Numerical investigation of ES-FEM with various mass re-distribution for acoustic problems

The edge-based smoothed finite element method (ES-FEM) in two-dimensional (2D) proposed recently shows great accuracy in the dynamic and acoustic problems. In the ES-FEM, the generalized gradient smoothing operation has been applied on the constructed edge-based smoothing domains with the stiffness matrix modified, while the other parts i.e. mass matrix is obtained in the same way as traditional FEM. In this paper, the balance between the “smoothed stiffness” and various “mass” system of ES-FEM is further studied for acoustic problems. Theoretical studies on dispersion error showed that the ES-FEM using consistent mass matrix can provide higher order accuracy compared with the ES-FEM using lump mass matrix in 2D cases. Numerical studies have also verified the advantage of ES-FEM using consistent mass matrix, and this conclusion is also applicable to edge-based tetrahedral smoothed finite element method (ES-T-FEM) in three-dimensional (3D) cases.