Computing quark propagation in a gluon background

对于格子QCD模拟中计算量受限的任务，我们从数值线性代数出发，开发、分析和实现了改进的、新颖的方法。我们贡献了最先进的模拟技术，使这个研究单位的物理计划能够以所需的精度高效地进行。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，我们考虑将分层方法扩展到蒸馏方法，并将使用它来获得特殊情况下的特别有效的求解器，其中需要线性求解器来计算特征对。这与查莫宁的光谱计算特别相关。此外，我们还将考虑改进自适应代数多重网格方法的建立阶段，以及高效并行求解最粗网格系统的新方法。这些改进将加快涉及夸克传播子的光谱计算，并可用于HMC积分方法。我们的第二个主要目标是提供有效的方法来计算不相连的贡献，即给定时间片上Wilson-Dirac矩阵的逆(修改)的迹线的计算。我们将研究如何利用多水平蒙特卡罗原理在这里以与体积无关的方式减少随机估计的方差，而不是目前的通货紧缩方法。我们将进一步将多层蒙特卡罗方法与探测技术相结合，以获得进一步的改进。不相关会费的计算是本研究股的里程碑之一。

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.