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A critical analysis of multigrid methods on massively parallel computers. (English) Zbl 0830.65110
Hemker, P. W. (ed.) et al., Contributions to multigrid. A selection of contributions to the 4th European Multigrid Conference, held in Amsterdam, the Netherlands, July 6 - 9, 1993. Amsterdam: CWI. CWI Tracts. 103, 155-168 (1994).
The hierarchical nature of multigrid algorithms leaves domain parallel strategies with a deficiency of parallelism as the computation moves to coarser and coarser grids. To introduce more parallelism several strategies have been designed to project the original problem space into non-interferring subspaces, allowing all grids to relax concurrently.
Our objective is to understand the potential efficiency of standard and concurrent multigrid algorithms on existing and proposed massively parallel machines. We study model problems on simple domains discretized with finite difference techniques on block structured meshes in two and three dimensions with up to \(10^6\) and \(10^9\) points, respectively. Performance of the standard domain parallel \(V\) and \(F\) cycle schemes is compared to several proposed concurrent algorithms.
For the entire collection see [Zbl 0810.00028].

65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
65Y05 Parallel numerical computation
65N06 Finite difference methods for boundary value problems involving PDEs