Imaging a Non-Penetrable Target in a Waveguide Using the Topological Derivative

Using the topological derivative method, we study the shape reconstruction of a non-penetrable sound-soft obstacle located inside a tubular waveguide. We provide an expression for the topological derivative in terms of the solution of an auxiliary adjoint problem. The behavior of the topological derivative for different scatterer shapes, transducer locations, and numbers of transducers is demonstrated through numerical results in two dimensions.