Iterative methods for first-kind integral equations of convolution type

The authors consider a field computation problem in terms of an integral equation of the kind and typical of those obtained by planar structures, in which the operator has a convolution kernel. It is shown that by extending the domain of the operator, the first kind of equation may be formally transformed into an equation of a second kind. It is demonstrated that the spectral iterative technique (SIT) applied to the first kind of equation is exactly equivalent to a Neumann series solution of the second kind of equation. The conjugate gradient method (CGM) is applied to both the first kind of equation and second kind of equation. Some representative numerical results for the problem of plane-wave scattering by a strip show a superiority in the rate of convergence of the conjugate scheme for the second kind of equation compared with the convergence rate of the original kind of equation.<>