An Additive Multilevel Preconditioning Method

Nathalie Marco 1 Bruno Koobus 1 Alain Dervieux 1
1 SINUS - Numerical Simulation for the Engineering Sciences
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : This paper describes a new approach of the Multilevel method studied in \citenat2 and \citenat1, in order to solve the 2D Laplace equation. The first approach of the multilevel method is a multiplicative or serial method since each level is addressed sequentially~; it presents, as MG methods, a mesh-independent convergence rate. It is more costly than MG methods, but easier to implement. In order to smooth all the frequency components of the error, the V-cycle strategy is used and it results in several cost functional evaluations per cycle. In this paper, the proposed strategy is based on an additive approach. A preconditionner is deduced from this multilevel method, which provides a better efficiency than the previous method since all frequencies are addressed at the same time, while only one optimization iteration is needed. Furthermore, this method still presents a mesh-independent convergence rate.
Type de document :
Rapport
[Research Report] RR-2310, INRIA. 1994
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Soumis le : mercredi 24 mai 2006 - 15:09:16
Dernière modification le : samedi 27 janvier 2018 - 01:31:28
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Nathalie Marco, Bruno Koobus, Alain Dervieux. An Additive Multilevel Preconditioning Method. [Research Report] RR-2310, INRIA. 1994. 〈inria-00074363〉

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