  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.
