Many Masses on One Stroke: Economic Computation of Quark Propagators

The computational effort in the calculation of Wilson fermion quark propagators in Lattice Quantum Chromodynamics can be considerably reduced by exploiting the Wilson fermion matrix structure in inversion algorithms based on the non-symmetric Lanczos process. We consider two such methods: QMR (quasi minimal residual) and BCG (biconjugate gradients). Based on the decomposition $M/\kappa={\bf 1}/\kappa-D$ of the Wilson mass matrix, using QMR, one can carry out inversions on a {\em whole} trajectory of masses simultaneously, merely at the computational expense of a single propagator computation. In other words, one has to compute the propagator corresponding to the lightest mass only, while all the heavier masses are given for free, at the price of extra storage. Moreover, the symmetry $\gamma_5\, M= M^{\dagger}\,\gamma_5$ can be used to cut the computational effort in QMR and BCG by a factor of two. We show that both methods then become---in the critical regime of small quark masses---competitive to BiCGStab and significantly better than the standard MR method, with optimal relaxation factor, and CG as applied to the normal equations.Comment: 17 pages, uuencoded compressed postscrip

Dynamical Quark Effects in QCD

We discuss latest results of lattice QCD simulations with dynamical fermions. Special emphasis is paid to the subjects of the static quark potential, the light hadron spectrum, $\Upsilon$ spectrum, and the pion-nucleon-sigma term.Comment: 6 pages, 9 figures, invited talk at LAT9

String Breaking in Quenched QCD

We present preliminary quenched results on a new operator for the investigation of string-breaking within SU(2)-colour QCD. The ground-state of a spatially-separated static-light meson-antimeson pair is a combination of a state with two distinct mesons, expected to dominate for large separations, and a state where the light-quarks have annihilated, which contributes for short distances. The crossover between these two regimes provides a measure of the string-breaking scale length.Comment: LATTICE98(confine), 3 pages, 4 figure

Lattice QCD with Two Dynamical Wilson Fermions on APE100 Parallel Systems

The cost for stochastic sampling of QCD vacuum configurations outweighs by far the costs of the remaining computational tasks in Lattice QCD, due to the nonlocal forces arising from the dynamics of fermion loops in the vacuum fluctuations. The evaluation of quality and hence efficiency of sampling algorithms is largely determined by the assessment of their decorrelation capacity along the Monte Carlo time series. In order to gain control over statistical errors, state-of-the-art research and development on QCD sampling algorithms needs substantial amount of Teraflopshours. Over the past years two German-Italian collaborations, SESAM and TØL, carried out exploratory simulations, joining their resources in a meta-computing effort on various computer platforms in Italy and Germany. In this article, we shall discuss the practical aspects of this work, present highlights of autocorrelation measurements, illustrate the impact of unquenching on some fundamental parameters of QCD and describe ..

Highly Optimized Code for Lattice Quantum Chromodynamics on the CRAY T3E

In lattice quantum chromodynamics, large systems of linear equations have to be solved to compute physical quantities. The availability of efficient parallel Krylov subspace solvers plays a vital role in the solution of these systems. We present a detailed analysis of the performance of the stabilised biconjugate gradient (BiCGStab) algorithm with symmetric successive over-relaxed (SSOR) preconditioning on a massively parallel CRAY T3E system. 1. Lattice Gauge Theory Computations The numerical investigation of quantum chromodynamics (QCD) on a four-dimensional space-time grid is one of the grand challenges in high-performance scientific 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 nonperturbative analytical approach, and it is by now widely believed that the controlled numerical treatment of the theory on the lattice on very fast parallel supercomputers i