Collaborative Research: SI2-SSI: Scalable Hierarchical Algorithms for Extreme Computing (SHARE)

该奖项支持在高性能图形处理单元(GPU)集群上开发用于高级算法的软件工具。该文库的最初目标将集中于单一驱动应用程序，即核力的基本数值研究(晶格量子色动力学：LQCD)，以及第二个目标应用程序，即激动人心的石墨烯纳米技术的数值模拟。这些都是适合在多核架构上通过多尺度算法来解决的多费米子问题。这个试点项目借鉴了波士顿大学和哈佛大学的一个小团队在开发格子场理论的狄拉克解算器方面所获得的经验。先前研究的两个基础是(1)为LQCD的Wilson Dirac算子构建自适应多重网格(MG)解算器，与生产代码中最好的Krylov解算器相比，该解算器的加速比为20倍；(2)在GPU(但没有多重网格)上为同一操作符构建高度优化的Krylov解算器，实现了比传统集群的10倍的性价比。该库将统一这些功能并概括它们的适用范围。作为更广泛影响的一个例子，据估计，将这两种技术(MG算法和GPU架构)相结合将使LQCD模拟中计算最密集的组件的性价比提高100倍。这样的进步将真正具有变革性，对核物理和粒子物理学产生立竿见影的影响。同时，它将作为将分层算法映射到异类体系结构上的更一般问题的原型，这是通往亿级的道路上最重要的挑战。软件库的设计将为石墨烯技术带来类似的好处，并将进行演变，以适应额外的目标应用程序和额外的区域分解算法，以缓解亿级设计的通信瓶颈。该奖项将为在该项目中发挥重要作用的两名博士后学者提供部分支持。

This award supports the development of software tools for advanced algorithms on a cluster of high performance graphics processing units(GPUs). The initial goal of this library will focus on a single driver application, the fundamental numerical study of Nuclear Forces (Lattice Quantum Chromodynamics: LQCD), and a second target application, the numerical simulation of the exciting nano-technology of graphene. These are both multi-fermion problems well suited to solution via multi-scale algorithms on many-core architectures. This pilot project draws on experience gained by the small team at Boston University and Harvard in developing Dirac solvers for lattice field theory. Two building blocks from prior research are (1) the construction of an adaptive multigrid (MG) solver for the Wilson Dirac operator of LQCD, which demonstrates a 20x speedup compared to the best Krylov solvers in production code and (2) a highly optimized Krylov solver for the same operator on GPUs (but without multigrid), realizing a 10x improvement in price/performance over traditional clusters. The library will unite these feature and generalize their domain of applicability. As an example of the broader impact, it is estimated that combining these two technologies (MG algorithms and GPU architectures) will yield a 100-fold improvement in price/performance for the most compute-intensive component of LQCD simulations. Such an advance would be truly transformative, making an immediate impact in nuclear and particle physics. At the same time, it will serve as a prototype of the more generic problem of mapping hierarchical algorithms onto heterogeneous architectures, a challenge of paramount importance on the path to the exascale. The software library will be designed to bring similar benefits to graphene technology and to evolve to accommodate additional target application and additional domain decomposition algorithm to mitigate the communication bottleneck of Exascale designs. The award will provide partial support for two postdoctoral scholars who play essential roles in this project.