On the inverse acoustic scattering problem by an open arc: the sound-hard case

This paper studies the inverse scattering problem by an open sound-hard arc. We prove a uniqueness theorem for this problem. For the foundation of Newton methods we establish the Fréchet differentiability of the far-field operator with respect to the open arc and show that the Fréchet derivative can be obtained as the solution of a hypersingular integral equation. We describe regularized Newton-type methods for approximately solving the inverse scattering problem and present numerical results for a number of differently chosen ansatz functions and arcs.