几何多重网格法在CPU -- GPU异构计算机上的数值研究
Numerical Study of Geometric Multigrid Methods on CPU--GPU Heterogeneous Computers
摘要：
几何多重网格法是求解椭圆型偏微分方程离散代数系统的有效方法之一。GMG利用网格或离散化的层次结构，并同时减少了许多频率的误差。图形处理单元（GPU）最近突然出现在科学计算领域，作为一种技术，它已经产生了显着的性能和能源效率的改进。然而，在GPU上实现GMG的一个核心挑战是，粗略级别的计算工作无法充分利用GPU的容量。在这项工作中，我们进行数值研究的GMG的CPU-GPU异构计算机上。此外，我们比较我们的实现与一个高效的CPU实现GMG和最流行的快速泊松求解器，快速傅里叶变换，在由NVIDIA开发的cuFFT库。
英文摘要：
The geometric multigrid method (GMG) is one of the most efficient solving techniques for discrete algebraic systems arising from elliptic partial differential equations. GMG utilizes a hierarchy of grids or discretizations and reduces the error at a number of frequencies simultaneously. Graphics processing units (GPUs) have recently burst onto the scientific computing scene as a technology that has yielded substantial performance and energy-efficiency improvements. A central challenge in implementing GMG on GPUs, though, is that computational work on coarse levels cannot fully utilize the capacity of a GPU. In this work, we perform numerical studies of GMG on CPU--GPU heterogeneous computers. Furthermore, we compare our implementation with an efficient CPU implementation of GMG and with the most popular fast Poisson solver, Fast Fourier Transform, in the cuFFT library developed by NVIDIA.
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