Acceleration of Perturbation-Based Electric Field Integral Equations Using Fast Fourier Transform

In this communication, the computation of the perturbation-based electric field integral equation of the form R^n-1, n = 0, 1, 2, ⋯, is accelerated by using fast Fourier transform (FFT) technique. As an effective solution of the low-frequency problem, the perturbation method employs the Taylor expansion of the scalar Green's function in free space. However, multiple impedance matrices have to be solved at different frequency orders, and the computational cost becomes extremely high, especially for large-scale problems. Since the perturbed kernels still satisfy Toeplitz property on the uniform Cartesian grid, the FFT based on Lagrange interpolation can be well incorporated to accelerate the multiple matrix vector products. Because of the nonsingularity property of high-order kernels when n ≥ 1, we do not need to do any near field amendment. Finally, the efficiency of the proposed method is validated in an iterative solver with numerical examples.