Title: Shape Taylor expansions for wave scattering problems: theory and computation
Abstract: Shape derivative is an important analytical tool for studying wave scattering problems involving perturbations in scatterers. Many applications, including inverse scattering, optimal design, and uncertainty quantification, are based on shape derivatives. However, computing high order shape derivatives is challenging due to the complexity of shape calculus. In this talk, we will introduce a comprehensive method for computing shape Taylor expansions using exterior calculus and recurrence formulas. The approach is applicable to both the acoustic and Maxwell equations under Dirichlet, Neumann, impedance, and transmission boundary conditions. Additionally, we apply the shape Taylor expansion to uncertainty quantification in wave scattering, enabling high order moment estimation for the scattered field under random boundary perturbations.