A parallel numerical acoustic simulation on a GPU using an edge-based smoothed finite element method

Abstract

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.