A conjugate gradient algorithm of a 1D inverse scattering problem

Abstract

In this study, we are interested in finding the relative permittivity εr of the dielectric slab from the measured scattered field under the illumination of the incident field. We have used the conjugate gradient algorithm to reconstruct the relative permittivity εr in the interval[0,h]aftersolvingthewell-posed(intheweaksense)forwardandadjointproblems by using the finite element method. After a numerical implementation in Matlab, we observe from the numerical results that when we increase the number of layers in the dielectric slab from 5 to 10, the numerical reflection coefficient matches the analytical one. We also observe in that case that the number of iterations reduces from 50 to 40. Hencetheconjugategradientalgorithmsuggestedinthisstudycanbeusedtoreconstruct the relative permittivity for one dimensional inverse scattering problem.