Parallel SSOR preconditioning for lattice QCD

The locally lexicographic symmetric successive overrelaxation algorithm (ll -SSOR) is the most effective parallel preconditioner known for iterative so lvers used in lattice gauge theory. After reviewing the basic properties of ll-SSOR, the focus of this contribution is put on its parallel aspects: th e administrative overhead of the parallel implementation of ll-SSOR, which is due to many conditional operations, decreases its efficiency by a factor of up to one third. A simple generalization of the algorithm is proposed t hat allows the application of the lexicographic ordering along specified ax es, while along the other dimensions odd-even preconditioning is used. In t his way one can tune the preconditioner towards optimal performance by bala ncing ll-SSOR effectivity and administrative overhead. (C) 1999 Elsevier Sc ience B.V. All rights reserved.