New Multigrid Solver Advances in TOPS

Abstract. In this paper, we highlight new multigrid solver advances in the Terascale Optimal PDE Simulations (TOPS) project in the Scienti¯c Discovery Through Advanced Computing (SciDAC) program. We discuss two new algebraic multigrid (AMG) developments in TOPS: the adaptive smoothed aggregation method (®SA) and a coarse-grid selection algorithm based on compatible relaxation (CR). The ®SA method is showing promising results in initial studies for Quantum Chromodynamics (QCD) applications. The CR method has the potential to greatly improve the applicability of AMG. 1