The stable node-based smoothed finite element method for analyzing acoustic radiation problems

In this paper, the stable node-based smoothed finite element method (SNS-FEM) and the well-known Dirichlet-to-Neumann (DtN) boundary condition are coupled together to reduce the dispersion error in analyzing acoustic radiation problems. An artificial boundary is introduced to truncate the infinite domain and the DtN boundary condition is imposed on the artificial boundary to guarantee the uniqueness of the solution. In the SNS-FEM formulation, a stable item which contains the gradient variance items is constructed without any uncertain parameter to strengthen the system stiffness. Through this operation, a perfect balance between the stiffness and mass matrices is established and the dispersion error is reduced significantly. Two benchmark cases and two practical engineering problems are employed to investigate the performance of the SNS-FEM. The results demonstrate that the SNS-FEM achieves super accuracy and super convergence. Additionally, the SNS-FEM is less sensitive to the wave number and high-efficiency.