by Nakasato, Naohito
Journal of Computational Science, 2011; See our recent update at http://galaxy.u-aizu.ac.jp/trac/note/wiki/Octree_On_GPU

The kd-tree is a fundamental tool in computer science. Among other applications, the application of kd-tree search (by the tree method) to the fast evaluation of particle interactions and neighbor search is highly important, since the computational complexity of these problems is reduced from O(N^2) for a brute force method to O(N log N) for the tree method, where N is the number of particles. In this paper, we present a parallel implementation of the tree method running on a graphics processing unit (GPU). We present a detailed description of how we have implemented the tree method on a Cypress GPU. An optimization that we found important is localized particle ordering to effectively utilize cache memory. We present a number of test results and performance measurements. Our results show that the execution of the tree traversal in a force calculation on a GPU is practical and efficient.

by Herrmann, Frank and Silberholz, John and Bellone, Matias and Guerberoff, Gustavo and Tiglio, Manuel
Added one reference

We report on early results of a numerical and statistical study of binary black hole inspirals. The two black holes are evolved using post-Newtonian approximations starting with initially randomly distributed spin vectors. We characterize certain aspects of the distribution shortly before merger. In particular we note the uniform distribution of black hole spin vector dot products shortly before merger and a high correlation between the initial and final black hole spin vector dot products in the equal-mass, maximally spinning case. These simulations were performed on Graphics Processing Units, and we demonstrate a speed-up of a factor 50 over a more conventional CPU implementation.