A Numerical Method For Solving The Inverse Electromagnetic Scattering For A Locally Perturbed Perfectly Conducting Plate

This dissertation is trying to offer a feasible method for solving the inverse Electro-magnetic scattering problem for a local perturbation of a perfectly conducting plate. As this problem is one kind of the inverse scattering problems, we briefly introduce the background of acoustic and electromagnetic scattering problems and some specific prob-lems related to scattering problems, like obstacle scattering problems, cavity problem-s, source problems, medium problems. Furthermore, we review the development of methods for solving those problems. At the same time, we also introduce the frontier on acoustic and electromagnetic scattering problems. Then, we introduce the background of inverse acoustic and electromagnetic scattering problems and the methods for solving those problems. Moreover, in this dissertation, since we use the linear sampling method to solve the inverse scattering problems, we introduce two kinds of Sampling method-s, linear sampling methods and factorization method and their key ideas, applications and development. Furthermore, As we consider a simple but fully three-dimensional inverse problem to determine the shape of a local perturbation of a perfectly conduct-ing plate from far-field measurements of time harmonic electromagnetic fields. For this purpose we reformulate the model problem as an exterior Maxwell problem for a symmetric domain, and prove a equivalence between the model problem and its refor-mulation. Then, linear sampling method is applied to solve the reformulated problem. we illustrate the feasibility of this method by some numerical examples.