Optimization Method in 2D Thermal Cloaking Problems

TL;DR

This paper develops an optimization approach using particle swarm algorithms to design efficient 2D thermal cloaking shells, achieving high cloaking performance with minimal material complexity.

Contribution

It introduces a novel optimization framework for thermal cloaking design, enabling high efficiency with simple multilayer isotropic materials.

Findings

High cloaking efficiency with anisotropic single-layer shells

Effective multilayer shells with only three isotropic materials

Optimization reduces complex inverse problems to control 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.