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

Abstract

Inverse scattering acoustics find practical appli- cations in the detection and imaging of objects embedded in continuous media as well as in finding the optimum geomet- ric configuration of an object to produce a given radiation per- formance. This work introduces a boundary element method (BEM) approach for the solution of acoustic identification and optimization problems via a topological-shape sensitiv- ity 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 topolog- ical derivative formulation and to deal with infinite domains. The objectives for the identification and optimization prob- lems are to achieve a prescribed sound pressure at a given region of the problem domain. The locus giving extreme val- ues for the topological derivative indicates the optimum posi- tions 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.