A Highly Accurate FGG-FG-FFT for the Combined Field Integral Equation

In this paper, a novel realization of the Integral Equation in combination with the fast Fourier transform for the CFIE is established by Fitting both the Green's function and its Gradient onto the nodes of a uniform Cartesian grid. The new method has been compared with several existing popular FFT-based methods, including the AIM, the IE-FFT, and the p-FFT. The accuracy of the proposed method is significantly higher than other FFT-based methods, and the method is not sensitive to both the grid spacing and the expansion order. The outstanding merit of the proposed method is that the fitting procedure is independent of the basis functions. Therefore, when the higher order basis functions would be adopted in the method of moments, only one fitting procedure for the Green's function and its gradient on a basis function support is needed to meet all of basis functions defined on this support. Some numerical examples are provided in this paper to demonstrate the accuracy and efficiency of the proposed method.