Application of the edge-based gradient smoothing technique to acoustic radiation and acoustic scattering from rigid and elastic structures in two dimensions

As is well-known to all, the conventional finite element method (FEM) is constrained by the “numerical dispersion error” issue for solving acoustic problems at high frequencies. In this paper, the gradient smoothing technique (GST) which is based on the edges of the elements is combined with the conventional FEM to construct a novel edge-based smoothed FEM (ES-FEM) for two dimensional exterior structural-acoustic problems. The smoothed gradient field is obtained by performing the GST over the obtained smoothing domains (SDs). The present ES-FEM is able to provide a relatively appropriate stiffness of the real system owing to the “softening effects” from the GST. Therefore, the accuracy of the numerical solutions can be significantly improved. To effectively handle the exterior Helmholtz equation in unbounded domains, a predefined artificial boundary B is employed to obtain a bounded computational domain and the well-known Dirichlet-to-Neumann (DtN) map is used to prevent the possible reflections from the far-field. Several supporting numerical examples indicated that the ES-FEM with DtN map was very effective for exterior structural-acoustic problems and could produce more accurate numerical results than the conventional FEM.