Plane wave basis in Galerkin BEM for bidimensional wave scattering

This paper considers the problem of scattering of a time-harmonic acoustic incident wave by a bidimensional hard obstacle. The numerical solution to this problem is found using a Galerkin wave boundary integral formulation whereby the functional space is built as the product of conventional low order piecewise polynomials with a set of plane waves propagating in various directions. In this work we improve the original method by presenting new strategies when dealing with irregular meshes and corners. Numerical results clearly demonstrate that these improvements allow the handling of scatterers with complicated geometries while maintaining a low discretization level of 2.5–3 degrees of freedom per full wavelength. This makes the method a reliable tool for tackling high-frequency scattering problems.