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

适用于异构硬件架构的可扩展、可递归配置、大规模并行 FEM 多重网格求解器 - FEAST 中的设计、分析和实现以及流体力学应用

基本信息

批准号：
243173035
负责人：
Professor Dr. Dominik Göddeke
金额：
--
依托单位：
Lehrstuhl III: Angewandte Mathematik und Numerik
依托单位国家：
德国
项目类别：
Research Grants
财政年份：
2013
资助国家：
德国
起止时间：
2012-12-31 至 2016-12-31
项目状态：
已结题

来源：
https://gepris.dfg.de/gepris/projekt/243173035?language=en
关键词：
Scalable recursively configurable massively parallel

项目摘要

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.

该联合项目研究变阶数有限元离散的大规模并行多重网格法的数值方法。特别强调了在现代异类硬件体系结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，该混合系统包括传统的类似CPU的处理器与诸如图形处理器(GPU)等吞吐量优化的加速器设计相结合。统一可伸缩性的目标非常具有挑战性，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)、最小化甚至避免混合系统的所有并行层上的顺序组件、所有计算资源的同等利用程度，以及数值稳定且健壮的异步和容错并行执行。此外，还开发和分析了新的数值方法和适当的实现技术(面向硬件的数值)，以便有效地同时进行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。这一研究项目中的联合工作被纳入独立可用的库以及在过去几年中专门开发的公共FEAST软件包中，以便能够实现和分析在不同硬件平台上的大规模并行多重网格方法的数值健壮、可伸缩和递归可配置的方法。