Numerical Study of Geometric Multigrid Methods on CPU-GPU Heterogeneous Computers (Advances in Applied Mathematics and Mechanics, 2014)
The geometric multigrid method (GMG) is one of the most efficient solvingtechniques for discrete algebraic systems arising from elliptic partialdifferential equations. GMG utilizes a hierarchy of grids or discretizationsand reduces the error at a number of frequencies simultaneously. Graphicsprocessing units (GPUs) have recently burst onto the scientific computingscene as a technology that has yielded substantial performance and energy-efficiencyimprovements. A central challenge in implementing GMG on GPUs, though, is thatcomputational work on coarse levels cannot fully utilize the capacity of a GPU.In this work, we perform numerical studies of GMG on CPU-GPU heterogeneouscomputers. Furthermore, we compare our implementation with an efficient CPUimplementation of GMG and with the most popular fast Poisson solver, FastFourier Transform, in the cuFFT library developed by NVIDIA.