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SUMMARYWe report on a generalization of the Bayliss-Gunzburger-Turkel non-re ecting boundary conditions to arbitrarily shaped convex artiÿcial boundaries. For elongated scatterers such as submarines, we show that this generalization can improve signiÿcantly the computational e ciency of ÿnite element methods applied to the solution of three-dimensional acoustic scattering problems.

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For elongated scatterers such as submarines, we show that the generalization of the Bayliss–Turkel nonreflecting boundary conditions to arbitrarily shaped convex artificial boundaries improves significantly the computational efficiency of finite element methods for the solution of acoustic scattering problems.

We present a computational methodology for retrieving the shape of an impenetrable obstacle from the knowledge of some acoustic far-field patterns. This methodology is based on the well known regularized Newton algorithm, but distinguishes itself from similar optimization procedures by (a) a frequency-aware multi-stage solution strategy, (b) a computationally efficient usage of the exact sensitivities of the far-field pattern to the specified shape parameters, and (c) a numerically scalable domain decomposition method for the fast solution of three-dimensional direct acoustic scattering problems. We illustrate the salient features and highlight the performance characteristics of the proposed computational methodology with the solution on a parallel processor of various inverse mockup submarine problems.