An edge-based smoothed finite element method for wave scattering by an obstacle in elastic media

摘要

Scattering of a time-harmonic plane elastic wave by a rigid obstacle embedded in an isotropic homogeneous elastic medium has wide applications in science and engineering. This paper presents a novel method to study elastic wave scattering problems satisfying the Navier equation and Helmholtz equations with coupled boundary obtained by Helmholtz decomposition. We derive first smoothed Galerkin weak forms of Navier equation and Helmholtz equations to create effective smoothed finite element method (S-FEM) models. On the top of a three-noded triangular mesh, an edge-based S-FEM (ES-FEM-T3) combining with the perfectly matched layer (PML) technique is then established for solving the elastic wave scattering in bounded domains with PML to eliminate wave reflections. Some numerical experiments demonstrate that ES-FEM-T3 is more stable and accurate than the standard FEM for the elastic wave scattering.