Analysis of Aggregation-Based Multigrid

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