Computing quark propagation in a gluon background

我们开发，分析和实现改进的和新的方法，从数值线性代数的格子QCD模拟的计算限制的任务。我们提供最先进的模拟技术，使该研究单位的物理计划能够有效地进行，并具有所需的精度。我们的第一个主要目标是进一步利用分层概念来解决涉及威尔逊-狄拉克矩阵的系统。特别是，我们考虑扩展的分层方法的蒸馏方法，并将使用此获得特别有效的求解器的特殊情况下，需要线性求解器的计算特征对。 这对于粲偶素的光谱计算特别相关。此外，我们将考虑改进的自适应代数多重网格方法和新的方法，有效地解决并行粗网格系统的设置阶段。这些改进将加快涉及夸克传播子的光谱计算，并可用于HMC integration methods.我们的第二个主要目标是提供有效的方法来计算断开的贡献，即在给定的时间片上的威尔逊-狄拉克矩阵的逆（修改）的痕迹。我们将研究如何利用多级蒙特-卡罗原则，在这里减少随机估计量的方差在体积独立的方式，而不是目前的通货紧缩的方法。我们将进一步联合收割机的多级蒙特-卡罗方法与探测技术，以获得进一步的改进。计算不连续的捐款是该研究股的一个里程碑。

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.