Scalable, recursively configurable, massively-parallel FEM-multigrid solvers for heterogeneous hardware architectures -- Design, analysis and realisation in FEAST with applications in fluid mechanics

这个联合项目研究了用于可变阶有限元离散化的并行多重网格方法的数值方法。特别强调的技术，使现代异构硬件架构的鲁棒性和统一的可扩展性，特别是在混合系统，包括传统的CPU类处理器结合吞吐量优化的加速器设计，如图形处理器（GPU）。统一的可扩展性的目标是非常具有挑战性的，包括数值可扩展性（收敛速度独立于问题的大小和问题的分区），最小化，甚至避免顺序组件的所有并行层的混合系统，所有计算资源的利用率相等的程度，以及数值稳定和强大的异步和容错并行执行方面。此外，新的数值方法沿着与适当的实施技术的开发和分析（面向硬件的数值），使高效-同时wrt。数值、并行和硬件--离散化和求解技术可用于广泛的流动问题。在这个研究项目中的联合工作被纳入独立可用的库，以及共同的FEAST软件包，已在过去几年中intinsively开发，使一个强大的数字，可扩展的和递归配置的方法，异构硬件平台上的并行多重网格方法可以实现和分析。

This joint project examines numerical methods for massively-parallel multigrid methods for finite element discretisations of variable order. Special emphasis is placed on techniques that enable robustness and uniform scalability on modern heterogeneous hardware architectures, in particular on hybrid systems comprising conventional CPU-like processors combined with throughput-optimised accelerator designs like graphics processors (GPUs). The goal of uniform scalability is very challenging and embraces aspects of numerical scalability (convergence rates independent of problem size and problem partitioning), the minimisation or even avoidance of sequential components on all parallelism layers of hybrid systems, the equal degree of utilisation of all compute resources, and the numerically stable and robust asynchronous and fault-tolerant parallel execution. In addition, novel numerical methods along with suitable implementation techniques are developed and analysed (hardware-oriented numerics), so that efficient -- simultaneously wrt. numerics, parallelism and hardware -- discretisation and solution techniques can be provided for a broad range of flow problems. Joint work in this research project is incorporated both in independently usable libraries as well as the common FEAST software package that has been developed intinsively during the last years, so that a numerically robust, scalable and recursively configurable methodology for massively-parallel multigrid methods on heterogeneous hardware platforms can be realised and analysed.