GPU accelerated Monte Carlo simulation of Brownian motors dynamics with CUDA

This work presents an updated and extended guide on methods of a proper acceleration of the Monte Carlo integration of stochastic differential equations with the commonly available NVIDIA Graphics Processing Units using the CUDA programming environment. We outline the general aspects of the scientific computing on graphics cards and demonstrate them with two models of a well known phenomenon of the noise induced transport of Brownian motors in periodic structures. As a source of fluctuations in the considered systems we selected the three most commonly occurring noises: the Gaussian white noise, the white Poissonian noise and the dichotomous process also known as a random telegraph signal. The detailed discussion on various aspects of the applied numerical schemes is also presented. The measured speedup can be of the astonishing order of about 3000 when compared to a typical CPU. This number significantly expands the range of problems solvable by use of stochastic simulations, allowing even an interactive research in some cases. Program Summary Program title: Poisson, dich Catalogue identifier: AEVP_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEVP_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU Lesser General Public License. version 3 No. of lines in distributed program, including test data, etc.: 3338 No. of bytes in distributed program, including test data, etc.: 45009 Distribution format: tar.gz Programming language: CUDA C. Computer: Any with CUDA-compliant GPU. Operating system: No limits (tested on Linux). RAM: Hundreds of megabytes for typical case Classification: 4.3, 23. External routines: The NVIDIA CUDA Random Number Generation library (cuRAND) Nature of problem: Graphics processing unit accelerated numerical simulation of stochastic differential equation. Solution method: The jump-adapted simplified weak order 2.0 predictor-corrector method is employed to integrate the Langevin equation of motion. Ensemble-averaged quantities of interest are obtained through averaging over multiple independent realizations of the system generated by means of the Monte Carlo method. Unusual features: The actual numerical simulation runs exclusively on the graphics processing unit using the CUDA environment. This allows for a speedup as large as about 3000 when compared to a typical CPU. Running time: A few seconds (C) 2015 Elsevier B.V. All rights reserved.