This paper discusses 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 that 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 as well as the artificial reflected power is minimized without compromising the sparsity of the finite element matrix. Performance analysis indicates that the absorbing boundary operator increases the accuracy from O(1/r3/2) to O(1/r9/2). The numerical results are compared with analytical solutions of cylindrical scatterers of different sizes and at different frequencies. Also, the flexibility of the model is demonstrated by simulating inhomogeneous scatterers and multi-scattering configurations.
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Gan et al. (1993) studied this question.