Computational methods for Quantum Chromodynamics

The numerical treatment of QCD (lattice QCD) is by now well developed and understood. Nevertheless it still faces severe challenges, especially for simulations with physical quark masses and large volumes. This thesis introduces and tests new methods which aim at reducing the computing power required in such simulations. In Part I we study preconditioners for Krylov subspace inverters, in particular the Schwarz method with non-minimal overlap, an optimized Schwarz method, and a Schur complement method with non-overlapping subdomains. The former two perform similarly well as the commonly used Schwarz method with minimal overlap, whereas the latter is significantly worse. In Part II, which consists of previously published work, we introduce two methods for an efficient computation of the sign function of a complex matrix. This is important for the overlap operator of QCD, a formulation that explicitly obeys chiral symmetry. Both yield a considerable improvement over previously known methods. In Part III a variant of the Hybrid Monte Carlo algorithm with explicit scale separation is introduced. We obtain good results for a model problem, however the method does not seem applicable to gauge theories.