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

solver We extend the parallel SSOR procedure for the eecient preconditioning of modern Krylov subspace solvers 1], recently introduced in 2] towards higher order, quantum-improved discretization schemes 3] for lattice quantum chromodynamics 4]. 1. Solving linear systems in LGT. Lattice gauge theory (LGT) deals with the controlled numerical evaluation of gauge theories like quantum chromodynamics (QCD) put on a 4-dimensional space-time-grid which, in the low energy regime, cannot be solved by non-perturbative analytical methods. QCD 5] is considered as the fundamental theory of the strong forces that bind quarks with gluons to form the known hadrons like the proton or the neutron. Very large scale LGT simulations become more and more essential to provide theoretical input for current and future accelerator experiments that attempt to observe new physics beyond the Standard Model of elementary particle physics 6]. The most heavy computational demands in LGT arise from the repeated computation of a huge system of linear equations, Mx = ; (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 coeecients of the discretized diierential operators in M are taken from a stochastic background eld that represents the gluons in lattice QCD. Since it turned out that multi