基于GPU的快速有限元法求解密度场  

A fast finite element method based on GPU to solve density field

作　　者：李果阳 严华[1] 张征宇[2] 陈沁梅 祝福顺 LI Guoyang;YAN Hua;ZHANG Zhengyu;CHEN Qinmei;ZHU Fushun(College of Electronics Information Engineering,Sichuan University,Chengdu 610065,China;High Speed Aerdynamics Institute,China Aerodynamics Research and Development Center,Mianyang 621000,China)

机构地区：[1]四川大学电子信息学院,成都610065 [2]中国空气动力研究与发展中心高速空气动力研究所,绵阳621000

出　　处：《北京航空航天大学学报》2021年第10期2088-2096,共9页Journal of Beijing University of Aeronautics and Astronautics

基　　金：国家自然科学基金(11872069)。

摘　　要：为了快速计算分析利用视频测量方法测得的高速风洞试验密度场在扰动流场作用下的实验数据,针对密度场的数值求解问题,经过光线偏折理论分析密度场得到的二阶偏微分方程,对其研究实现了CPU串行有限元法求解。在此基础上提出了基于GPU的快速有限元求解密度场的方法,该方法经过对串行有限元法求解过程效率分析后,将耗时的神经网络拟合、总刚度矩阵和总载荷向量的求解进行了基于GPU的并行加速。实验结果表明:在精度满足实际工程要求的前提下,相对于CPU串行求解方法,所提方法可大大提高求解效率,且随着网格剖分成倍加密,其加速比成倍增加。In order to quickly calculate and analyze the experimental data under the action of turbulence field,which are measured by video measurement method in high-speed wind tunnel test density projection field,and aimed at the numerical solution of density projection field,the second-order partial differential equation of density projection field is analyzed by ray deflection theory.And the CPU serial finite element method is realized to solve the problem.On this basis,a GPU-based fast finite element method for solving density field is proposed.After analyzing the efficiency of the serial finite element method solving process,the time-consuming neural network fitting,total stiffness matrix and total load vector are solved and then GPU-based parallel acceleration are carried out.The experimental results show that,under the premise that the accuracy meets the actual engineering requirements,the proposed method can greatly improve the solving efficiency compared with the CPU serial solution method,and the acceleration ratio is multiplied with the grid subdivision and multiplied encryption.

关 键 词：密度投影场 有限元 并行加速 二阶偏微分方程 刚度矩阵 

分 类 号：TP301.6[自动化与计算机技术—计算机系统结构]