FE-EFG耦合法的GPU并行加速及应用研究

doi:10.3901/JME.2018.11.197

机械工程学报 ›› 2018, Vol. 54 ›› Issue (11): 197-204.doi: 10.3901/JME.2018.11.197

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FE-EFG耦合法的GPU并行加速及应用研究

龚曙光, 廖宇梨, 谢桂兰, 张建平

湘潭大学机械工程学院湘潭 411105

收稿日期:2017-08-04 修回日期:2018-02-26 出版日期:2018-06-05 发布日期:2018-06-05
通讯作者: 龚曙光(通信作者),男,1964年出生,博士,教授,博士研究生导师。主要研究方向为多学科结构优化、CAE技术的理论与应用。E-mail:gongsg@xtu.edu.cn
作者简介:廖宇梨,男,1990年出生,硕士研究生。主要研究方向为多学科结构优化、CAE技术的理论与应用。E-mail:845462685@qq.com;谢桂兰,女,1966年出生,博士,教授,博士研究生导师。主要研究方向为新材料力学性能、塑性成形过程模拟与优化。E-mail:xieguilan@xtu.edu.cn;张建平,男,1981年出生,博士,副教授,硕士研究生导师。主要研究方向为多学科结构优化、CAE技术的理论与应用。E-mail:zhangjp@xtu.edu.cn
基金资助:
国家自然科学基金资助项目（51375417，51475403，51405415）。

Study on GPU Parallel Speedup and Application of FE-EFG Coupling Method

GONG Shuguang, LIAO Yuli, XIE Guilan, ZHANG Jianping

School of Mechanical Engineering, Xiangtan University, Xiangtan 411105

Received:2017-08-04 Revised:2018-02-26 Online:2018-06-05 Published:2018-06-05

摘要/Abstract

摘要： 有限元（Finite element，FE）-无网格Galerkin法（Element-free Galerkin，EFG）耦合能充分发挥有限元和无网格法各自具有的优势，为进一步提高FE-EFG耦合法在大规模工程应用中的计算效率，提出了一种FE-EFG耦合法的图形处理器（Graphic processing unit，GPU）并行加速算法，通过采用局域搜索法搜索EFG区域中节点影响域内的节点或积分点，以及积分点定义域内的节点；利用统一计算架构（Compute unified device architecture，CUDA）特点，在全求解域内引入交叉节点法实现了总体刚度矩阵的并行组装及按行压缩（Compress sparse row，CSR）存储；利用CUDA库函数并结合预条件共轭梯度（Preconditioned conjugate gradient，PCG）法对总体离散方程进行了迭代求解，2个数值算例验证了所提方法的可行性和计算精度，所得结果显示FE-EFG耦合法的计算效率得到显著提高，且其加速比会随计算规模的增加而增大，从而为大规模工程计算提供了一种高效的耦合算法。

关键词: FE-EFG耦合法, GPU并行计算, 交叉节点对, 局域搜索法, 组配法

Abstract: The finite element (FE)-element free Galerkin (EFG) coupling method can make full use of the respective advantages of finite element method and element-free Galerkin method. In order to further improve the computational efficiency of FE-EFG coupling method in large-scale engineering application, Graphic processing unit parallel speedup algorithm of coupled FE-EFG method is presented. Nodes or integral points in the nodal influence field, and the nodes in the integral point definition field are found efficiently by using the local search method in the EFG domain. Based on the characteristics of compute unified device architecture (CUDA), the idea of interacting node pair is introduced to parallel assemble the total stiffness matrix and store it by compress sparse row storage format. The preconditioned conjugate gradient is used to solve the total discrete equations based on the CUDA library function. Two numerical examples verified the feasibility and computational accuracy of presented coupling method. The results show that computational efficiency of FE-EFG coupling method is improved remarkably, and its speedup ratio will increase with the increase of computing scale. Thus, a highly efficient coupling algorithm is offered to large-scale engineering computation.

Key words: collocation approach, coupled FE-EFG method, GPU parallel computing, interaction node pair, local search method

中图分类号:

TH123
O241

龚曙光, 廖宇梨, 谢桂兰, 张建平. FE-EFG耦合法的GPU并行加速及应用研究[J]. 机械工程学报, 2018, 54(11): 197-204.

GONG Shuguang, LIAO Yuli, XIE Guilan, ZHANG Jianping. Study on GPU Parallel Speedup and Application of FE-EFG Coupling Method[J]. Journal of Mechanical Engineering, 2018, 54(11): 197-204.

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FE-EFG耦合法的GPU并行加速及应用研究

Study on GPU Parallel Speedup and Application of FE-EFG Coupling Method

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