A generalized BPX multigrid framework covering nonnested V-cycle methods
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- by Huo-Yuan Duan, Shao-Qin Gao, Roger C. E. Tan and Shangyou Zhang PDF
- Math. Comp. 76 (2007), 137-152 Request permission
Erratum: Math. Comp. 76 (2007), 2251-2251.
Abstract:
More than a decade ago, Bramble, Pasciak and Xu developed a framework in analyzing the multigrid methods with nonnested spaces or noninherited 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.References
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Additional Information
- Huo-Yuan Duan
- Affiliation: Department of Mathematics, National University of Singapore, 2 Science Drive 2, Singapore 117543
- Email: scidhy@nus.edu.sg
- Shao-Qin Gao
- Affiliation: College of Mathematics and Computers, Hebei University, 071002, 1 Hezuo Road, Baoding, Hebei, China
- Email: gaoshq@amss.ac.cn.
- Roger C. E. Tan
- Affiliation: Department of Mathematics, National University of Singapore, 2 Science Drive 2, Singapore 117543
- Email: scitance@nus.edu.sg.
- Shangyou Zhang
- Affiliation: Department of Mathematical Sciences, University of Delaware, Newark, Delaware 19716
- MR Author ID: 261174
- Email: szhang@udel.edu
- Received by editor(s): July 21, 2001
- Received by editor(s) in revised form: November 27, 2005
- Published electronically: August 31, 2006
- © Copyright 2006 American Mathematical Society
- Journal: Math. Comp. 76 (2007), 137-152
- MSC (2000): Primary 65N55, 65N30, 65F10
- DOI: https://doi.org/10.1090/S0025-5718-06-01897-7
- MathSciNet review: 2261015