XPS: FULL: DSD: Asynchronous PDE Algorithms for Turbulent Flows at Exascale

XPS：完整：DSD：百亿亿级湍流的异步 PDE 算法

• 批准号: 1439145
• 负责人: Diego Donzis
• 金额: $ 85万
• 依托单位: Texas A&M Engineering Experiment Station
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2014
• 资助国家: 美国
• 起止时间: 2014-08-15 至 2019-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1439145&HistoricalAwards=false
• 关键词: XPS; FULL; DSD; Asynchronous; PDE

Future exascale computing systems will be available to study important,compute-intensive applications such as multi-physics multi-scale naturalphenomena and engineering systems typically modeled accurately by partialdifferential equations (PDEs).  A prime example is turbulence at high Reynoldsnumbers, typically found in natural and engineering systems, which comprise anextremely wide range of spatial and temporal scales and has thus became a GrandChallenge in scientific computing.Many challenges exists that must be overcome before exascale systemscan be utilized effectively. These include communication betweenprocessing elements as well as global synchronizations both of which willlikely be a main bottleneck when millions of billions of processing elementsare utilized in a simulation.In this project, the PIs develop novel exascale numerical schemes for PDEs,especially those describing turbulent flows, that exploit asynchrony from the mathematical tothe software level. These are based on widely used finite differences, compact differentiation and spectral schemes.Asynchrony offers better performance but also introduces errors in the solution. The new schemes willbe able to trade-off accuracy and performance in a quantitative and predictable manner.The approach includes (i) rigorous mathematical studies of stability andaccuracy based on numerical analysis and dynamical systems, which will alsoprovide a framework for the development of new schemes and quantify itsuncertainty, (ii) development of specific elements in a scalable library for parallelcomputing to enable portable implementations on current and future machines,and (iii) physics based modeling of numerical perturbations inrealistic flows.The tools, techniques and simulation data in this projectwill be integrated in the PIs' educational efforts through graduate mentoring, undergraduateresearch and as material for courses in high-performance computing, fluid dynamics and dynamical systemstaught by the PIs.

未来的百亿亿次计算系统将可用于研究重要的计算密集型应用，如多物理场多尺度自然现象和通常由偏微分方程（PDEs）精确建模的工程系统。一个典型的例子是高雷诺数的湍流，通常在自然和工程系统中发现，它包含了非常广泛的空间和时间尺度，因此成为科学计算的一个重大挑战。在有效利用百亿亿级系统之前，必须克服许多挑战。这包括处理元素之间的通信以及全局同步，当在模拟中使用数百万亿个处理元素时，这两者都可能成为主要瓶颈。在这个项目中，pi为pde开发了新的百亿级数值方案，特别是那些描述湍流的方案，从数学到软件层面利用了异步性。这些是基于广泛使用的有限差分、紧凑微分和谱格式。异步提供了更好的性能，但也在解决方案中引入了错误。新方案将能够以定量和可预测的方式权衡准确性和性能。该方法包括(i)基于数值分析和动力系统的稳定性和准确性的严格数学研究，这也将为开发新方案和量化其不确定性提供框架，（ii）在可扩展的并行计算库中开发特定元素，以便在当前和未来的机器上实现便携式实现，以及（iii）基于物理的数值扰动非现实流建模。该项目中的工具、技术和模拟数据将通过研究生指导、本科生研究和高性能计算、流体动力学和动力系统课程的材料整合到pi的教育工作中。