The Green's function perturbation method for solution of electromagnetic scattering problems _ Summary

Abstract

In this summary paper we will outline a new approximate method for solving large scale two-dimensional electromagnetic boundary value problems over perfect electric conductors PEC. Specifically, we will expand the Green's function in the kernel of the electric field integral equation EFIE [1] as a perturbation series with respect to the arc length variable s . The series is restricted by demanding that the first term is Toeplitz [2] with respect to s . The approximation is achieved by using the series form of the Green's function, truncated after Toeplitz term, in the EFIE. The reasoning behind such a scheme lies in the computational efficiency of inverting Toeplitz operators. In particular, Toeplitz operators can be inverted, using the fast Fourier transform FFT [3] thus reducing an O(N³) operation, where N is the number of discretizations along the scatterer, to an O(N log N) operation. There is also a saving in core storage from O(N²) to O(N).