OpenCL parallel integration of ordinary differential equations: Applications in computational dynamics

Abstract

In many physical problems the use of numerical simulations presents the only path to obtain insight into the behavior and evolution of the system of interest. GPU, CPU and MIC technologies are frequently employed for simulations on computational dynamics and we present results comparing different schemes for the numerical integration of ordinary differential systems (ODEs) in these architectures. The use of adapted methods with low memory storage (Low storage Runge–Kutta methods) gives good results for low precision studies, whereas the Taylor series method provides a powerful technique for high precision. We show how the computation of several dynamics indicators, such as a fast chaos indicator (FLI) or a phase shift indicator in small neuron networks (Central Pattern Generators), can be efficiently computed on these architectures by means of the numerical ODE methods executed through OpenCL. This high computational time reduction allows real-time simulations or generating video media. Program summaryProgram title: OCL-TIDES, OCL-RKCatalogue identifier: AEVW_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEVW_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 1836No. of bytes in distributed program, including test data, etc.: 10,617Distribution format: tar.gzProgramming language: C and OpenCL.Computer: Any computer with a CPU or a GPU or a Xeon Phi.Operating system: Linux, MacOS, Windows.Has the code been vectorized or parallelized?: Yes, using the parallelization methods from OpenCL.RAM: Problem dependentSupplementary material: A video with a Fast Lyapunov indicator simulation is available (see Appendix A).Classification: 4.3, 6.5.External routines: OpenCL version 1.2Nature of problem: Solution of ODE problems in generic OpenCL environment oriented to large scale independent sets of initial conditions.Solution method: OpenCL parallel integrator based in Runge–Kutta or Taylor Series Method suitable for large sets of independent sets of initial conditions. Both are able to run either on CPU or in a GPU, using the parallelization methods from OpenCL.Running time: Problem dependent, sample tests take less than a minute to run.