Optimization Method in 2D Thermal Cloaking Problems

Abstract

Inverse problems associated with designing cylindrical thermal cloaking shells are studied. Using the optimization method these inverse problems are reduced to corresponding control problems in which the diagonal components of diagonal in polar coordinates tensor of thermal conductivities play the role of passive controls. A numerical algorithm based on the particle swarm optimization is proposed and the results of numerical experiments are discussed. Rigorous optimization analysis shows that high cloaking efficiency of the shell can be achieved either using a highly anisotropic single-layer shell or using a multilayer shell composed of only three isotropic natural materials with optimally selected thermal conductivities.