求解CMFD的改进流水线并行GMRES方法  

An Improved Pipeline Parallel GMRES Method for Solving Coarse Mesh Finite Difference Linear System

作　　者：郝琛 韩立会 程有莹 HAO Chen;HAN Li-hui;CHENG You-ying(College of Nuclear Science and Technology,Harbin Engineering University,Harbin 150001,China;National Nuclear Emergency Response Technical Assistance Center,Beijing 100080,China)

机构地区：[1]哈尔滨工程大学核科学与技术学院,哈尔滨150001 [2]国家核应急响应技术支持中心,北京100080

出　　处：《现代应用物理》2021年第1期35-41,共7页Modern Applied Physics

基　　金：国家重点研发计划资助项目(2018YFE0180900);国家自然科学基金资助项目(12075067)。

摘　　要：基于经典的Gram-Schmidt正交化方法,对求解大型稀疏非对称线性系统的广义极小残差算法(GMRES)进行重构,实现了每次迭代仅1次全局通信即可完成全部点积计算,提出了异步全局归约方法,可实现全局通信与其他信息传递及计算的有效重叠,最大限度地覆盖全局通信造成的延迟;开发了流水线式并行GMRES求解器,并应用于精细化中子物理计算程序HNET中。数值结果表明,本文开发的流水线式并行GMRES求解器的计算速度显著高于标准GMRES算法,可实现GMRES在大规模并行计算环境下高效求解CMFD线性系统。In this paper,based on the classical Gram-Schmidt orthogonalization method,the generalized minimal residual algorithm(GMRES)for solving large sparse and asymmetric linear system is reconstructed,the whole dot products is calculated by only one global communication per iteration,and an asynchronous global reduction method is proposed.It can realize the effective overlap between global communication and other information transmission and computation,and cover the delay caused by global communication to a maximum extent.At the same time,a pipeline parallel GMRES solver is developed and applied in HNET.The numerical results show that the computation speed of the pipeline parallel GMRES solver developed in this paper is significantly higher than that of the standard GMRES algorithm,which can be used to solve the coarse mesh finite difference(CMFD)linear system efficiently in large-scale parallel computing environment.

关 键 词：粗网有限差分 极小残差算法 并行计算 流水线式 全局归约 

分 类 号：TP29[自动化与计算机技术—检测技术与自动化装置] TL32[自动化与计算机技术—控制科学与工程]