Performance analysis of direct N-body algorithms for astrophysical simulations on distributed systems

Abstract

We discuss the performance of direct summation codes used in the simulation of astrophysical stellar systems on highly distributed architectures. These codes compute the gravitational interaction among stars in an exact way and have an O(N^2) scaling with the number of particles. They can be applied to a variety of astrophysical problems, like the evolution of star clusters, the dynamics of black holes, the formation of planetary systems, and cosmological simulations. The simulation of realistic star clusters with sufficiently high accuracy cannot be performed on a single workstation but may be possible on parallel computers or grids. We have implemented two parallel schemes for a direct N-body code and we study their performance on general purpose parallel computers and large computational grids. We present the results of timing analyzes conducted on the different architectures and compare them with the predictions from theoretical models. We conclude that the simulation of star clusters with up to a million particles will be possible on large distributed computers in the next decade. Simulating entire galaxies however will in addition require new hybrid methods to speedup the calculation

Simulating N-Body Systems on the Grid Using Dedicated Hardware

“…Earlier experiments indicate that a grid of regular PCs across Europe improves overall performance for relatively small N [5], but these results do not necessarily extend to a global grid of GRAPEs, which has intercontinental network lines connecting special purpose nodes. We address the question for which problem size a world-wide grid has practical usage, and how to optimize our simulations to take advantage of the grid.…”

“…For our experiments we use two implementations of an N -body integrator. One of these codes runs on a single PC with and without GRAPE, whereas the other is parallelized with MPI using the ring algorithm (see [5] for more details).…”

“…This is a compute-intensive operation that requires the use of parallel algorithms or dedicated hardware (such as GRAPEs [2], or GPUs [3]) for simulating more than a few thousand stars. Several parallel algorithms have been developed for N-body simulations, including a copy algorithm [4], where updated particles are exchanged between all processes, and a ring algorithm [5].…”

“…Parallelization of GRAPEs appears to be an efficient way to reduce the wallclock time for individual simulations [4,5,6]. The gravitational N -body problem has calculation time complexity O(N 2 ), whereas the communication scales only with O(N ).…”

Towards Distributed Petascale Computing

“…[29] For PFlop/s scale computing we can assume that such required large granularity will be reached. Recently a Computation-centric application running in parallel on compute elements located in Poland, Cyprus, Portugal, and the Netherlands was successfully demonstrated [30,31].…”