Optimization-based numerical analysis of three-dimensional magnetic cloaking problems

Inverse problems for a three-dimensional magnetostatic model arising in the design of axisymmetric multilayered shielding and cloaking devices are stated. Assuming that the designed device consists of a finite number of spherical layers, each filled with a homogeneous isotropic medium, an optimization-based numerical algorithm is proposed for solving the problems. As a result, the considered inverse problems are reduced to finite-dimensional optimization ones in which the role of controls is played by the magnetic permeabilities of each elementary layer. The desired controls are found by applying particle swarm optimization. By analyzing numerical results, it is shown that the obtained optimal solutions correspond to cloaking devices having the highest efficiency in the considered class of devices and provide the simplicity of technical implementation.