Numerical Precision and Benchmarking Very-High-Order Integration of Particle Dynamics on GPU Accelerators
Ken A. Hawick, Daniel Peter Playne, Mitchell G.B. Johnson · 2011
GPUs offer a powerful acceleration platform for many scientific applications. Numerical integration of classical Newtonian dynamical particles often requires very high-order numerical accuracy. We assess the floatingpoint precision and performance of various GPUs for applications involving high-order time-step integration methods for particle model simulations using N-squared interactions. We demonstrate how high-order algorithms can be expressed in Compute Unified Device Architecture (CUDA) and present some detailed benchmark data. We show the high numerical power of high-order integration methods such as Hairer’s 10 th order method and relate its performance to its precision requirements. KEY WORDS time-stepping; numerical precision; GPU; CUDA; high-order integration. support 64-bit floating point[2]. This support does vary however and in some cases the double precision floating point units are in fact shared across a group of compute cores within the GPU. Figure 1: The motion trails of three interacting particles. Numerically integrated using the Hairer 10th order integration method. 1