Increasing arithmetic intensity in multigrid methods on GPUs using block smoothers

Abstract

Block smoothers that relax small blocks of unknowns provide a way to increase the amount of arithmetic operations needed per smoothing iteration. If the block sizes are small, the variables associated to these blocks fit in fast local memories, thus allowing for a better exploitation of modern computer architectures. At the same time block smoothers are efficient smoothers that allow for more aggressive coarsening resulting in less coarse grids. We implemented block smoothers in combination with aggressive coarsening in OpenCL, targeting GPUs. Two different data layouts were compared for the smoother. The results show that while the more advanced data layout does not yield a better performance, the introduction of block smoothers in multigrid methods can indeed reduce the time to solution on a GPU.