A Numerical Method for Computing the Scattering Matrix by the Boundary Element Method with Applications to Phononic Band Analysis

We present a numerical method for computing scattering matrices (S-matrices) of periodic elastic structures using the boundary element method (BEM) with periodic Green's function. We first analyse elastic wave scattering of a single grating composed of a host matrix and periodic inclusions by the BEM and then construct the S-matrix from the obtained solutions and integral representations of reflection and transmission coefficients. In this paper, we demonstrate a numerical example of a phononic band calculation as an application of the S-matrix and confirm the effectiveness of our proposed method.