High-frequency asymptotic expansions for multiple scattering problems with Neumann boundary conditions ☆

We consider the two-dimensional high-frequency plane wave scattering problem in the exterior of a finite collection of disjoint, compact, smooth (C infinity), strictly convex obstacles with Neumann boundary conditions. Using integral equation formulations, we determine the H & ouml;rmander classes and derive Melrose-Taylor type high-frequency asymptotic expansions of the total fields corresponding to multiple scattering iterations on the boundaries of the scattering obstacles. These asymptotic expansions are used to obtain sharp wavenumber dependent estimates on the derivatives of multiple scattering total fields. Numerical experiments supporting the validity of these expansions are presented. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.