Convergence of Algebraic Multigrid Based on Smoothed Aggregation II: Extension to a Petrov-Galerkin Method - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Reports Year : 1999

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

Ales Janka
  • Function : Author
Hervé Guillard

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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Dates and versions

inria-00072986 , version 1 (24-05-2006)

Identifiers

  • HAL Id : inria-00072986 , version 1

Cite

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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