基于GPU的几类分数阶微分方程的并行算法研究及其实现

项目名称： 基于GPU的几类分数阶微分方程的并行算法研究及其实现

项目编号： No.11501238

项目类型： 青年科学基金项目

立项/批准年度： 2016

项目学科： 数理科学和化学

项目作者： 杨水平

作者单位： 惠州学院

项目金额： 18万元

中文摘要： 随着分数阶微分方程在众多的领域内得到广泛应用，高效快速的数值求解变得尤为重要。由于分数阶导数具有记忆性，数值求解分数阶微分方程会面临很大的计算量。本课题将致力于此方面的研究，期待取得重要进展。主要内容包括：（1）搭建GPU和CPU异构计算系统，利用基于方法分割、系统分割、时间分割三种研究策略设计分数阶常微分系统的高效并行算法并实现；（2）结合区域分解等技术对时间分数阶扩散方程进行空间离散，得到分数阶常微分系统，进一步结合分数阶常微分系统的并行算法，获得基于GPU的时间分数阶扩散方程的高效并行算法。本项目获得的成果将能有助于推动分数阶微分方程并行数值算法的发展，具有重要的科学意义和实践意义。

中文关键词： 分数阶常微分系统；时间分数阶扩散方程；GPU；并行算法

英文摘要： As fractional order differential equations have been widely used in more and more fields, the efficient and fast numerical methods for fractional differential equations have become particularly important. Usually, the numerical methods for fractional differential equations have huge computational loads because of memory effect of the fractional order operators. In this project, we will focus on solving this problem, and the detailed contents include the following two parts: (1) Through constructing the CPU-GPU heterogeneous system, the design and implementation of efficient parallel algorithms for the system of fractional order ordinary differential system will be studied by using three kinds of techniques; (2) Combined with domain decomposition method, spatial discretization of the time fractional diffusion equation will lead to a system of fractional ordinarily differential equations, which can be solved by the efficient parallel algorithms. Hence, it is possible to obtain the efficient parallel algorithms for the time fractional diffusion equation based on the CPU-GPU heterogeneous system. The outcomes of this project will effectively promote the rapid development of numerical methods for fractional differential equations. And these results will have important scientific significance and practical significance.

英文关键词： fractional ordinary differential system;the time fractional diffusion equation; graphics processor unit (GPU);parallel algorithm