Ultrasound Obstacle Identification using the Boundary Element and Topological Derivative Methods

Abstract

This chapter gathers together the key concepts of acoustic scattering and the inverse identification problems, the explicit expressions of the topological derivative for sound-hard and penetrable obstacles, and the key features of to solve the inverse identification problem numerically using the Boundary Ele- ment Method. Special attention is given to the implementation for the cases in which the search area has pre-existent obstacles, either sound-hard, penetrable or combination of both. Thus, a general BEM implementation framework is provided, which might be used by the reader to develop its own specific appli- cation. Several examples for sound-hard obstacles are used to demonstrate the performance of the method.