An efficient space partitioning technique based on linear kd-trees for simulation of short-range interactions in particle methods

We present an efficient pruning algorithm for selecting candidate short-range interaction pairs in particle-based discretization methods such as the discrete element method or smoothed particle hydrodynamics. Geometrically, our technique is based on a recursive bisection of space, forming a particular type of kd-tree. But instead of relying on a tree data structure, our algorithm traverses an implicit tree stored as an associative array. We study its time and memory complexity, and compare the performance of our implementation with that of other algorithms (namely Sweep and Prune and Delaunay triangulation). Preliminary tests show that the linear kd-tree performs more than fifty times faster than the other methods on conventional computers, for highly dynamic simulations with a few thousand elements or more. We also conclude that simulations of several million elements are feasible on a single processor in less than ten seconds per time step.