The Chamomile Scheme: An Optimized Algorithm for N-body simulations on Programmable Graphics Processing Units

We present an algorithm named "Chamomile Scheme". The scheme is fully optimized for calculating gravitational interactions on the latest programmable Graphics Processing Unit (GPU), NVIDIA GeForce8800GTX, which has (a) small but fast shared memories (16 K Bytes * 16) with no broadcasting mechanism and (b) floating point arithmetic hardware of 500 Gflop/s but only for single precision. Based on this scheme, we have developed a library for gravitational N-body simulations, "CUNBODY-1", whose measured performance reaches to 173 Gflop/s for 2048 particles and 256 Gflop/s for 131072 particles