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Analysis of an algebraic Petrov-Galerkin smoothed aggregation multigrid method

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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https://hal.inria.fr/hal-00871721
Contributor : Herve Guillard Connect in order to contact the contributor
Submitted on : Thursday, October 10, 2013 - 11:36:17 AM
Last modification on : Saturday, June 25, 2022 - 11:11:45 PM

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Hervé Guillard, Aleš Janka, Petr Vaněk. Analysis of an algebraic Petrov-Galerkin smoothed aggregation multigrid method. Applied Numerical Mathematics, Elsevier, 2008, 58 (12), pp.1861-1874. ⟨10.1016/j.apnum.2007.11.008⟩. ⟨hal-00871721⟩

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