Hybrid smoothed finite element method for acoustic problems

It is well known that "overly-stiff" finite element (FE) model fails to provide accurate results to the Helmholtz equation with large wave numbers due to the well-known "pollution error" caused by the numerical dispersion. In this paper, the hybrid smoothed finite element method (HS-FEM) using triangular (2D) and tetrahedron (3D) elements that can be generated automatically for any complicated domain is formulated to solve acoustic problems in order to overcome the shortcomings of standard finite element method (FEM). In the formulation, a parameter α is equipped into HS-FEM, and the strain field is further assumed to be the weighted average between compatible strains from standard FEM and smoothed strains from node-based smoothed finite element method (NS-FEM). The smoothing technique can provide a softening effect to the model and have a very close-to-exact stiffness of the continuous system and hence significantly improve the accuracy of solution in both structural and acoustic analyses. Intensive numerical studies have been conducted here to demonstrate the effectiveness of the HS-FEM.