Application of FFT and the conjugate gradient method for the solution of electromagnetic radiation from electrically large and small conducting bodies

Abstract
A novel combination of the conjugate gradient (CG) method with the fast Fourier transform technique (FFT) is presented. With this combination, the computational time required to solve large scatterer problems is much less than the time required by the ordinary conjugate gradient method and the method of moments. On the other hand, since the spatial derivatives are replaced with simple multiplications in the transformed domain, some of the computational difficulties present in the ordinary conjugate gradient method and the method of moments do not exist here. Therefore, electrically small structures can also be handled more easily. Finally, since the method is iterative, it is possible to know the accuracy in a problem solution. Two types of scatterers are analyzed: wires (both very long and very short) and square plates (very large and small). The details of the computational procedure are presented along with numerical results for some of the scatterers analyzed.