Parallel Smoothed Aggregation Multigrid : Aggregation Strategies on Massively Parallel Machines

Algebraic multigrid methods offer the hope that multigrid convergence can be achieved (for at least some important applications) without a great deal of effort from engineers and scientists wishing to solve linear systems. In this paper we consider parallelization of the smoothed aggregation multigrid method. Smoothed aggregation is one of the most promising algebraic multigrid methods. Therefore, developing parallel variants with both good convergence and efficiency properties is of great importance. However, par- allelization is nontrivial due to the somewhat sequential aggregation (or grid coarsening) phase. In this paper, we discuss three difibrent parallel aggre- gation algorithms and illustrate the advantages and disadvantages of each variant in terms of parallelism and convergence. Numerical results will be shown on the Intel Teraflop computer for some large problems coming from nontrivial codes: quasi-static electric potential simulation and a fluid flow calculation.