Analysis of underwater acoustic scattering problems using stable node-based smoothed finite element method

A stable node-based smoothed finite element method (SNS-FEM) is presented that cures the “overly-soft” property of the original node-based smoothed finite element method for the analysis of underwater acoustic scattering problems. In the SNS-FEM model, the node-based smoothed gradient field is enhanced by additional stabilization term related to the gradient variance items. It is demonstrated that SNS-FEM provides an ideal stiffness of the continuous system and improves the performance of the NS-FEM and FEM. In order to handle the acoustic scattering problems in unbounded domain, the well known Dirichlet-to-Neumann (DtN) boundary condition is combined with the present SNS-FEM to give a SNS-FEM-DtN model for exterior acoustic problems. Several numerical examples are investigated and the results show that the SNS-FEM-DtN model can achieve more accurate solutions compared to the NS-FEM and FEM.