Analysis of Large Nonregular Printed Scatterers Using the Contour-FFT

In fast Fourier transform (FFT)-based iterative methods for electromagnetic analysis of planar structures, the convolution between Green's function (GF) and the basis functions is carried out by a product in the spectral domain. In layered media, the GF is known analytically but exhibits singularities in the spectral domain, giving rise to numerical inaccuracy when processed by a direct FFT. We propose a direct spectral approach where the convolution is carried out with due account for the presence of a singular kernel. Using Contour-FFT, the integration contour is deformed and the spatial convolution is expressed as a rapidly converging series of FFTs. We also introduce a novel inverse Contour-FFT operator required for the process. As other FFT-based methods, the short-range interactions are corrected using a precomputed sparse operator, to which we propose an implementation compatible with the Contour-FFT. We control the accuracy of the method with a simple scheme that adapts the method's parameters to the problem at hand. Several practical numerical examples demonstrate the efficiency and accuracy of the method for the analysis of large nonregular printed structures.