  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.
