publication . Preprint . Article . 2015

Using hybrid GPU/CPU kernel splitting to accelerate spherical convolutions

Paul M. Sutter; Benjamin D. Wandelt; Franz Elsner;
Open Access English
  • Published: 24 Mar 2015
  • Publisher: HAL CCSD
  • Country: France
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.
Comment: 9 pages, 11 figures, 1 table, accepted by Astronomy & Computing w/ minor revisions. arXiv admin note: substantial text overlap with arXiv:1211.3556
Persistent Identifiers
ACM Computing Classification System: ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION
free text keywords: Cosmology: theory, Methods: numerical, [ SDU.ASTR ] Sciences of the Universe [physics]/Astrophysics [astro-ph], [SDU.ASTR]Sciences of the Universe [physics]/Astrophysics [astro-ph], Astrophysics - Cosmology and Nongalactic Astrophysics, Astrophysics - Instrumentation and Methods for Astrophysics, Computer Science Applications, Astronomy and Astrophysics, Space and Planetary Science, Speedup, Frequency domain, Approximation error, Algorithm, Cosmic microwave background, Convolution, Computer science, Kernel (image processing), Planck, symbols.namesake, symbols, Spherical harmonics
Funded by
NSF| Collaborative Research: Simulation of Systematic Efffects in Interferometry for Studies of the Cosmic Microwave Background
  • Funder: National Science Foundation (NSF)
  • Project Code: 0908902
  • Funding stream: Directorate for Mathematical & Physical Sciences | Division of Astronomical Sciences
Understanding the Origin of Cosmic Structure
  • Funder: European Commission (EC)
  • Project Code: 306478
  • Funding stream: FP7 | SP2 | ERC
NSF| Programs on Critical Problems in Physics, Astrophysics and Biophysics at the Aspen Center for Physics
  • Funder: National Science Foundation (NSF)
  • Project Code: 1066293
  • Funding stream: Directorate for Mathematical & Physical Sciences | Division of Physics
Sorbonne Universités à Paris pour l'Enseignement et la Recherche
  • Funder: French National Research Agency (ANR) (ANR)
  • Project Code: ANR-11-IDEX-0004
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