Optimization analysis of electrostatic cloaking problems

Under consideration are the inverse problems of electrostatics that arise in designing two-dimensional multilayer shielding and cloaking devices. Using optimization, we reduce these inverse problems to the finite-dimensional extremal problems in which the roles of control parameters are played by the constant dielectric permittivities of the layers. Basing on particle swarm optimization, we develop some numerical algorithm for solving these problems. We also show that the devices designed by the algorithm have the highest cloaking efficiency and simplicity of technical implementation.