Enhancing the performance of the DCA when forming and solving the equations of motion for multibody systems

Abstract

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 equationsof- motion of a simple n-length pendulum using the GPU is compared with a standard serialCPUimplementation, a rudimentary parallelization on theCPUusing OpenMP, and some combinations of theCPUand theGPU.The hybrid version uses theGPUfor 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.