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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


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


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


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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



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