2nd Order Shape Optimization using Wavelet BEM

This present paper is concerned with second order methods for a class of shape optimization problems. We employ a complete boundary integral representation of the shape Hessian which involves first and second order derivatives of the state and the adjoint state function, as well as normal derivatives of its local shape derivatives. We introduce a boundary integral formulation to compute these quantities. The derived boundary integral equations are solved efficiently by a wavelet Galerkin scheme. A numerical example validates that, in spite of the higher effort of the Newton method compared to first order algorithms, we obtain more accurate solutions in less computational time