Wave scattering is present in many applications regarding non destructive testing, namely medical imaging. In particular, in the context of inverse scattering problems, the goal is to find unknown properties of the obstacle (scatterer) from the knowledge of the incident field and the measurement of the scattered field or far-field patern.

In this talk we will focus on numerical methods  to solve mathematical models for time-harmonic inverse scattering problems. It is important to notice that inverse scattering problems are usually ill-conditioned and nonlinear, so these two aspects have to be taken into account for the numerical approach.