Efficient calculation of the integral equation for simulating 2D TE scattering in a homogeneous medium using the Ewald method and a Gabor frame discretization

Abstract

We utilize the domain integral equation formulation to simulate two-dimensional transverse electric scattering in a homogeneous medium and a summation of modulated Gaussian functions to approximate the dual Gabor window. Then we apply Ewald Green function transformation to separate the integrals related to x and z in the integral equation, which produce Gaussian functions. These Gaussian functions in the integrands can be integrated analytically, which greatly simplifies the calculation process. Finally, we discuss the convergence and the selection of the Ewald splitting parameter E.