An edge-based smoothed finite element method for two-dimensional underwater acoustic scattering problems

An edge-based smoothed finite element method (ES-FEM) is presented that cures the "overly-stiff" property of the original standard finite element method (FEM) for the analysis of two-dimensional underwater acoustic scattering problems. In the ES-FEM model, the gradient of the acoustic pressure (the acoustic particle velocity) is smoothed and the numerical integration is implemented using Green's theorem and Gauss integration, then the discretized linear system equations are established using smoothed Galerkin weak form with smoothing domains associated with the edges of the triangular elements. Due to the proper softening effect provided by the edge-based gradient smoothing operation, a "close-to-exact" stiffness of the system can be obtained, and then the numerical dispersion error can be significantly decreased. In order to handle the underwater acoustic scattering problems in an infinite domain, the unbounded domain is truncated by an artificial boundary on which the well-known Dirichlet-to-Neumann (DtN) boundary condition is imposed to replace the Sommerfeld condition at infinity in this paper. Several numerical examples are investigated and the results show that the ES-FEM can achieve more accutate solutions compared to the standard FEM.