面向国产异构超级计算机的高性能矩量法关键技术研究

The electromagnetic analysis and design of complex systems have put forward higher requirements on the capability and efficiency of accurate electromagnetic methods. As one of the classical and numerically accurate methods, the Method of Moments (MoM) and its heterogeneous computing techniques have attracted considerable attentions. However, the heterogeneous parallel MoM based on domestically-made supercomputer heterogeneous systems has not been studied, and it will face great challenges in scalability, computational efficiency and so on. Therefore, based on the characteristics of both domestically-made heterogeneous system architectures and the MoM, this project will focus on the high-performance MoM heterogeneous collaborative computing. According to the system architectures, a parallel programming model and a load balancing strategy adapted to the systems will be designed to facilitate the implementation of the highly scalable heterogeneous parallel MoM. To improve the scalability of the parallel MoM, a parallel matrix filling strategy with reduced redundant computation will be studied, and moreover, a novel parallel pivoting strategy of a direct solver based on the matrix features will be proposed to hide or reduce communication. Consequently, a heterogeneous parallel direct solver will be developed for efficiently solving large MoM matrix equations. To further improve the performance of the MoM, optimization schemes including minimizing communication will be explored. Finally, an accurate and efficient MoM will be developed for the domestically-made heterogeneous parallel systems, which is able to provide a powerful tool for electromagnetic analysis and design in major projects.

复杂系统电磁分析与设计对精确电磁算法的求解规模和效率提出了更高要求。作为高精度的经典电磁数值算法，矩量法（MoM）的异构计算研究得到广泛关注。然而，基于国产异构超级计算机的高性能MoM研究尚未开展，其在可扩展性、计算效率等方面面临巨大挑战。因此，本项目将开展国产异构系统体系结构和MoM算法特征双驱动的高性能MoM异构计算研究。针对国产异构众核体系结构特征，设计高适配的并行编程模型和负载均衡策略，克服异构并行MoM可扩展性瓶颈；提出降低冗余计算的MoM阻抗矩阵并行填充策略及通信隐藏与消除的大型矩阵方程并行直接求解策略，开发高适配的MoM矩阵方程并行直接求解器，突破MoM大型矩阵方程求解瓶颈；探索基于MoM算法特征与国产异构系统特点的极小化通信等性能优化方案，揭示并行MoM异构计算性能瓶颈，形成自主可控的国产异构并行MoM电磁精确模拟器，支撑导弹瞄准线分析等国家重大工程应用。

为满足复杂系统电磁分析与设计对高精度、大规模、高效率电磁计算的需求，本项目开展了面向新一代国产众核处理器（如申威、飞腾、海光处理器）超级计算机的高性能MoM异构计算研究。深入分析了国产众核处理器架构和MoM应用特征，设计了基于国产异构众核架构和MoM算法特征的异构并行编程模型，实现了“二维块循环分布”与“细粒度任务划分”的两级并行策略，确保了MoM异构协同计算的负载均衡。研究了MoM大型阻抗矩阵的高效并行填充、矩阵方程并行直接求解方法，改进了MoM网格和基函数循环策略，降低了阻抗矩阵并行填充的冗余计算，提升了填充效率；实现了基于树形结构和MoM阻抗矩阵特征的复数稠密矩阵方程并行直接求解算法，减少了MoM矩阵方程并行求解的通信量和通信次数，提升了求解效率。研究了MoM异构并行计算的性能优化方法，基于国产众核处理器架构特征，突破了计算与通信重叠的异步通信技术，实现了通信隐藏或消除，提升了MoM异构并行计算的效率。开发了适配于国产众核处理器超级计算机的高精度、高可扩展的MoM异构并行计算程序，在神威新一代超级计算机中实现了4000万核以上（E级机全系统）的高阶MoM异构并行计算，并实现了447万维复数稠密矩阵方程的并行直接求解；在天河新一代超级计算机中实现了千万核以上规模的高阶MoM异构并行计算；在西安超级计算中心实现了百万核以上（全系统）规模的高阶MoM异构并行计算；MoM并行规模和精确计算能力达到国际先进水平。

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