有限元GPU加速计算的实现方法  

Implementation method of GPU-accelerated finite element calculation

作　　者：张健飞[1] 沈德飞[1] 

机构地区：[1]河海大学力学与材料学院,南京210098

出　　处：《计算机辅助工程》2014年第2期41-45,共5页Computer Aided Engineering

基　　金：国家自然科学基金(51109072)

摘　　要：研究基于GPU的有限元求解中的总刚矩阵生成和线性方程组求解问题.通过对单元着色和分组完成总刚矩阵的生成,并以行压缩存储(Compressed Sparse Row,CSR)格式存储,用预处理共轭梯度法求解所生成的大规模线性稀疏方程组.在CUDA(Compute Unified Device Architecture)平台上完成程序设计,并用GT430 GPU对弹性力学的平面问题和空间问题进行试验.结果表明,总刚矩阵生成和方程组求解分别得到最高11.7和8的计算加速比.The global stiffness matrix generation and the linear equations solution in finite element solution based on GPU is researched. The global stiffness matrix is generated using element coloring and grouping technique and stored in Compressed Sparse Row （CSR） format, and the preconditioned conjugate gradient method is used to solve the generated large-scale sparse linear equations. The code is programmed on Compute Unified Device Architecture （CUDA） platform and the plane and 3D elasticity matters are tested by GT430 GPU. The results show that the calculation speedups of the global stiffness matrix generation and linear equations solution reach 11.7 and 8 respectively.

关 键 词：GPU计算 有限元法 刚度矩阵 预处理共轭梯度法 

分 类 号：O241.82[理学—计算数学]