Enhancing the Performance of the DCA When Forming and Solving the Equations of Motion for Multibody Systems

This chapter provides an initial investigation into using the Graphics Processing Unit (GPU) (or similar hardware) to execute the Divide-and-Conquer Algorithm (DCA), which forms and solves the equations-of-motion for articulated multibody systems. The computational time required to form and solve the equations-of-motion of a simple n-length pendulum using the GPU is compared with a standard serial CPU implementation, a rudimentary parallelization on the CPU using OpenMP, and some combinations of the CPU and the GPU. The hybrid version uses the GPU for a select number of levels in the recursive sweeps and uses an OpenMP parallelization on a multi-core CPU for the remaining levels of recursion. The results demonstrate a significant performance increase when the GPU is used despite recursive algorithms being ill-suited to hardware designed for Single Instruction Multi-Data (SIMD). This is largely due to the tree-type structure of recursive processes, with half of the required operations being contained in the first level of recursion for a binary tree.