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A generalized BPX multigrid framework covering nonnested V-cycle methods


Authors: Huo-Yuan Duan, Shao-Qin Gao, Roger C. E. Tan and Shangyou Zhang
Journal: Math. Comp. 76 (2007), 137-152
MSC (2000): Primary 65N55, 65N30, 65F10
DOI: https://doi.org/10.1090/S0025-5718-06-01897-7
Published electronically: August 31, 2006
Erratum: Math. Comp 76 (2007), 2251
MathSciNet review: 2261015
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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.


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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
Email: szhang@udel.edu

DOI: https://doi.org/10.1090/S0025-5718-06-01897-7
Keywords: V-cycle nonnested multigrid method
Received by editor(s): July 21, 2001
Received by editor(s) in revised form: November 27, 2005
Published electronically: August 31, 2006
Article copyright: © Copyright 2006 American Mathematical Society

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