The Atomistic Green’s Function method for acoustic and elastic wave-scattering problems

Abstract

In this paper, we study the problem of wave scattering from finite heterogeneities (in 1- and 2-D) by using the Atomistic Green’s Function (AGF) technique. The application of AGF to classical wave scattering problems is novel and it allows us to compute the Green’s function of the scatterers, which is central to understanding the dynamics of the problem and is, in general, difficult to obtain. The AGF method also allows us to efficiently compute the numerically exact transmission and reflection coefficients without the need for any artificial truncating boundaries such as perfectly matched layers or Dirichlet to Neumann (DtN) maps. The technique generates the effective Hamiltonian of the wave scatterer and uses it to compute the numerically exact Green’s function of the scatterer. The formalism presented here is especially suited to scattering problems involving waveguides, phononic crystals, metamaterials, and metasurfaces. To illustrate the utility of the technique, we demonstrate the application of the method to three scattering problems: scattering from a slab (1D), scattering from a finite phononic crystal (1D), and scattering from defects in a waveguide (2D).