Hybrid smoothed finite element method for two-dimensional underwater acoustic scattering problems

Abstract

It is well known that the standard finite element method (FEM) is unreliable to solve acoustic problems governed by the Helmholtz equation with large wave numbers due to the “overly-stiff” nature of the FEM. In order to overcome this shortcoming, the hybrid smoothed finite element method (HS-FEM) using triangular elements is presented for the two-dimensional underwater acoustic scattering problems. In the HS-FEM, a scale factor α∈ [0, 1] is introduced to establish the area-weighted gradient field that contains contributions from both the standard FEM and the node-based smoothed finite element method (NS-FEM). The HS-FEM can provide a close-to-exact stiffness of the continuous system, thus the numerical dispersion error can be significantly decreased. To handle the underwater acoustic scattering problems in an infinite fluid medium, the bounded computational domain is obtained by introducing an artificial boundary on which the Dirichlet-to-Neumann (DtN) condition is imposed. Several numerical examples are investigated and the results showed that HS-FEM can provide more accurate solutions than the standard FEM. Therefore, the present method can be applied to practical underwater acoustic scattering problems such as sonar mine-hunting and sonar detection in ocean acoustics.