Shape optimization via a levelset and a Gauss-Newton method

In the context of shape optimization via level-set methods, we propose a general framework for a Gauss-Newton method to optimize quadratic functionals. Our approach provides a natural extension of the shape derivative as a vector field defined in the whole working domain. We implement and discuss this method in two cases: first a least-square error minimization reminiscent of the Electrical Impedance Tomography problem, and second the compliance problem with volume constraints.