Spectral Galerkin boundary element methods for high-frequency sound-hard scattering problems

This paper is concerned with the design of two different classes Galerkin boundary element methods for solution high-frequency sound-hard scattering problems in exterior two-dimensional smooth convex scatterers. We prove this that both require a small increase (in order \(k^\epsilon \) any \(\epsilon > 0\)) number degrees freedom to guarantee frequency independent precisions increasing wavenumber k. In addition, accuracy numerical solutions are provided sufficiently many terms asymptotic expansion incorporated into integral equation formulation. Numerical results validating \(\mathcal {O}(k^\epsilon )\) algorithms presented.