Accelerating numerical solution of stochastic differential equations with CUDA

This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2018)

Abstract
Numerical integration of stochastic differential equations is commonly used in many branches of science. In this paper we present how to accelerate this kind of numerical calculations with popular NVIDIA Graphics Processing Units using the CUDA programming environment. We address general aspects of numerical programming on stream processors and illustrate them by two examples: the noisy phase dynamics in a Josephson junction and the noisy Kuramoto model. In presented cases the measured speedu...

Title of program: SDE
Catalogue Id: AEFG_v1_0

Nature of problem
Direct numerical integration of stochastic differential equations is a computationally intensive problem, due to the necessity of calculating multiple independent realizations of the system. We exploit the inherent parallelism of this problem and perform the calculations on GPUs using the CUDA programming environment. The GPU's ability to execute hundreds of threads simultaneously makes it possible to speed up the computation by over two orders of magnitude, compared to a typical modern CPU.

Versions of this program held in the CPC repository in Mendeley Data
AEFG_v1_0; SDE; 10.1016/j.cpc.2009.09.009

本程序源自贝尔法斯特女王大学（Queen's University Belfast）馆藏的CPC程序库（1969-2018）。

摘要
随机微分方程的数值积分广泛应用于诸多科学分支领域。本文阐述了如何借助CUDA编程环境，利用主流NVIDIA图形处理器（Graphics Processing Units，GPU）加速此类数值计算。我们探讨了流处理器上数值编程的通用要点，并通过两个实例加以说明：约瑟夫森结（Josephson junction）中的噪声相位动力学，以及含噪声的库拉莫托（Kuramoto）模型。在上述案例中，实测的加速比...

程序名称：SDE
目录编号：AEFG_v1_0

问题本质
由于需要计算系统的多个独立实现，随机微分方程的直接数值积分属于计算密集型问题。我们利用该问题固有的并行性，借助CUDA编程环境在图形处理器上开展计算。与典型的现代中央处理器（Central Processing Unit，CPU）相比，GPU同时执行数百个线程的能力可将计算速度提升两个数量级以上。

孟德尔莱数据（Mendeley Data）平台下CPC程序库收录的本程序版本：AEFG_v1_0；SDE；10.1016/j.cpc.2009.09.009