On Hybrid Multigrid-Schwarz Algorithms

J. Lottes and P. Fischer (J. Sci. Comput. 24:45–78, [ 2005 ]) studied many smoothers or preconditioners for hybrid Multigrid-Schwarz algorithms for the spectral element method. The behavior of several of these smoothers or preconditioners are analyzed in the present paper. Here it is shown that the...

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Bibliographic Details
Published in:Journal of scientific computing 2008-08, Vol.36 (2), p.165-175
Main Authors: Loisel, Sébastien, Nabben, Reinhard, Szyld, Daniel B.
Format: Article
Language:English
Subjects:
Additives
Algorithms
Computation
Computational Mathematics and Numerical Analysis
Convergence
Equivalence
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Spectral element method
Theoretical
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Summary:J. Lottes and P. Fischer (J. Sci. Comput. 24:45–78, [ 2005 ]) studied many smoothers or preconditioners for hybrid Multigrid-Schwarz algorithms for the spectral element method. The behavior of several of these smoothers or preconditioners are analyzed in the present paper. Here it is shown that the Schwarz smoother that best performs in the above reference, is equivalent to a special case of the weighted restricted additive Schwarz, for which convergence analysis is presented. For other preconditioners which do not perform as well, examples and explanations are presented illustrating why this behavior may occur.
ISSN:0885-7474
1573-7691
DOI:10.1007/s10915-007-9183-3