一种基于敏捷集群计算系统的并行GMRES方法  

A Parallel GMRES Method Based on Agile Cluster Computing System

作　　者：何康馨 席国江 陈颖[1] HE Kangxin;XI Guojiang;CHEN Ying(Agile and Intelligent Computing Key Laboratory of Sichuan Province,Southwest China Institute of Electronic Technology,Chengdu 610065,China)

机构地区：[1]西南电子技术研究所敏捷智能计算四川省重点实验室,四川成都610065

出　　处：《无线电通信技术》2024年第1期162-167,共6页Radio Communications Technology

基　　金：四川省自然科学基金(2023NSFSC0497,2022YFG0231)。

摘　　要：随着通信系统和人工智能的飞速发展,以智慧城市、智慧工厂和智能制造等为代表的多种新型应用场景不断涌现,使得通信、感知和计算等系统的一体化成为技术发展的新趋势。人工智能新型应用场景对大规模高效敏捷计算提出了新的要求,基于敏捷集群计算系统,提出了一种并行广义最小残差(Generalized Minimal Residual, GMRES)方法,主要通过并行矩阵向量乘法和并行高瘦矩阵QR(Tall and Skinny QR,TSQR)分解实现Krylov子空间的高效并行构造,充分利用集群计算系统的计算和通信性能,实现大规模线性方程组Ax=b的快速求解,其中A为一个n×n的矩阵,在工程实践中,n可达数十万甚至百万规模。通过求解二维泊松方程的有限元离散得到的刚度方程,验证了算法的有效性。With the rapid development of communication systems and artificial intelligence,a variety of new application scenarios represented by smart cities,smart factories and intelligent manufacturing continue to emerge,making the integration of communication,perception and computing systems become a new trend in technology development.In order to implement a large scale solver for application scenarios of artificial intelligence,a parallel Generalized Minimal Residual(GMRES)method,which parallelly constructs the Krylov subspace using parallel matrix-vector product and parallel Tall and Skinny QR(TSQR)factorization,is proposed.Therefore,the computing and communication capabilities of cluster computing system are fully utilized to efficiently solve a large linear system Ax=b,where A is an n×n matrix,and in practice,n can be 105 or even 106.The effectiveness of the algorithm is validated with the finite element discretization of Poisson equation.

关 键 词：敏捷集群计算 并行广义最小残差方法 KRYLOV子空间 大规模线性方程组 

分 类 号：TN919.23[电子电信—通信与信息系统]