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

Abstract

We consider the two-dimensional high-frequency plane wave scattering problem in the exterior of a finite collection of disjoint, compact, smooth ($C^{\infty }$), strictly convex obstacles with Neumann boundary conditions. Using integral equation formulations, we determine the Hörmander 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.