Massively parallel least squares finite element method with graphic processing unit

Abstract

For the reason of enormous computational expense, although the least squares finite element method has the advantages of high accuracy, robustness and strong versatility, the application of it is limited in computational fluid dynamics. The problems solved in this article include the rewriting of branching statements and the kernel function, variable distribution and data transfer between graphic processing units, and library functions rewriting. To the best knowledge of the authors, this article is the first time to develop the parallel computing codes for single and multiple graphic processing units based on the least squares finite element method. The computational results of single and multiple graphic processing units are verified by lid-driven cavity flow. Compared with a single central processing unit on the condition of 120 3 grids, the acceleration ratios of single and dual graphic processing units are up to 70.5 times and 95.2 times, respectively, which is much higher than the previous value of 7.7. With the increase in the grid number, the acceleration ratio of single and multiple graphic processing units is expected to increase, which can greatly enhance the computational efficiency of the least squares finite element method. Therefore, it is possible to solve the massive turbulence computing by the least squares finite element method with higher efficiency.