Optimization-based method of solving 2D thermal cloaking problems

Abstract

Abstract We consider inverse problems for 2D heat conduction model concerning with designing cylindrical thermal cloaking shells. The shells are assumed consisting of a finite number of layers every of which is filled with homogeneous isotropic medium. Using the optimization method these inverse problems are reduced to corresponding control problems. Thermal conductivities of the shell layers 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 using a multilayer shell composed of only three isotropic nature materials with optimally selected thermal conductivities.