基于Matlab平台有限元方法的GPU加速  

GPU Acceleration of the Finite Element Method Based on Matlab Platform

作　　者：苏辉 邱夏青 马文鹏 SU Hui;QIU Xiaqing;MA Wenpeng(Network Information and Calculating Center,Xinyang Normal University,Xinyang 464000,China;College of Computer and Information Technology, Xinyang Normal University,Xinyang 464000,China)

机构地区：[1]信阳师范学院网络信息与计算中心,河南信阳464000 [2]信阳师范学院计算机与信息技术学院,河南信阳464000

出　　处：《信阳师范学院学报（自然科学版）》2018年第4期677-680,共4页Journal of Xinyang Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(61402303;61501393);河南省高等学校重点科研项目(17B520034);河南省教育厅教改项目(2017-JSJYYB-055)

摘　　要：基于Matlab平台,采用有限元方法实现了对二维拉普拉斯(Laplace)方程在GPU平台上的加速.通过对物理问题的分析与物理模型的构建,完成总体CSR格式存储的刚度矩阵的生成;使用Matlab和CUDA混合编程,在Matlab平台上实现该有限元问题的并行加速;并结合Cu Blas数值计算库采用PCG算法求解装配后的大型线性稀疏方程组,从而高效地迭代出各格点的速度势.该算法既充分发挥了Matlab在数值计算方面的高效性,又充分发挥了GPU在细粒度并行加速方面的优势.The acceleration of the two-dimensional Laplace equation on the GPU platform was realized by using the finite element method based on Matlab platform.Through the analysis of the physical problem and the construction of the physical model,the generation of the stiffness matrix of the whole CSR format was completed.Parallel programming of the finite element problem was implemented on the Matlab platform using the mixed programming of Matlab and CUDA.Combining with the CuBlas numerical calculation library,the PCG algorithm was used to solve the large linear sparse system of the assembly,and the velocity potential of each lattice can be iterated efficiently.This algorithm not only gives full play to the efficiency of Matlab in numerical calculation,but also gives full play to the advantages of GPU in fine-grained parallel acceleration.

关 键 词：CUDA程序设计 有限元方法 GPU 预处理共轭梯度算法 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]