Accelerated A-EFIE with perturbation method using fast fourier transform

In this paper, we apply the fast Fourier transform on the perturbation-based augmented electric field integral equation (A-EFIE). The main idea lies on the Lagrangian interpolation of a series Rⁿ, n = -1, 0, 1, 2, ..., obtained by expanding Green´s function using Taylor series. By utilizing the Toeplitz property of the Rⁿ on the uniform cartesian grids, the multiplication of expanded kernels in the vector and scalar potentials can be accelerated effectively. The oscillation of these expanded kernels has less variation compared to the original kernel with e^ikR/R. In addition, we do not need to do any near field amendment when n ≥ 0. Numerical example validates the feasibility and validity of this method.