# Analysis of aggregation-based multigrid

## Abstract

Aggregation-based multigrid with standard piecewise constant like prolongation is investigated. Unknowns are aggregated either by pairs or by quadruplets; in the latter case the grouping may be either linewise or boxwise. A Fourier analysis is developed for a model twodimensional anisotropic problem. Most of the results are stated for an arbitrary smoother (which fits with the Fourier analysis framework). It turns out that the convergence factor of two-grid schemes can be bounded independently of the grid size. With a sensible choice of the (linewise or boxwise) coarsening, the bound is also uniform with respect to the anisotropy ratio, without requiring a specialized smoother. The bound is too large to guarantee optimal convergence properties with the V-cycle or the standard W-cycle, but a W-cycle scheme accelerated by the recursive use of the conjugate gradient method exhibits near grid independent convergence

## Authors

Adrian C. Muresan
Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy

Yvan Notay
Universite Libre de Bruxelles, Service de Metrologie Nucleaire (C.P. 165/84), 50, Av. F.D. Roosevelt, B-1050 Brussels, Belgium

## Keywords

multigrid; aggregation; Fourier analysis; Krylov subspace method; conjugate gradient; preconditioning

### References

See the expanding block below.

## Paper coordinates

A.C. Muresan, Y. Notay,  Analysis of aggregation-based multigrid, SIAM J. SCI. COMPUT. c 2008 Society for Industrial and Applied Mathematics, Vol. 30, No. 2, pp. 1082–1103, 10.1137/060678397

## PDF

http://doi.org/10.1137/060678397

## About this paper

##### Journal

SIAM Journal  on Scientific Computing

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