可扩展至数十万核的全隐式时空耦合并行区域分解算法研究

Petascale supercomputers are extremely powerful, and the architecture is so complex that traditional parallel algorithms cannot be straightforwardly implemented with such a high level of scalability. The scalability issue is becoming a bottleneck in high performance computing, and this makes the study of highly scalable algorithms and the corresponding software a very important task. In the proposed project, we plan to investigate a class of important applications, namely the control of fluid flows using some fully implicit, coupled space-time domain decomposition algorithms, as well as the nonlinear Newton-Krylov solver. The coupled space-time approach provides more much parallelism than the standard space-only domain decomposition methods, and is therefore more suitable for supercomputers with a very large number of heterogeneous processors. We will develop several critical algorithms and software for the target application problems and study their performance on machines including the current Tianhe and Xingyun with 10,000-100,000 processor-cores. The work will provide valuable experiences for the future development of scalable algorithms and software on petascale, or even exascale, computers and their applications in China.

由于千万亿次级超级计算机具有庞大的系统规模和复杂的体系结构，传统的并行算法和预条件子技术难以直接移植并实现较高的可扩展性，加强面向千万亿次科学计算的基础研究，特别是可扩展算法和应用软件实现技术的研究，成为高性能计算领域急需突破的瓶颈。本项目拟针对计算流体力学中最典型也是最难的一类应用——流体控制问题，结合全隐式的时空并行算法、区域分解算法和全耦合的Newton-Krylov类方法，兼顾并行数值算法的创新和适应异构、众核环境的并行程序设计和优化技术，进行面向千万亿次超级计算机的大规模可扩展算法研究；力争在以天河、星云等为代表的国产千万亿次超级计算机上，高效实现数十万核的可扩展性以及数百亿未知数规模以上的大规模数值模拟，为面向千万亿次科学计算的可扩展算法和应用软件实现技术提供思路，努力推动国产超级计算机的应用。

本项目针对计算流体力学中的两类典型应用——流体控制问题和非稳态反问题，充分考虑大型异构系统的发展趋势及以重点应用领域的问题特征，深入研究基于时空并行区域分解框架的隐式求解方法。在以天河等为代表的国产千万亿次超级计算机上，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，高效实现了好的可扩展性以及数亿未知数规模以上的大规模数值模拟。相关成果发表在国际SCI期刊《SIAM Journal on Scientific Computing》, 《SIAM Journal on Numerical Analysis》, 《Journal of Scientific Computing》，《Computers and Fluids》和《Inverse Problems and Imaging》上。