Accelerating convolutions on the sphere with hybrid GPU/CPU kernel splitting

P.M. Sutter, Benjamin D. Wandelt, Franz Elsner
Department of Physics, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
arXiv:1211.3556 [astro-ph.IM] (15 Nov 2012)


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

   title={"{Accelerating convolutions on the sphere with hybrid GPU/CPU kernel splitting}"},

   journal={ArXiv e-prints},




   keywords={Astrophysics – Instrumentation and Methods for Astrophysics, Astrophysics – Cosmology and Extragalactic 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 function on the sphere with a radially-symmetric kernel. Our method splits the kernel into a compact real-space, and a compact spherical harmonic space component that can then be convolved in parallel using an inexpensive commodity GPU and a CPU, respectively. 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 sky map at the resolution typical of the high resolution maps of the cosmic microwave background anisotropies produced by the Planck space craft. 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 10^-5 in the (power spectrum of the) output map.
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