An ES-FEM for accurate analysis of 3D mid-frequency acoustics using tetrahedron mesh

► An ES-FEM is proposed for 3D acoustics problems in the mid-frequency range. ► The gradient smoothing operation is applied on a new smoothing domain for this method. ► The ES-FEM provides more accurate results and higher efficiency than FEM and MIR. An edge-based smoothed finite element method (ES-FEM) is proposed to solve 3D acoustic problems in the mid-frequency range, using the simplest linear tetrahedron meshes that can be generated automatically for complicated geometry. In present ES-FEM, the gradient smoothing operation is performed with respect to each edge-based smoothing domain, which is also serving as building blocks in the assembly of the stiffness matrix. It turns out the ES-FEM provides an ideal amount of softening effect, and significantly reduces the numerical dispersion error in low- to mid-frequency range. Several numerical examples demonstrate the superiority of the ES-FEM for 3D acoustic analysis, especially at mid-frequency.