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Optimizing convolution operators is an important issue as they are used in numerous domains including electromagnetic computations, image processing and nanosimuations. In this paper we present our optimizations for 3D convolutions in the BigDFT nanosimulation software. We focus on processors with vector units and on GPU acceleration and experiment with several architectures. Exploiting the relation between algorithmic specifics and hardware architecture, we obtain performance gains of around x2 on CPU and up to x20 on GPU.

Optimizing 3D Convolutions for Wavelet Transforms on CPUs with SSE Units and GPUs