V-cycle nonnested multigrid methods. Some of them were proven previously only for two-level and W-cycle iterations. Some numerical results are presented to support the theoretical analysis of this paper. © 2006 American Mathematical Society.
Source Title: Mathematics of Computation
ISSN: 00255718
DOI: 10.1090/S0025-5718-06-01897-7
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