Second Order Shape Optimization for an Interface Identification Problem constrained by Nonlocal Models (2406.09118v1)

Abstract: Since shape optimization methods have been proven useful for identifying interfaces in models governed by partial differential equations, we show how shape optimization techniques can also be applied to an interface identification problem constrained by a nonlocal Dirichlet problem. Here, we focus on deriving the second shape derivative of the corresponding reduced functional and we further investigate a second order optimization algorithm.