Shape optimization by pursuing diffeomorphisms

Abstract

We consider PDE constrained shape optimization in the framework of nite element discretizationof the underlying boundary value problem. We present an algorithm tailored to preserve and exploit the ap-proximation properties of the nite element method, and that allows for arbitrarily high resolution of shapes.It employs (i) B-spline based representations of the deformation di eomorphism, and (ii) superconvergentdomain integral expressions for the shape gradient. We provide numerical evidence of the performance ofthis method both on prototypical well-posed and ill-posed shape optimization problems.