Parallel implementation of hyper-dimensional dynamical particle system on CUDA

Abstract

The presented paper deals with possible approaches to parallel implementation of solution of a hyper-dimensional dynamical particle system. The proposed implementation approaches are generally applicable for similar particle systems of interest in various research and engineering fields. The original motivation for the present work was a simulation of particles that represent a space-filling design to be optimized for further use in design of experiments. Due to the underlying purpose of this particle system, the dimension of the particle system of interest is considered to be entirely arbitrary. Such a hyper-dimensional space is further folded into a periodically repeated domain.The theoretical background of the proposed particle system is provided along with the derivation of equations of motion of the dynamical system. As the complexity of the system is not limited by the number of particles nor the number of dimensions, the possibilities of utilizing the GPGPU platform are more restricted in comparison with today’s fast parallel implementations of common particle systems.Two distinct approaches to parallel implementation are presented, one aiming at a generalized usage of the fast on-chip resources, the other entirely relying on the GPU’s on-board global memory. Despite unambiguous mutual differences in their performance, both parallel implementations deliver major speedup compared to the single-thread CPU solution as well as a better scaling of execution time when increasing both the number of particles and dimensions.