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