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On Hybrid Multigrid-Schwarz Algorithms

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics, Temple University (038-16), 1805 N. Broad Street, Philadelphia, PA, 19122-6094, USA

    Sébastien Loisel & Daniel B. Szyld

  2. Institut für Mathematik, Technische Universität Berlin, 10623, Berlin, Germany

    Reinhard Nabben

Authors
  1. Sébastien Loisel
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  2. Reinhard Nabben
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  3. Daniel B. Szyld
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Correspondence to Daniel B. Szyld.

Additional information

S. Loisel and D.B. Szyld are supported in part by the U.S. Department of Energy under grant DE-FG02-05ER25672.

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Loisel, S., Nabben, R. & Szyld, D.B. On Hybrid Multigrid-Schwarz Algorithms. J Sci Comput 36, 165–175 (2008). https://doi.org/10.1007/s10915-007-9183-3

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