Adaptive smoothed aggregation in lattice QCD

Summary. The linear systems arising in lattice quantum chromodynamics (QCD) pose significant challenges for traditional iterative solvers. The Dirac operator as-sociated with these systems is nearly singular, indicating the need for efficient pre-conditioners. Multilevel preconditioners cannot, however, be easily constructed for these systems becasue the Dirac operator has multiple locally distinct near-kernel components (the so-called slow-to-converge error components of relaxation) that are generally both oscillatory and not known a priori. This paper presents heuristic ar-guments and numerical results demonstrating that the recently developed adaptive smoothed aggregation (αSA) [BFM+04] methodology can be used to overcome the challenges posed by these systems.