Implementation of a parallel tree method on a GPU

Abstract

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.

Particle-in-cell plasma simulation on heterogeneous cluster systems

“…The substantial component of global GPU memory usage optimization is achieving coalescing [17], which in this particular case means processing of memory-wise nearby particles by index-wise nearby work-items in the same work-group. We can achieve it by keeping local ordering of particles which seems to be a common optimization strategy for a wide set of particle-mesh algorithms [18,19].…”

GOTHIC: Gravitational oct-tree code accelerated by hierarchical time step controlling

“…Adopting the tree method is a common way to accelerate collisionless N-body simulations in astrophysics, even on GPU. Many earlier studies presented tree codes efficiently running on GPU(s), yet none had coupled their code with the block time step (Nakasato, 2012;Ogiya et al, 2013;Bédorf et al, 2012Bédorf et al, , 2014Watanabe and Nakasato, 2014). Since the block time step can also accelerate N-body simulations significantly, we have developed a gravitational octree code (GOTHIC), which is accelerated by the block time step.…”

Bigger Buffer k-d Trees on Multi-Many-Core Systems

“…The focus of this work is on massivelyparallel processing of k-d trees. While several implementations have been proposed that address such traversals from a more general perspective (e.g., in the context of ray tracing) [13,17,20,26], these approaches are not suited for nearest neighbor search in moderate-sized feature spaces (i.e., d > 3), except for the recently proposed buffer k-d tree extension [11].…”