Block-asynchronous Multigrid Smoothers for GPU-accelerated Systems

Abstract This paper explores the need for asynchronous iteration algorithms as smoothers in multigrid methods. The hardware tar-get for the new algorithms is top-of-the-line, highly parallel hybrid architectures – multicore-based systems enhanced with GPGPUs. These architectures are the most likely candidates for future high-end supercomputers. To pave the road for their efficient use, we must resolve challenges related to the fact that data movement, not floating-point operations, is the bottleneck to performance. Our work is in this direction — we designed block-asynchronous multi-grid smoothers that perform more flops in order to reduce syn-chronization, and hence data movement. We show that the extra flops are done for “free, ” while synchronization is reduced and the convergence properties of multigrid with classical smoothers like Gauss-Seidel can be preserved