CRII: CI: Scalable Multigrid Algorithms for Solving Elliptic PDEs on Power-Efficient Clusters

虽然新兴的极端规模计算系统可以为科学发现提供前所未有的资源，但两个主要挑战是成本和运行和冷却这些系统所需的能源。与桌面或服务器处理器相比，在移动设备市场上广泛使用的片上系统（SoC）组件更便宜，更节能，并且代表了未来系统的一个有前途的选择。这个项目解决了新兴的极端规模计算系统面临的三个挑战：向移动处理器的潜在迁移、并发性水平的提高以及对能源效率的需求。开发共享基础设施以加速跨学科和协作研究。这是解决低能量系统上的科学计算问题的数学和计算方法发展的第一步，可以降低科学发现的总体成本，促进科学的进步。该项目为椭圆偏微分方程（PDEs）开发了一种可扩展且节能的并行多网格求解器，目标是新兴的极端规模计算系统。椭圆偏微分方程在自然、工程和社会系统中无处不在，作为该项目的一部分，正在开发的高效多网格求解器有利于跨多个学科的研究。该项目还开发了一个功率性能模型，以帮助在每个节点级别进行应用程序控制的功率性能管理。由于低功耗集群中常见的较慢的互连，该项目开发了一类新的并行算法，以降低计算与通信重叠的功耗。这与传统的做法相反，在传统的做法中，通信成本通过与计算的重叠而隐藏起来。此外，这些算法利用的计算节点在任何时候都不是计算活动的——这是一种完全不同的方法，创建了一类新的节能可扩展并行算法。这项研究最初将使用一个16节点的Tegra/ arm集群进行评估，最终将使用犹他大学的CloudLab集群进行评估。开发的软件将使用开源许可证进行传播。可扩展性实验将在美国国家科学基金会支持的CloudLab集群上运行，该集群由犹他大学托管，允许其他用户重新创建用于实验的硬件和软件堆栈。由此产生的系统将是世界上第一个大规模的低能量集群。

While emerging extreme-scale computing systems could provide unprecedented resources for scientific discovery, two major challenges are the cost and the energy required to run and cool these systems. The system-on-a-chip (SoC) components widely used in the mobile device market are substantially cheaper and more energy efficient compared to desktop or server processors, and represent a promising option for future systems. This project addresses three challenges for emerging extreme-scale computing systems: the potential move to mobile processors, the increasing levels of concurrency, and the need for energy efficiency. Shared infrastructure is developed to accelerate interdisciplinary and collaborative research. This is a first step in the development of mathematical and computational methods for solving scientific computing problems on low-energy systems that can reduce the overall cost of scientific discoveries and promote the progress of science. The project develops a scalable and power efficient parallel multigrid solver for elliptic partial differential equations (PDEs) that targets emerging extreme scale computing systems. Elliptic PDEs are ubiquitous in natural, engineered and societal systems, and the efficient multigrid solvers being developed as part of this project are beneficial to research across several disciplines. The project also develops a power-performance model to aid in application-controlled power-performance management, at the per-node level. Motivated by the slower interconnections common on low-power clusters, the project develops a new class of parallel algorithms that lower the power utilization of computations to overlap with the communication. This is the reverse of what has conventionally been done, where communication costs are hidden by overlapping with computation. Additionally, the algorithms utilize compute nodes that are not computationally active at all times -- a radically different approach that creates a new class of energy-efficient scalable parallel algorithms. The research will be evaluated initially using a 16 node Tegra/ARM-based cluster and ultimately, the CloudLab cluster at the University of Utah. The developed software will be disseminated using an open source license. The scalability experiments will be run on the NSF-supported CloudLab cluster, hosted at the University of Utah, allowing other users to re-create both the hardware and software stack used for the experiments. The resulting system will be among the first large scale low-energy clusters available anywhere.