Abstract

Co-Authors: Anastasia Kisil, Raphael Assier Acoustic wave scattering by semi-infinite two-dimensional lattice structures is an essential but difficult subject to study in acoustic metamaterial research. In this talk, we consider diffraction by various configurations of many point scatterers. In recent decades, the Wiener-Hopf method has proven to be very useful in determining solutions to diffraction problems with a periodic arrangement of point scatterers. A particular case that will be considered here is when there is a doubly periodic quarter square lattice. This leads to a Wiener-Hopf equation in two variables with three unknown functions for which we can reduce and solve exactly using a new analytic method. After some suitable truncations, the solution can be numerically computed and is also compared to a numerical least squares collocation approach as well as to our previous method where we decomposed the lattice into rows or columns.