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

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

Abstract

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

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.

Figures/Tables 6

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.)

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

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

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

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

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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