Shape sensitivity calculations for exterior acoustics problems

The purpose of this paper is to present a method to calculate the derivativ e of a functional that depends on the shape of an object. This functional d epends on the solution of a linear acoustic problem posed in an unbounded d omain. We rewrite this problem in terms of another one posed in a bounded d omain using the Dirichlet-to-Neumann (DtN) map oi the modified DtN map. Usi ng a classical method in shape sensitivity analysis, called the adjoint met hod, we are able to calculate the derivative of the functional using the so lution of an auxiliary problem. This method is particularly efficient becau se the cost of calculating the derivatives is independent of the number of parameters used to approximate the shape of the domain. The resulting varia tional problems are discretized using the finite-element method and solved using an efficient Krylov-subspace iterative scheme. Numerical examples tha t illustrate the efficacy of our approach are presented.