Using hybrid GPU/CPU kernel splitting to accelerate spherical convolutions

TL;DR

This paper introduces a hybrid GPU/CPU kernel splitting method that significantly accelerates spherical convolutions, enabling faster CMB map simulations with controlled accuracy.

Contribution

The authors propose a novel kernel splitting technique that leverages GPU and CPU parallelism to accelerate spherical convolutions by over ten times.

Findings

Achieved over tenfold speedup in CMB map simulations.

Provided models to optimize kernel split for minimal computation time.

Maintained acceptable error bounds in the power spectrum.

Abstract

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.