Modeling and optimization in cloaking problems for Maxwell equation

Abstract

We study control problem for the 2D model of electromagnetic field describing the scattering TM-polarized electromagnetic waves by anisotropic permeable dielectric obstacle with the boundary partially coated for masking. This problem arise while developing the design technologies of electromagnetic cloaking devices. The role of controls is played by refraction index and by boundary conductivity of the coated part of the boundary. Solvability of the control problem is proved and the optimality system is derived. Based on its analysis the uniqueness and stability of optimal solutions with respect to certain perturbations of both cost functional and incident field are established. A numerical algorithm is proposed and discussed.