Highly Optimized Code for Lattice Quantum Chromodynamics on the CRAY T3E

In order to compute physical quantities in lattice quantum chromodynamics huge systems of linear equations have to be solved. The availability of eecient parallel Krylov subspace solvers plays a vital role in the solution of these systems. We present a detailed analysis of the performance of the stabilized biconjugate gradient (BiCGStab) algorithm with symmetric successive over-relaxed (SSOR) preconditioning on a massively parallel CRAY T3E system. The numerical investigation of quantum chromodynamics (QCD) on a four-dimensional space-time grid is one of the grand challenges in high-performance scientiic computing 1]. QCD is generally considered to be the fundamental theory which describes the strong forces binding quarks with gluons to form the known hadrons like the proton or neutron 2]. Even after 20 years of research, QCD still has not been solved in a non-perturbative analytical approach, and it is by now widely believed that the controlled numerical treatment of the theory on the lattice using very fast parallel supercomputers is the only viable scheme to extract quantitative physical results 3]. The results from lattice gauge theory (LGT) simulations are urgently needed as theoretical input for current and future accelerator experiments that attempt to observe new physics beyond the Standard Model of elementary particle physics 4]. LGT computes functional integrals using Monte Carlo methods known from statistical physics 5]. A representative ensemble of eld conngurations is generated by a Markov process (simulation phase). These conngurations are subsequently analysed by constructing (and averaging over) hadronic correlators from quark Green's functions (analysis phase). Subsequently correlators serve to extract physical observables of interest like hadron masses and decay constants.