Scalable Parallel SSOR Preconditioning for Lattice Computations in Gauce Theories

We discuss a parallelization scheme for SSOR precondition-ing of Krylov subspace solvers as applied in lattice gauge theory computations. Our preconditioner is based on a locally lexicographic ordering of the lattice points leading to a parallelism adapted to the parallel system's size. By exploitation of thèEisenstat-trick' within the bi-conjugate gradient stabilized iterative solver, we achieve a gain factor of about 2 in the number of iterations compared to conventional state-of-the-art odd-even preconditioning. We describe the implementation of the scheme on the APE100/Quadrics SIMD parallel computer in the realistic setting of a large scale lattice quantum chromodynamics simulation.