Convergence of Algebraic Multigrid Based on Smoothed Aggregation II: Extension to a Petrov-Galerkin Method

Petr Vanek 1 Ales Janka Hervé Guillard
1 SINUS - Numerical Simulation for the Engineering Sciences
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : We give a convergence estimate for a Petrov-Galerkin Algebraic Multigrid method. In this method, the prolongations are defined using the concept of smoothed aggregation while the restrictions are simple aggregation operators. The analysis is carried out by showing that these methods can be interpreted as variational Ritz-Galerkin ones using modified transfer and smoothing operators. The estimate depends only on a weak approximation property for the aggregation operators. For a scalar second order elliptic problem using linear elements, this assumption is shown to hold using simple geometrical arguments on the aggregates.
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RR-3683, INRIA. 1999
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Soumis le : mercredi 24 mai 2006 - 11:31:23
Dernière modification le : samedi 27 janvier 2018 - 01:31:28
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Petr Vanek, Ales Janka, Hervé Guillard. Convergence of Algebraic Multigrid Based on Smoothed Aggregation II: Extension to a Petrov-Galerkin Method. RR-3683, INRIA. 1999. 〈inria-00072986〉

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