Optimal internal dissipation of a damped wave equation using a topological approach - Münch, Arnaud (Zielona Góra: Uniwersytet Zielonogórski)
We consider a linear damped wave equation defined on a two-dimensional domain ?, with a dissipative term localized in a subset ?. We address the shape design problem which consists in optimizing the shape of ? in order to minimize the energy of the system at a given time T. By introducing an adjoint problem, we first obtain explicitly the (shape) derivative of the energy at time T with respect to the variation in ?.
Keywords: shape design; wave equation; level set; topological derivative; numerical viscosity