A fast algorithm for simulating finite scattering configurations featuring Rayleigh-Bloch waves

Rayleigh–Bloch (RB) waves are a class of guided waves that occur in periodic structures, specifically in one-dimensional (1D) arrays of scatterers, and decay exponentially away from the array. RB waves can also be identified on large finite arrays, and contribute significantly to their response to incident wave forcing. Moreover, RB waves can be utilised to design arrays with specific characteristics, such as trapping, blocking, or amplifying waves. However, simulating wave interactions with these arrays poses challenges due to the large number of scatterers. Additionally, the existence of RB waves is linked to poor conditioning of the associated linear systems. We address these challenges by employing a recently developed fast matrix–vector product boundary integral equation algorithm for simulating wave interactions in large configurations. We combine state-of-the-art iterative solvers with effective preconditioners, for periodic structures containing hundreds of penetrable 2D scatterers.