多CPU+多GPU协同计算的三维泊松方程求解

3-Dimension Poisson Equation Solver Based on Multiple CPUs-GPUs Heterogeneous Platform

三维泊松方程求解算法被广泛应用在电磁、流体、地质等领域,有着极其重要的现实意义.但现有实现方法无法满足高精度网格下的性能需求,针对该问题,提出一种基于多GPU加速的三维泊松方程求解算法(MGPES).MPGES通过分析泊松方程求解过程中的计算和访存特征,发掘可并行的热点函数,将计算任务均分给多个同构GPU.根据CPU和GPU下的计算速度和访存性能,提出一种基于CPU/GPU协同计算下的负载均衡模型.在该模型的基础上,充分利用空闲CPU的计算能力,提出一种基于多CPU+GPU协同异构平台的三维泊松方程求解算法(COPES).实验结果表明,在8GPU平台下,MGPES最高并行加速比能达到7.72,COPES的最高并行加速比能达到7.81.两种算法均可以达到线性加速比,拥有良好的可扩展性.

Three-dimension Poisson Equation solver is widely used in the fields of electromagnetic, fluid, geology, etc., and it has a very important practical significance. However, the existing methods cannot meet the performance demand for the large scale mesh grids. To solve this problem, this paper analyzes the characteristics of calculation and memory access in the solution process, searches the hot functions that can be paraUelized,divides the kernel tasks to several homogeneous GPUs, and proposes a 3-dimension Poisson Equation solver（ MGPES ） based on multi-GPUs platforms. Moreover, this paper presents a load balancing model based on multiple CPUs-GPUs heterogeneous platform. Based on the model, this paper proposes a 3-dimension Poisson Equation solver （ COPES ） on the multiple CPUs-GPUs heterogeneous platform that can take advantage of the calculation capacity of idle CPUs. Experimental results show that the speedup ratio of MGPES reaches 7.72 and COPES reaches 7.81 on the 8 GPUs platform. Results also demonstrate that both of the solvers can reach the linear speedup and have good scalability.