Solution stability of iterative schemes utilizing the discrete Fourier transform (EM scattering)

The Fredholm integral equation of the first kind can be solved numerically using iterative schemes which minimize the integral square error. When the kernal is of the convolution type, the discrete Fourier transform (DFT) can be used when evaluating the operator equation in the iterative schemes. However, the DFT imposes an artificial periodicity, thus changing the nature of the problem. The effect of this on the solution has been studied and convergence investigated by comparison with a method of moments solution. A proposed method of avoiding the periodicity problem has been studied. The effect of introducing losses in the medium surrounding the scatterer has been investigated; provided losses are low, there is little effect on the solution.<>