Theoretical and Numerical Analysis of the Magnetic Cloaking Problem

Abstract

We consider the control problems for the 2D model of magnetic scattering by a permeable anisotropic obstacle having the form of a cylindrical layer. These problems arise in designing magnetic cloaking devices using the optimization method. The solvability of direct and optimization problems for the magnetic scattering model under study is proved. The optimality system which describes the necessary conditions of extremum is derived. Based on its analysis the sufficient conditions providing local uniqueness and stability of optimal solutions are established. Numerical aspects of applying the optimization approach are discussed.