Computing quark propagation in a gluon background

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We develop, analyze and implement improved and novel methods from numerical linear algebra for those tasks in the Lattice QCD simulation which are computation bound. We contribute state-of-the-art simulation technology, enabling the physics program of this Research Unit to be pursued efficiently and with the required accuracy.Our first major objective is to further exploit hierarchical concepts to solve systems involving the Wilson-Dirac matrix. In particular, we consider the extension of hierarchical methods to the distillation approach and will use this to obtain particularly efficient solvers for the special situations where linear solvers are needed for the computation of eigenpairs. This is particularly relevant for the spectroscopy calculations of charmonium. In addition, we will consider improvements for the setup phase in the adaptive algebraic multigrid methods and novel approaches to efficiently solve the coarsest grid systems in parallel. These improvements will speed-up spectroscopy calculations involving quark propagators and can be used in HMC integration methods.Our second major objective is to provide efficient methods for the computation of disconnected contributions, i.e. of the traces of the inverse of (modifications of) the Wilson-Dirac matrix on a given time slice. We will investigate how the multilevel Monte-Carlo principle can be exploited here to reduce the variance in stochastic estimators in a volume-independent manner, as opposed to current deflation approaches. We will further combine the multilevel Monte-Carlo approach with probing techniques to obtain further improvements. The computation of disconnected contributions represents one of the milestones of this Research Unit.