A Newton method for solving the inverse scattering problem for a sound-hard obstacle

We present a Newton method for solving the ill-posed and nonlinear inverse scattering problem. For its foundation we establish the Frechet differentiability of the far-field operator with respect to the boundary and show that the Frechet derivative can be obtained as the solution of a hypersingular integral equation. In order to derive the right-hand sides of this integral equation we use a quadrature method. We describe the numerical solution method and give some numerical results.