图形处理器在大规模力学问题计算中的应用进展

ADVANCES IN GRAPHICS PROCESSING UNITS' APPLICATIONS TO THE COMPUTATION OF LARGE-SCALE MECHANICAL PROBLEMS

现代图形处理器(graphics processing units,GPU)具有较强的并行数值运算功能.该文简单介绍了GPU的硬件结构,基于GPU通用计算的数据结构和实现方法,以及用于编写片元程序的OpenGL着色语言.介绍了应用GPU计算大规模力学问题的研究进展.简要介绍了以下内容:应用GPU模拟自然界的流体现象,其实质是使用有限差分法求解Navier-Stokes方程;应用GPU实现有限元法计算,使用基于GPU的共轭梯度法求解有限元方程组;应用GPU实现分子动力学计算,用GPU计算原子间短程作用力,并生成邻近原子列表;应用GPU实现量子力学Monte Carlo计算;应用GPU实现n个物体的引力相互作用,用GPU纹理存储n个物体的位置、质量、速度和加速度等.对基于图象处理器和中央处理器的计算作比较,已完成了以下基于GPU的计算:实现求解线性方程组的高斯消元法和共轭梯度法,并应用于大规模的有限元计算;加速无网格法计算;加速线性和非线性分子结构力学方法计算;用于计算分析碳纳米管的力学性能.指出GPU在大规模力学计算中的研究方向.

Modern graphics processing units （GPUs） are powerful parallel processors. The hardware architectures of modern graphics processing units, the data structures and implementations for general purpose GPU （GPGPU） computations, and the OpenGL shading language which is used to compile fragment programs are briefly described. The GPUs＇ applications for solving large scale mechanical problems are presented, with emphasis laid on the following aspects. GPUs are used to simulate natural fluid phenomena, and Navier-Stokes equations are solved by the finite difference method; GPUs are used to implement the finite element method computations, and the finite element method equations are solved by the conjugate gradient method on GPUs; GPUs are used to implement molecular dynamics computations, and short range pair forces are computed and the atom neighbor lists are built by GPUs; Quantum Monte Carlo simulations are computed on GPUs; GPUs are used to implement gravitational N-body simulations, and GPU textures are used to store the N bodies＇ positions, masses, velocities, and accelerations. The computations on GPUs and on central processing units （CPUs） are compared. The authors have performed the following computations on GPUs. The Gauss elimination method and the conjugate gradient method for solving linear equations, which are applied to large scale finite element method computations; Accelerations for the meshless method; Accelerations for linear and non- linear molecular structural mechanics approach, which are used to analyze the carbon nanotubes＇ mechanical properties. Further research trend of large scale mechanical computations on GPUs are suggested at the end of paper.