Shape sensitivity calculations for exterior acoustics problems

The purpose of this paper is to present a method to calculate the derivative of a functional that depends on the shape of an object. This functional depends on the solution of a linear acoustic problem posed in an unbounded domain. We rewrite this problem in terms of another one posed in a bounded domain using the Dirichlet-to-Neumann (DtN) map of the modified DtN map. Using a classical method in shape sensitivity analysis, called the adjoint method, we are able to calculate the derivative of the functional using the solution of an auxiliary problem. This method is particularly efficient because the cost of calculating the derivatives is independent of the number of parameters used to approximate the shape of the domain. The resulting variational problems are discretized using the finite-element method and solved using an efficient Krylov-subspace iterative scheme. Numerical examples that illustrate the efficacy of our approach are presented.