大型异构系统上数百万核可扩展的新型区域分裂隐式求解器研究

Many-core heterogeneous supercomputing systems, such as the Tianhe, Shenwei and Nebula series, have become an important trend in high performance computing. However, many traditional implicit algorithms for solving partial differential equation are no longer suitable or even completely inapplicable on such kind of systems. It is therefore of great importance to develop heterogeneity-friendly parallel algorithms and software. To that end, under the support of the previous NFSC grant, we proposed a new class of heterogeneous domain decomposition methods for the explicit solution of partial differential equations and scaled to O(100,000) and O(1,000,000) cores on the CPU-GPU-based Tianhe-1A and the CPU-MIC-based Tianhe-2, respectively. In addition, an attempt was done by applying the heterogeneous domain decomposition methods in a typical fully implicit solver in the new HPCG benchmark, which successfully led to a full system scale, top 1 HPCG performance on Tianhe-2 with 3.12 million cores. Based on the previous work, we plan to continue, concise, and sublimate the research, by focusing on the trends and characteristics of heterogeneous systems and the key characteristics of typical geo-scientific applications, in order to further study fully implicit domain decomposition methods on heterogeneous systems. In the proposed research, we also plan to combine the domain decomposition methods with advanced algorithms for solving linear and nonlinear system, and effective techniques on performance optimization, so as to seek the balance among the convergence, the parallelism, and the architecture. Finally, we plan to develop a highly efficient and scalable implicit algorithm library that is able to exploit multi-million parallelisms on state-of-the-art domestic heterogeneous platforms.

以天河、神威、星云等为代表的异构、众核系统已成为重要趋势，对应的高可扩展偏微分方程隐式求解算法和软件已成为亟待突破的一大瓶颈。鉴此，上期培育项目：（1）提出了面向显式模拟的新型区域分裂方法，在天河1A、天河2等平台进行了十万及百万核级的大规模实算；（2）初步探索了其在隐式求解中的可行性，成功用于HPCG新型基准测试的算法设计和优化，在天河2上扩展至整机312万核并取得国际HPCG排行榜榜首。本项目拟延续、凝练、升华前期成果，充分考虑大型异构系统的发展趋势及以地学计算为代表的重点应用领域的问题特征，进一步深入研究基于异构区域分裂框架的隐式求解方法，并结合相应的线性、非线性系统并行求解算法及自适应负载均衡、多级通信优化和多粒度性能调优技术，寻求收敛性、并行性、体系结构友好性之间的平衡，形成一套高效的异构并行隐式求解算法库，并在国产顶级大型异构系统上实现数百、上千万核的高可扩展计算。

本项目延续、凝练、升华前期成果，充分考虑大型异构系统的发展趋势及以地学计算为代表的重点应用领域的问题特征，进一步深入研究基于异构区域分裂框架的隐式求解方法,并结合相应的线性、非线性系统并行 求解算法及自适应负载均衡、多级通信优化和多粒度性能调优技术,寻求收敛性、并行性、体系结构友好性之间的平衡，形成了一套高效的异构并行隐式求解算法库，在国产顶级大型异构系统上实现数百、上千万核的高可扩展计算，发表多篇高水平学术论文，并取得了高性能计算应用领域的世界最高学术奖项——ACM Gordon Bell奖，实现了我国在该奖项自1987年设立以来零的突破，成为我国高性能计算应用发展的一个新的里程碑。