Local absorbing boundaries of elliptical shape for scalar waves Original Research Article

We discuss the performance of a family of local and weakly-non-local in space and time absorbing boundary conditions, prescribed on truncation boundaries of elliptical shape for the solution of the two-dimensional wave equation in both the time- and frequency-domains. The elliptical artificial boundaries are derived as particular cases of general convex boundaries for which the absorbing conditions have been developed. The conditions, via an operator-splitting scheme, are shown to lend themselves to easy incorporation in a variational form that, in turn, leads to a standard Galerkin finite element approach. The resulting wave absorbing finite elements are shown to preserve the sparsity and symmetry of standard finite element schemes in both the time- and frequency-domains. Numerical experiments for transient and time-harmonic cases attest to the computational savings realized when elongated scatterers are surrounded by elliptically-shaped boundaries, as opposed to the more commonly used circular truncation geometries.