Optimization approach for axisymmetric electric field cloaking and shielding

Abstract

In this paper we study inverse problems of electric conductivity that arise in the design of spherical shielding or cloaking shells and other functional devices used to control static electric fields. The shells are considered consisting of a finite number of layers filled with homogeneous isotropic or anisotropic medium. The inverse problems under study are reduced to control problems with the layers electric conductivities taken as controls. A different choice of minimized functionals allows us to solve a wide range of design problems using one approach. A numerical algorithm to solve these problems is based on particle swarm optimization. Various results of numerical experiments are discussed in order to find the most effective designs. The findings obtained in this study describe a broad set of specific easy-to-manufacture structures that have the highest cloaking or shielding performance in the class of layered shells.

Keywords:

• Conductivity problem
• shielding problem
• cloaking problem
• inverse problems
• numerical optimization
• PSO algorithm

2010 Mathematics Subject Classifications:

• 35J57
• 35R30
• 65K10

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The first and second authors were supported by the Ministry of Science and Higher Education of the Russian Federation (project no. 075-01095-20-00). Third author was supported by the Russian Foundation for Basic Research (project no. 18-57-45001).