Asymptotic expansions of high-frequency multiple scattering iterations for sound hard scattering problems

TL;DR

This paper derives high-frequency asymptotic expansions for multiple scattering problems involving sound-hard obstacles, enabling improved numerical methods and sharper estimates for wave scattering analysis.

Contribution

It introduces novel asymptotic expansions for multiple scattering iterations, enhancing the accuracy and efficiency of boundary element methods for high-frequency sound-hard scattering.

Findings

Derived asymptotic expansions for total fields

Obtained sharp wavenumber-dependent estimates

Validated expansions with numerical experiments

Abstract

We consider the two-dimensional high-frequency plane wave scattering problem in the exterior of a finite collection of disjoint, compact, smooth, strictly convex obstacles with Neumann boundary conditions. Using integral equation formulations, we determine the H\"{o}rmander classes and derive 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 which, in turn, allow for the optimal design and numerical analysis of Galerkin boundary element methods for the efficient (frequency independent) approximation of sound hard multiple scattering returns. Numerical experiments supporting the validity of these expansions are presented.