Hybrid smoothed finite element method for two dimensional acoustic radiation problems

Abstract

It is well known that one key difficulty of solving the boundary-value problems governed by the Helmholtz equation using standard finite element method (FEM) is the loss of accuracy with increasing wave number due to the “numerical dispersion error”. In order to overcome this issue, the hybrid smoothed finite element method (HS-FEM) using linear triangular elements is presented to analyze two dimensional radiation problems. An important feature of HS-FEM is the introduction of a scale factor α∈ [0, 1] which is designed to establish the area-weighted strain field that contains contributions from both the standard FEM and the node-based smoothed finite element method (NS-FEM). The gradient smoothing technique used in the HS-FEM guarantees the numerical model can provide a close-to-exact stiffness to the continuous system and hence significantly reduces the numerical dispersion error. To solve the acoustic radiation problems in an infinite fluid domain, the HS-FEM is combined with the Dirichlet-to-Neumann (DtN) boundary condition to give a HS-FEM-DtN model for two dimensional acoustic radiation problems. Several numerical examples are given and it is found that HS-FEM can provide more accurate results than FEM with the same mesh.