Optimization Method for Solving Cloaking and Shielding Problems for a 3D Model of Electrostatics

Gennadii Alekseev () and Alexey Lobanov ()
Additional contact information
Gennadii Alekseev: Institute of Applied Mathematics FEB RAS, 7, Radio St., 690041 Vladivostok, Russia
Alexey Lobanov: Institute of Applied Mathematics FEB RAS, 7, Radio St., 690041 Vladivostok, Russia

Mathematics, 2023, vol. 11, issue 6, 1-17

Abstract: Inverse problems for a 3D model of electrostatics, which arise when developing technologies for designing electric cloaking and shielding devices, are studied. It is assumed that the devices being designed to consist of a finite number of concentric spherical layers filled with homogeneous anisotropic or isotropic media. A mathematical technique for solving these problems has been developed. It is based on the formulation of cloaking or shielding problems in the form of inverse problems for the electrostatic model under consideration, reducing the latter problems to finite-dimensional extremum problems, and finding their solutions using one of the global minimization methods. Using the developed technology, the inverse problems are replaced by control problems, in which the role of controls is played by the permittivities of separate layers composing the device being designed. To solve them, a numerical algorithm based on the particle swarm optimization method is proposed. Important properties of optimal solutions are established, one of which is the bang-bang property. It is shown on the base of the computational experiments that cloaking and shielding devices designed using the developed algorithm have the simplicity of technical implementation and the highest performance in the class of devices under consideration.

Keywords: inverse problems; electrostatic cloaking; optimization method; particle swarm optimization method; bang-bang property (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/11/6/1395/pdf (application/pdf)
https://www.mdpi.com/2227-7390/11/6/1395/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:11:y:2023:i:6:p:1395-:d:1096164

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().