Boundary integral equation for inclusion and cavity shape sensitivity in harmonic elastodynamics

The formulation is implemented and tested for the case of arbitrarily shaped cavities and inclusions in a bounded or unbounded solid in the case of harmonic elastodynamics in 2D. The formulation is developed and studied independently of the discretization and of the parametrization of the change of geometry. The gradient is compared to some simple analytically solvable problems as well as complicated ones solved by centered finite differences for the sake of comparison. All of the cases give very stable and accurate results, both in static and dynamic elasticity.