二维球坐标系中子输运方程的一种并行SN算法

doi:10.19596/j.cnki.1001-246x.8381

计算物理 ›› 2022, Vol. 39 ›› Issue (2): 143-152.DOI: 10.19596/j.cnki.1001-246x.8381

二维球坐标系中子输运方程的一种并行SN算法

蔡颖¹(), 张存波¹, 刘旭²^,³^,*(), 范征锋¹^,⁴, 刘元元¹, 徐小文²^,³, 张爱清²^,³

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

收稿日期:2021-04-19 出版日期:2022-03-25 发布日期:2022-06-24
通讯作者: 刘旭
作者简介:
蔡颖，女，博士，助理研究员，研究方向为高性能计算，E-mail：cai_ying@iapcm.ac.cn
基金资助:
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)

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

Ying CAI¹(), Cunbo ZHANG¹, Xu LIU²^,³^,*(), Zhengfeng FAN¹^,⁴, Yuanyuan LIU¹, Xiaowen XU²^,³, Aiqing ZHANG²^,³

1. Institute of Applied Physics and Computational Mathematics, Beijing 100094, China
2. Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing 100088, China
3. CAEP Software Center for High Performance Numerical Simulation, Beijing 100088, China
4. HEDPS, Center for Applied Physics and Technology, Peking University, Beijing 100871, China

Received:2021-04-19 Online:2022-03-25 Published:2022-06-24
Contact: Xu LIU

摘要/Abstract

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。

关键词: 中子输运方程, 源迭代SN算法, 有向图, 并行算法

Abstract:

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 960 000 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.

Key words: neutron transport equation, source iteration SN algorithm, directed graph, parallel computing

蔡颖, 张存波, 刘旭, 范征锋, 刘元元, 徐小文, 张爱清. 二维球坐标系中子输运方程的一种并行SN算法[J]. 计算物理, 2022, 39(2): 143-152.

Ying CAI, Cunbo ZHANG, Xu LIU, Zhengfeng FAN, Yuanyuan LIU, Xiaowen XU, Aiqing ZHANG. A Parallel SN Method for Neutron Transport Equation in 2-D Spherical Coordinate[J]. Chinese Journal of Computational Physics, 2022, 39(2): 143-152.

图/表 6

图1 二维球坐标系中子输运方程离散网格与SN扫描计算依赖关系(a) 横坐标为空间半径，纵坐标为方向极角的余弦；(b) 横坐标为空间角度，纵坐标为方向方位角(红箭头表示SN扫描计算中的数据依赖关系。)

Fig.1 Discrete grid of the neutron transport equation in two-dimensional spherical coordinate system and corresponding SN sweeping data dependencies (a) The abscissa is the space radius, and the ordinate is the cosine of the polar angle; (b) The abscissa is the space angle, and the ordinate is the direction azimuth (The red arrows indicate data dependency in SN sweeping computation.)

图2 空间-角度并行度挖掘简要示意图

Fig.2 A brief sketch of spatial-angle parallelism mining

图3 能群并行度挖掘(a)能群克隆；(b)能群流水(左侧：中子源计算，右侧：扫描计算)

Fig.3 Energy group parallelism mining (a) energy group cloning; (b) energy group pipelining

图4 扫描计算平均运行时间随结点粒度的变化

Fig.4 Average running time of sweeping computation as functions of node granularity

表1 能群流水并行与克隆并行性能

Table 1 Performance of the energy group pipelining and energy group cloning

并行方式	克隆数	计算时间/s
并行方式	克隆数	扫描	克隆开销	源项计算	总时间
流水线		238.19	0	223.91	721.57
	2	189.28	266.04	309.02	1 187.29
	4	154.85	371.66	514.29	1 936.55
克隆	6	216.74	558.52	412.27	2 361.21
	12	133.3	1 004.17	578.77	4 065.39
	24	166.76	1 860.63	699.13	7 049.77

表2 并行可扩展性测试

Table 2 Parallel scalability test

进程数	扫描计算			源项计算			总性能
进程数	时间/s	加速比	并行效率	时间/s	加速比	并行效率	时间/s	加速比	并行效率
120	1 090.78	1	1	2 614.16	1	1	5 490.55	1	1
240	534.80	2.04	1.02	1 165.10	2.24	1.12	2 662.71	2.06	1.03
480	345.16	3.16	0.79	474.80	5.51	1.38	1 295.72	4.24	1.06
960	238.19	4.58	0.57	223.91	11.68	1.46	721.57	7.61	0.95
1 920	212.86	5.12	0.32	118.83	22.00	1.37	481.38	11.41	0.71

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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

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