A Scalable Parallel SSOR Preconditioner for Efficient Lattice Computations in Gauge Theories

F54.16> OE; (1) with M being the quark matrix (in analogy to the discretized Laplace equation of classical electrodynamics). Its solution, a Green's function x, describes the time behavior of the quarks [7] and allows to extract physical observables like hadron masses or decay constants. The size of the solution vector is of order O(10 7 ) elements in todays state-of-the-art simulations. The coefficients of the discretized differential operators in M are taken from a stochastic background field that represents the gluons in lattice QCD. Since it turned out that multigrid methods are not very useful in order to improve the speed of the computation of x, attempts have been made to use preconditioning techniques in order to accelerate Krylov subspace solvers like BiCGStab as the current method of choice [8]. 2 1.1. Locally Lexicographic SSOR Preconditioning. Recently