A fast N-body scheme for computational cosmology

We provide a novel and efficient algorithm for computing accelerations in the periodic large-N-body problem that is at the same time significantly faster and more accurate than previous methods. Our representation of the periodic acceleration is precisely mathematically equivalent to that determined by Ewald summation and is computed directly as an infinite lattice sum using the Newtonian kernel (|r|-1). Retaining this kernel implies that one can (i) extend the standard open boundary numerical algorithms and (ii) harness the tremendous computational speed possessed by Graphics Processing Units (GPUs) in computing Newtonian kernels straightforwardly to the periodic domain. The precise form of our direct interactions is based upon the adaptive softening length methodology introduced for open boundary conditions by Price and Monaghan. Furthermore, we describe a new Fast Multipole Method (FMM) that represents the multipoles and Taylor series as collections of pseudoparticles. Using these techniques we have computed forces to machine precision throughout the evolution of a 1 billion particle cosmological simulation with a price/performance ratio more than 100 times that of current numerical techniques operating at much lower accuracy.