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GPU accelerated geometric multigrid method: Performance comparison on recent NVIDIA architectures

During the past decade Graphics Processing Units (GPU) have been increasingly employed for speeding up compute intensive scientific applications. In this field, the geometric multigrid method (GMG) is one of the most efficient algorithms for solving large sparse linear systems of equations. Herein we analyze the performance of an optimized GPU based implementation of the GMG method on different state-of-the-art NVIDIA GPUs. The GTX Titan Black card, set-up with increased double precision performance leads to the smallest execution time. It is marginally faster than the more recently released GTX Titan X card which has considerably lower double precision performance. Moreover, an energy efficiency analysis reveals that the GTX 660M and the more powerful Titan cards require a similar amount of energy for running the GMG algorithm: the larger execution time is compensated by the lower power consumption.