非结构网格上求解中子输运方程的并行流水线S_n扫描算法

Parallel Pipelined S_ n Sweeping Algorithm for Neutron Transport on Unstructured Grid

间断有限元离散纵标方法 (Sn)是广泛应用于求解高维非定常中子输运方程的数值方法 ,它涉及几何网格空间、速度相空间和中子能群的离散 ,计算量很大 .该文基于非结构网格 ,提出了基于区域分解的并行流水线Sn扫描算法 ,通过设计具有不同内在并行度和通信面体比的区域分解方法和队列插入算法 ,对两个不同物理模型 ,分别使用两台并行机的 92个和 2 5 6个CPU ,获得 72倍和 78倍以上的加速 .可扩展性能分析表明 ,算法的性能非常依赖于并行机的点对点通信延迟 .

Discontinuous finite element discrete ordinates numerical method is widely used to solve high dimensional time dependent neutron transport equation in recent years, and it needs huge calculations arising from discretizations of time, geometric space, velocity angle direction and neutron energy. However, the scalable parallel computing of such numerical method is challenging especially on unstructured grid because of the intrinsic data dependence of neutron flux refreshment on elements along each discrete velocity angle direction. For the realistic applications under cylinder symmetrical coordinate system, many related works have implied that domain decomposition is the unique strategy for scalable parallel computing of such numerical method. This paper presents a parallel pipelined Sn sweeping algorithm with scalable performance on domain decomposition of unstructured grid. By well incorporating different domain decomposition methods with different priority queuing algorithms for ordering of internal grid elements in each decomposed subdomain, the MPI implementation of this algorithm has achieved speedup larger than 72 with 92 processors in a distributed shared memory parallel computer with network latency less than 2 microseconds and speedup larger than 77 with 256 processors in another MPP machine with network latency equal to 10 microseconds. Except from the numerical experiments, theoretical scalability analysis of this algorithm is also given, and it shows that the scalability of this algorithm heavily depends on the point-to-point network latency of parallel computers.