Geodesic
Numerical optimization in the problems of designing multilayer magnetic cloaking shells
Dalʹnevostočnyj matematičeskij žurnal, Tome 23 (2023) no. 2, pp. 264-269.

Voir la notice de l'article provenant de la source Math-Net.Ru

A multiparameter optimization problem of magnetic cloaking is solved for a two-dimensional model of magnetostatics. This problem arises when designing cylindrical multilayer cloaking devices filled with anisotropic or isotropic magnetic media with tensor, in the general case, magnetic permeabilities. Applying the optimization method for solving inverse problems the considered problem of magnetic cloaking is reduced to a finite-dimensional extremum problem. The results of applying the developed numerical algorithm based on the particle swarm optimization method to solve the extremum problem confirm its high efficiency and make it possible to establish the important property of the obtained optimal solutions. 
@article{DVMG_2023_23_2_a11,
     author = {Yu. E. Spivak},
     title = {Numerical optimization in the problems of designing multilayer magnetic cloaking shells},
     journal = {Dalʹnevosto\v{c}nyj matemati\v{c}eskij \v{z}urnal},
     pages = {264--269},
     publisher = {mathdoc},
     volume = {23},
     number = {2},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DVMG_2023_23_2_a11/}
}
TY  - JOUR
AU  - Yu. E. Spivak
TI  - Numerical optimization in the problems of designing multilayer magnetic cloaking shells
JO  - Dalʹnevostočnyj matematičeskij žurnal
PY  - 2023
SP  - 264
EP  - 269
VL  - 23
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DVMG_2023_23_2_a11/
LA  - ru
ID  - DVMG_2023_23_2_a11
ER  - 
%0 Journal Article
%A Yu. E. Spivak
%T Numerical optimization in the problems of designing multilayer magnetic cloaking shells
%J Dalʹnevostočnyj matematičeskij žurnal
%D 2023
%P 264-269
%V 23
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DVMG_2023_23_2_a11/
%G ru
%F DVMG_2023_23_2_a11
Yu. E. Spivak. Numerical optimization in the problems of designing multilayer magnetic cloaking shells. Dalʹnevostočnyj matematičeskij žurnal, Tome 23 (2023) no. 2, pp. 264-269. http://geodesic.mathdoc.fr/item/DVMG_2023_23_2_a11/

[1] A. Michaloglou, N. L. Tsitsas, “Feasible optimal solutions of electromagnetic cloaking problems by chaotic accelerated particle swarm optimization”, Mathematics, 9 (2021), 2725, 23 pp. | DOI

[2] Z. Yang, X. Huang, “An acoustic cloaking design based on topology optimization”, J. Acoust. Soc. Am., 152 (2022), 3510–3521 | DOI

[3] S. Guenneau, C. Amra, D. Veynante, “Transformation thermodynamics: cloaking and concentrating heat flux”, Opt. Express., 20 (2012), 8207–8218 | DOI

[4] B. Wood, J. B. Pendry, “Metamaterials at zero frequency”, J. Phys.: Condens. Matter., 19 (2007), 076208, 9 pp. | DOI

[5] A. N. Tikhonov, V. Ya. Arsenin, Metody resheniya nekorrektnykh zadach, Nauka, M., 1986

[6] G. V. Alekseev, V. A. Levin, D. A. Tereshko, Analiz i optimizatsiya v zadachakh dizaina ustroistv nevidimosti materialnykh tel, FIZMATLIT, M., 2021

[7] G. V. Alekseev, D. A. Tereshko, Y. V. Shestopalov, “Optimization approach for axisymmetric electric field cloaking and shielding”, Inv. Prob. Sci. Eng., 29 (2021), 40–55 | DOI | MR | Zbl

[8] Y. E. Spivak, “Computer design of cylindrical cloaking shell for the magnetostatics model”, Far Eastern Mathematical Journal, 22:2 (2022), 237–243 | MR

[9] G. V. Alekseev, A. V. Lobanov, “Optimization method for solving cloaking and shielding problems for a 3D model of electrostatics”, Mathematics, 11:6 (2023), 1395, 17 pp. | DOI | MR

[10] J. Kennedy, R. Eberhart, “Particle Swarm Optimization”, Proc. IEEE Int. Conf. on N.N., IV (1995), 1942–1948

[11] Q. Bai, “Analysis of particle swarm optimization algorithm”, Computer and Information Science, 3:1 (2010), 180–184 | DOI

[12] Z. Bai, W. Li, L. Wang, “Emittance Optimization Using Particle Swarm Algorithm”, Proc. IPAC2011, v. 1, 2011, 2271–2273

[13] S. M. Anlage, “The physics and applications of superconducting metamaterials”, J. Opt., 13 (2011), 024001, 10 pp. | DOI