Using hybrid GPU/CPU kernel splitting to accelerate spherical convolutions

P. M. Sutter, Benjamin D. Wandelt, Franz Elsner
INFN – National Institute for Nuclear Physics, via Valerio 2, I-34127 Trieste, Italy
arXiv:1409.4441 [astro-ph.CO], (15 Sep 2014)


   author={Sutter}, P.~M. and {Wandelt}, B.~D. and {Elsner}, F.},

   title={"{Using hybrid GPU/CPU kernel splitting to accelerate spherical convolutions}"},

   journal={ArXiv e-prints},



   keywords={Astrophysics – Cosmology and Nongalactic Astrophysics, Astrophysics – Instrumentation and Methods for Astrophysics},




   adsnote={Provided by the SAO/NASA Astrophysics Data System}


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We present a general method for accelerating by more than an order of magnitude the convolution of pixelated functions on the sphere with a radially-symmetric kernel. Our method splits the kernel into a compact real-space component and a compact spherical harmonic space component. These components can then be convolved in parallel using an inexpensive commodity GPU and a CPU. We provide models for the computational cost of both real-space and Fourier space convolutions and an estimate for the approximation error. Using these models we can determine the optimum split that minimizes the wall clock time for the convolution while satisfying the desired error bounds. We apply this technique to the problem of simulating a cosmic microwave background (CMB) anisotropy sky map at the resolution typical of the high resolution maps produced by the Planck mission. For the main Planck CMB science channels we achieve a speedup of over a factor of ten, assuming an acceptable fractional rms error of order 1.e-5 in the power spectrum of the output map.
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