Parallel Smoothed Aggregation Multigrid : Aggregation Strategies on Massively Parallel Machines

Abstract

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