Inverse scattering analysis in acoustics via the BEM and the topological-shape sensitivity method

Inverse scattering acoustics find practical applications in the detection and imaging of objects embedded in continuous media as well as in finding the optimum geometric configuration of an object to produce a given radiation performance. This work introduces a boundary element method (BEM) approach for the solution of acoustic identification and optimization problems via a topological-shape sensitivity method. The devised optimization tool takes advantage of the inherent characteristics of BEM to effectively solve the forward and adjoint acoustic problems arising in the topological derivative formulation and to deal with infinite domains. The objectives for the identification and optimization problems are to achieve a prescribed sound pressure at a given region of the problem domain. The locus giving extreme values for the topological derivative indicates the optimum positions for the placement of sound-hard scatterers in order to minimize the cost function. The proposed implementation has the ability to deal with initially empty design spaces as well as with design spaces containing pre-existent scatterers. The capabilities of the method are demonstrated by solving a number of identification and optimization problems.