A Fast N-Body Scheme for Computational Cosmology

Abstract

We provide a novel and efficient algorithm for computing accelerations in theperiodic large-N-body problem that is at the same time significantly fasterand more accurate than previous methods. Our representation of theperiodic acceleration is precisely mathematically equivalent to that determinedby Ewald summation and is computed directly as an infinite lattice sum usingthe Newtonian kernel. 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 ProcessingUnits (GPUs) in computing Newtonian kernels straightforwardly to the periodic domain.The precise form of our direct interactions is based upon the adaptive softeninglength methodology introduced for open boundary conditions by Price and Monaghan.Furthermore, we describe a new Fast Multipole Method (FMM) that represents themultipoles and Taylor series as collections of pseudoparticles. Using thesetechniques we have computed forces to machine precision throughout the evolution ofa 1 billion particle cosmological simulation with a price/performance ratio morethan 100 times that of current numerical techniques operating at much lower accuracy.