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On the solution of direct and inverse multiple scattering problems for mixed sound-soft, sound-hard and penetrable objects

In this work we consider a scattering problem governed by the two-dimensional Helmholtz equation, where some objects of different nature (sound-hard, sound-soft and penetrable) are present in the background medium. First we propose and analyze a system of boundary integral equations to solve the direct problem. After that, we propose a numerical method based on the computation of a multifrequency topological energy based imaging functional to find the shape of the objects (without knowing their nature) from measurements of the total field at a set of observation points. Numerical examples show that the proposed indicator function is able to detect objects of different nature and/or shape and size when processing noisy data for a rich enough range of frequencies.