苏辉, 邱夏青, 马文鹏. 基于Matlab平台有限元方法的GPU加速[J]. 信阳师范学院学报(自然科学版), 2018, 31(4): 677-680. doi: 10.3969/j.issn.1003-0972.2018.04.031 引用本文: 苏辉, 邱夏青, 马文鹏. 基于Matlab平台有限元方法的GPU加速[J]. 信阳师范学院学报(自然科学版), 2018, 31(4): 677-680. doi: 10.3969/j.issn.1003-0972.2018.04.031 SU Hui, QIU Xiaqing, MA Wenpeng. GPU Acceleration of the Finite Element Method Based on Matlab Platform[J]. Journal of Xinyang Normal University (Natural Science Edition), 2018, 31(4): 677-680. doi: 10.3969/j.issn.1003-0972.2018.04.031 Citation: SU Hui, QIU Xiaqing, MA Wenpeng. GPU Acceleration of the Finite Element Method Based on Matlab Platform[J]. Journal of Xinyang Normal University (Natural Science Edition) , 2018, 31(4): 677-680. doi: 10.3969/j.issn.1003-0972.2018.04.031 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CuBlas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. CUDA程序设计 /  有限元方法 /  GPU /  预处理共轭梯度算法 Abstract: 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. Key words: CUDA programming /  finite element method /  GPU /  preconditioned conjugate gradient algorithm

1. Network Information and Calculating Center, Xinyang Normal University, Xinyang 464000, China;

2. College of Computer and Information Technology, Xinyang Normal University, Xinyang 464000, China

Keywords:

CUDA programming /

finite element method /

GPU /

preconditioned conjugate gradient algorithm

Abstract: 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.

苏辉, 邱夏青, 马文鹏. 基于Matlab平台有限元方法的GPU加速[J]. 信阳师范学院学报(自然科学版), 2018, 31(4): 677-680. doi: 10.3969/j.issn.1003-0972.2018.04.031 引用本文: 苏辉, 邱夏青, 马文鹏. 基于Matlab平台有限元方法的GPU加速[J]. 信阳师范学院学报(自然科学版), 2018, 31(4): 677-680. doi: 10.3969/j.issn.1003-0972.2018.04.031 SU Hui, QIU Xiaqing, MA Wenpeng. GPU Acceleration of the Finite Element Method Based on Matlab Platform[J]. Journal of Xinyang Normal University (Natural Science Edition), 2018, 31(4): 677-680. doi: 10.3969/j.issn.1003-0972.2018.04.031 Citation: SU Hui, QIU Xiaqing, MA Wenpeng. GPU Acceleration of the Finite Element Method Based on Matlab Platform[J]. Journal of Xinyang Normal University (Natural Science Edition) , 2018, 31(4): 677-680. doi: 10.3969/j.issn.1003-0972.2018.04.031