Identification d'obstacles en acoustique dans des domaines tridimensionnels bornés

This communication addresses the identification of rigid scatterers in a three-dimensional acoustic medium of finite extent. The methodology is based on two main concepts. The first is a boundary element formulation of the relevant acoustic boundary value problems which is accelerated by means of the Fast Multipole Method, and thereby applicable to acoustic domains of relatively large size compared to the acoustic wavelength. The second is the topological gradient of the cost function associated with the inverse problem, a distribution whose computation indicates the spatial regions in the acoustic medium where the virtual introduction of a rigid scatterer of very small size induces a decrease of the cost function, thereby allowing e.g. a better-informed choice of initial conditions for a subsequent optimization-based inversion algorithm. Both concepts are presented and demonstrated on numerical examples.