An explicit formulation of the multiplicative Schwarz preconditioner

Authors:
Guy Antoine Atenekeng Kahou;Emmanuel Kamgnia;Bernard Philippe
Affiliations:
Department of Computer Science, University of Yaounde 1, PO Box 812, Yaounde, Cameroon and IRISA/INRIA, Campus Beaulieu, 35042 Rennes cedex, France;Department of Computer Science, University of Yaounde 1, PO Box 812, Yaounde, Cameroon;IRISA/INRIA, Campus Beaulieu, 35042 Rennes cedex, France
Venue:
Applied Numerical Mathematics
Year:
2007

Citing 3
Cited 2

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Abstract

Efficient preconditioners can be defined from domain decompositions with overlapping when solving linear systems arising from a PDE discretization. Partitioning of the domain entails a corresponding block partitioning of the matrix. It is known that Schwarz's methods (additive and multiplicative) correspond to given splittings of the matrix. An explicit formulation of the splitting was only known for the additive situation. An explicit splitting associated with the multiplicative Schwarz iteration is provided. The advantage of considering the explicit formulation, when the iteration is used as a preconditioner for a Krylov method, is shown.