二维球坐标系中子输运方程的一种并行SN算法  

A Parallel SN Method for Neutron Transport Equation in 2-D Spherical Coordinate

作　　者：蔡颖 张存波 刘旭[2,3] 范征锋 刘元元[1] 徐小文 张爱清 CAI Ying;ZHANG Cunbo;LIU Xu;FAN Zhengfeng;LIU Yuanyuan;XU Xiaowen;ZHANG Aiqing(Institute of Applied Physics and Computational Mathematics,Beijing 100094,China;Laboratory of Computational Physics,Institute of Applied Physics and Computational Mathematics,Beijing 100088,China;CAEP Software Center for High Performance Numerical Simulation,Beijing 100088,China;HEDPS,Center for Applied Physics and Technology,Peking University,Beijing 100871,China)

机构地区：[1]北京应用物理与计算数学研究所,北京100094 [2]北京应用物理与计算数学研究所,计算物理重点实验室,北京100088 [3]中物院高性能数值模拟软件中心,北京100088 [4]北京大学应用物理与技术研究中心,高能量密度物理数值模拟教育部重点实验室,北京100871

出　　处：《计算物理》2022年第2期143-152,共10页Chinese Journal of Computational Physics

基　　金：科技部重点研发计划高性能计算重点专项(2017YFB0202103);科学挑战专题(TZ2019-B1)资助项目。

摘　　要：针对二维球坐标系下中子输运方程的SN算法,提出基于(单元,方向)二元组的有向图模型,在已有的基于有向图的并行流水线算法基础上,设计粒度可控多级并行SN算法。其中,采用区域分解和并行流水线相结合的方式挖掘空间-角度方向的并行度,提出能群流水并行方法,并通过设置合适的流水线粒度来平衡有向图调度、通信和空闲等待开销。实验结果表明:该算法可以有效地求解二维球坐标系下的中子输运方程。在某国产并行机1920核上,对于96万网格、60个方向、24能群、数十亿自由度的典型中子输运问题,获得了71%的并行效率。Targeting at SN algorithm for the neutron transport equation in the two-dimensional spherical coordinate system,we propose a directed graph model based on a(cell,direction)two-tuple,and design a multi-level parallel SN algorithm with controllable granularity on the basis of the existing parallel pipeline algorithm based on directed graph.Among them,a combination of domain decomposition and parallel pipeline is used to mine parallelism in the space-angle direction,and an energy group pipeline parallel method is proposed.Furthermore,by setting appropriate pipeline granularity,the overhead of scheduling,communication and idle waiting are well balanced.Experimental results show that the algorithm can effectively solve the neutron transport equation in the two-dimensional spherical coordinate system.For a typical neutron transport problem with 960000 grids,60 directions,24 energy groups,and billions of degrees of freedom,the parallel program achieved 71%parallel efficiency on 1920 cores of a domestic parallel machine.

关 键 词：中子输运方程 源迭代SN算法 有向图 并行算法 

分 类 号：TP301.6[自动化与计算机技术—计算机系统结构]