The Discrete Convolution Method for Electromagnetic Problems

A discrete convolution method for electromagnetic problems is described. It is particularly well-suited to periodic structures such as linear and planar arrays, although some non-periodic structures may also be treated. The method may be applied to any structure for which a Moment Method formulation is available. The matrix equation becomes a discrete convolution equation which is treated by Discrete Fourier Transform methods using Fast Fourier Transform algorithms. An iterative procedure which converges rapidly is utilized. The number of complex multiplication and divisions is equal to kINlogN where N is the number of unknowns or expansion function, I is the number of iterations and k is a factor which depends on the type of problem treated. Typical results are presented for linear and planar arrays. Good agreement is obtained with direct methods such as Gaussian elimination.