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We describe a hybrid Fourier/direct space convolution algorithm for compactradial (azimuthally symmetric) kernels on the sphere. For high resolution mapscovering a large fraction of the sky, our implementation takes advantage of theinexpensive massive parallelism afforded by consumer graphics processing units(GPUs). Applications involve modeling of instrumental beam shapes in terms ofcompact kernels, computation of fine-scale wavelet transformations, and optimalfiltering for the detection of point sources. Our algorithm works for anypixelization where pixels are grouped into isolatitude rings. Even for kernelsthat are not bandwidth limited, ringing features are completely absent on anECP grid. We demonstrate that they can be highly suppressed on the popularHEALPix pixelization, for which we develop a freely available implementation ofthe algorithm. As an example application, we show that running on a high-endconsumer graphics card our method speeds up beam convolution for simulations ofa characteristic Planck high frequency instrument channel by two orders ofmagnitude compared to the commonly used HEALPix implementation on one CPU corewhile maintaining at typical a fractional RMS accuracy of about 1 part in 10^5.

ARKCoS: Artifact-Suppressed Accelerated Radial Kernel Convolution on the Sphere