Optimization analysis of the cloaking problems for a 2D model of magnetostatics

The inverse problems for a two-dimensional model of magnetostatics arising in the development of design technologies of devices for material body cloaking are considered. It is assumed that the cloaking devices to be designed consist of a finite number of concentric annular layers filled with homogeneous anisotropic or isotropic media. The optimization technology is developed by which the mentioned inverse problems are reduced to finite-dimensional extremum problems. The role of controls in them is played by the magnetic permeabilities of the individual layers that compose the designed device. For their numerical solution, the algorithm based on the particle swarm optimization method is used. Important properties of optimal solutions are established, one of which is the bang-bang property in the case when all separate layers are isotropic. It is shown on the basis of computational experiments that cloaking devices designed using the developed optimization technology have simplicity of technical implementation and the highest efficiency in the class of devices under consideration.