Hierarchical Diagonal Blocking and Precision Reduction Applied to Combinatorial Multigrid
Proceedings of the 2010 ACM/IEEE International Conference for High Performance Computing, Networking, Storage and Analysis
Smoothed Aggregation Multigrid for Markov Chains
SIAM Journal on Scientific Computing
Computer Vision and Image Understanding
On-the-Fly Adaptive Smoothed Aggregation Multigrid for Markov Chains
SIAM Journal on Scientific Computing
PowerRush: a linear simulator for power grid
Proceedings of the International Conference on Computer-Aided Design
An Algebraic Multigrid Method with Guaranteed Convergence Rate
SIAM Journal on Scientific Computing
| Hi-index | 0.01 |
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 two-dimensional 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.