The discrete Fourier transform method of solving differential-integral equations in scattering theory

An accurate and efficient numerical method is presented for solving many differential-integral equations arising from electromagnetic scattering theory. It uses the discrete Fourier transform technique to treat both the derivatives and the convolution integrals which often appear in these equations. As a consequence, this method is extremely simple to implement, uses less computer memory than comparable methods, and yields accurate predictions. The differential-integral equation is recast into a periodic form conducive to application of the discrete Fourier convolution theorem. The differential operators are approximated by appropriate finite-difference and discrete-convolution operators. All these quantities are computed by using the fast Fourier transform. An approximate solution is obtained by using the conjugate gradient method. Results are compared to experimental data or analytical solutions for a 3λ×3λ metal plate (where λ is the wavelength), a homogeneous and a layered infinite circular dielectric cylinder, and a dielectric sphere. The accuracy of the method is further illustrated by comparing predictions with independent measurements by R.A. Ross (1966) on a 2λ×1λ metal plate at grazing incidence. In all cases, agreement is excellent