Parallel SSOR preconditioning for lattice QCD

The locally-lexicographic symmetric successive overrelaxation algorithm (ll-SSOR) is the most eeective parallel preconditioner known for iterative solvers used in lattice gauge theory. After reviewing the basic properties of ll-SSOR, the focus of this contribution is put on its parallel aspects: the administrative overhead of the parallel implementation of ll-SSOR, which is due to many conditional operations, decreases its eeciency by a factor of up to one third. A simple generalization of the algorithm is proposed that allows the application of the lexicographic ordering along speciied axes, while along the other dimensions odd-even preconditioning is used. In this way one can tune the preconditioner towards optimal performance by balancing ll-SSOR eeectivity and administrative overhead.