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变阶有限元离散的大量并行多网格方法的数值方法。特别强调的是在现代异构硬件架构上实现健壮性和统一可扩展性的技术，特别是在混合系统上，包括传统的类cpu处理器和吞吐量优化的加速器设计，如图形处理器（gpu）。统一可伸缩性的目标是非常具有挑战性的，它包括数值可伸缩性（与问题大小和问题划分无关的收敛速度）、混合系统的所有并行层上的顺序组件的最小化甚至避免、所有计算资源的同等程度利用以及数值上稳定和健壮的异步和容错并行执行。此外，开发和分析了新颖的数值方法以及合适的实现技术（面向硬件的数值），以便高效-同时编写。数值，并行和硬件离散和解决技术可以提供广泛的流动问题。在这个研究项目中的联合工作被合并在独立可用的库中，以及在过去几年中密集开发的共同的FEAST软件包中，因此可以实现和分析异构硬件平台上大规模并行多网格方法的数字鲁棒性，可扩展和递归可配置的方法。

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.