In this paper we analyze communication patterns in the parallel three-dimensional Navier-Stokes solver Prism, and present performance results on the IBM SP2, the Cray T3D and the SGI Power Challenge XL. Prism is used for direct numerical simulation of turbulence in non-separable and multiply-connected domains. The numerical method used in the solver is based on mixed spectral element-Fourier expansions in (x-y) planes and z-direction, respectively. Each (or a group) of Fourier modes is computed on a separate processor as the linear contributions (Helmholtz solves) are completely uncoupled in the incompressible Navier-Stokes equations; coupling is obtained via the nonlinear contributions (convective terms). The transfer of data between physical and Fourier space requires a series of complete exchange operations, which dominate the communication cost for small number of processors. As the number of processors increases, global reduction and gather operations become important while complete exchange becomes more latency dominated. Predictive models for these communication operations are proposed and tested against measurements. A relatively large variation in communication timings per iteration is observed in simulations and quantified in terms of specific operations. A number of improvements are proposed that could significantly reduce the communications overhead with increasing numbers of processors, and {em generic} predictive maps are developed for the complete exchange operation, which remains the fundamental communication in Prism. Results presented in this paper are representative of a wider class of parallel spectral and finite element codes for computational mechanics which require similar communication operations.
在本文中,我们分析了并行三维Navier-Stokes求解器Prism中的通信模式,并给出了IBM SP2,Cray T3D和SGI Power Challenge XL的性能结果。棱镜用于不可分和多重连接域中湍流的直接数值模拟。求解器中使用的数值方法分别基于在(x-y)平面和z方向上的混合频谱元素-傅立叶展开。每个(或一组)傅里叶模式在单独的处理器上计算,因为线性贡献(Helmholtz解算)在不可压缩的Navier-Stokes方程中完全解耦。耦合是通过非线性贡献(对流项)获得的。物理空间和傅立叶空间之间的数据传输需要一系列完整的交换操作,这些操作支配了少量处理器的通信成本。随着处理器数量的增加,全局减少和收集操作变得很重要,而完整的交换则更多地受到延迟的支配。提出了用于这些通信操作的预测模型,并针对测量结果进行了测试。在仿真中观察到每次迭代的通信时序有相对较大的变化,并根据特定操作对其进行了量化。提出了许多改进,这些改进可以随着处理器数量的增加而显着减少通信开销,并且开发了{\ em general}预测图以实现完整的交换操作,这仍然是Prism的基本通信方法。本文提出的结果代表了需要类似通信操作的用于计算力学的一类更广泛的并行频谱和有限元代码。 P>
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