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.