The Unified Transform: A Spectral Collocation Method for Acoustic Scattering

Abstract

This paper employs the unified transform to present a boundary-based spectral collocation method suitable for solving acoustic scattering problems. The method is suitable for both interior and exterior scattering problems, and may be extended to three dimensions. A number of simple two-dimensional examples are presented to illustrate the versatility of this method, and, upon comparison with other spectral methods, or boundary-based methods the approach presented in this paper is shown to be very competitive.