Stencil operations are often a key component when performing acoustics simulations, for which the specific choice of implementation can have a significant effect on both accuracy and computational performance. This paper presents a detailed investigation of computational performance for GPU-based stencil operations in two-step finite difference schemes, using stencils of varying shape and size (ranging from seven to more than 450 points in size). Using an Nvidia K20 GPU, it is found that as the stencil size increases, compute times increase less than that naively expected by considering only the number of computational operations involved, because performance is instead determined by data transfer times throughout the GPU memory architecture. With regards to the effects of stencil shape, performance obtained with stencils that are compact in space is mainly due to efficient use of the read-only data (texture) cache on the K20, and performance obtained with standard high-order stencils is due to increased memory bandwidth usage, compensating for lower cache hit rates. Also in this study, a brief comparison is made with performance results from a related, recent study that used a shared memory approach on a GTX 670 GPU device. It is found that by making efficient use of a GTX 660Ti GPU—whose computational performance is generally lower than that of a GTX 670—similar or better performance to those results can be achieved without the use of shared memory.

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