Finite element formulation of acoustic scattering phenomena with absorbing boundary condition in the frequency domain

The authors discuss a finite element formulation with an absorbing boundary condition to simulate acoustic scattering phenomena in a general situation, that is, including density as well as sound velocity variations of single and multi-scatterers of arbitrary two dimensional cross sections. In this model, a Galerkin finite element formulation is incorporated with an absorbing boundary operator which explicitly accounts for the open field problem by mapping the Sommerfeld radiation condition from the far field to the near field. By applying the absorbing boundary operator on the artificial boundary of the finite domain, the truncation errors and the artifactual reflected power are minimized without compromising the sparsity of the finite element matrix. Numerical results are compared with analytical solutions of cylindrical scatterers of different sizes and at different frequencies. The flexibility of the model is demonstrated by simulating inhomogeneous scatterers and multi-scattering configurations