par Notay, Yvan 
;Muresan, Adrian
Référence SIAM journal on scientific computing, 30, page (1082-1103)
Publication Publié, 2008
;Muresan, Adrian Référence SIAM journal on scientific computing, 30, page (1082-1103)
Publication Publié, 2008
Article révisé par les pairs
| Résumé : | 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. © 2008 Society for Industrial and Applied Mathematics. |
