In this paper, a parallel computing scheme for performing implicit finite element calculations on acoustic problems running on a graphics processing unit (GPU) is proposed. This scheme combines the element-by-element (EBE) strategy and the edge-based smoothed finite element method (ES-FEM). A mapping strategy based on the ES-FEM is developed to parallel calculate various formulas for smoothing domains. A semi-parallel construction method for the smoothing domain is developed to address the fact that the smoothing domain is difficult to construct in parallel computing. This construction method is further developed into a pre-indexing method of the degrees of freedom (DOFs), which can be used with the parallel preconditioned conjugate gradient (PCG) method of solving linear equations to improve its computational efficiency. After the program flow diagram has been designed, Nvidia's CUDA is used to implement GPU-based parallel computing. Several numerical experiments are used to demonstrate the accuracy and efficiency of the proposed scheme.

在本文中，提出了一种并行计算方案，用于对在图形处理单元（GPU）上运行的声学问题执行隐式有限元计算。该方案结合了逐元素（EBE）策略和基于边缘的平滑有限元方法（ES-FEM）。开发了基于ES-FEM的映射策略，以并行计算用于平滑域的各种公式。针对平滑域难以在并行计算中构造的事实，开发了一种用于平滑域的半并行构造方法。此构造方法进一步发展为自由度（DOF）的预索引方法，可与求解线性方程的并行预处理共轭梯度（PCG）方法一起使用，以提高其计算效率。设计了程序流程图后，将使用Nvidia的CUDA来实现基于GPU的并行计算。几个数值实验被用来证明所提方案的准确性和效率。