Geodesic
Optimization analysis of electrostatic cloaking problems
Sibirskij žurnal industrialʹnoj matematiki, Tome 23 (2020) no. 4, pp. 5-17.

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Under consideration are the inverse problems of electrostatics that arise in designing two-dimensional multilayer shielding and cloaking devices. Using optimization, we reduce these inverse problems to the finite-dimensional extremal problems in which the roles of control parameters are played by the constant dielectric permittivities of the layers. Basing on particle swarm optimization, we develop some numerical algorithm for solving these problems. We also show that the devices designed by the algorithm have the highest cloaking efficiency and simplicity of technical implementation.
Keywords: inverse problem, electrostatic cloaking, particle swarm optimization. . 
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G. V. Alekseev; A. V. Lobanov. Optimization analysis of electrostatic cloaking problems. Sibirskij žurnal industrialʹnoj matematiki, Tome 23 (2020) no. 4, pp. 5-17. http://geodesic.mathdoc.fr/item/SJIM_2020_23_4_a0/

[1] S. Guenneau, C. Amra, D. Veynante, “Transformation thermodynamics: Cloaking and concentrating heat flux”, Opt. Express, 20:7 (2012), 8207–8218 | DOI

[2] S. Narayana, V. Sato, “Heat flux manipulation with engineered thermal materials”, Phys. Rev. Lett., 108 (2012), 214303 | DOI

[3] F. Yang, Z. L. Mei, T. Z. Jin, T. J. Cui, “DC electric invisibility cloak”, Phys. Review Lett., 109 (2012), 053902 | DOI

[4] C. W. Lan, Y. Yang, J. Zhou, B. Li, “Electrostatic field invisibility”, Cloak. Sci Rep., 5 (2015), 16416 | DOI

[5] J. B. Pendry, D. Shurig, D. R. Smith, “Controlling electromagnetic fields”, Science, 312 (2006), 1780–1782 | DOI | MR | Zbl

[6] U. Leonhardt, “Optical conformal mapping”, Science, 312 (2006), 1777–1780 | DOI | MR | Zbl

[7] A. N. Tikhonov, V. Ya. Arsenin, Methods of solution of ill-posed problems, Nauka, M., 1986 (in Russian)

[8] E. M. Dede, T. Nomura, J. Lee, “Thermal-composite design optimization for heat flux shielding, focusing, and reversal”, Struct. Multidisc. Optim., 49 (2014), 59–68 | DOI | MR

[9] G. V. Alekseev, V. A. Levin, D. A. Tereshko, “Optimization analysis of the thermal cloaking problem for a cylindrical body”, Dokl. Akad. Nauk, 472:4 (2017), 398–402 (in Russian) | MR

[10] G. V. Alekseev, V. A. Levin, D. A. Tereshko, “The optimization method in design problems on spherical layered thermal shells”, Dokl. Akad. Nauk, 476:5 (2017), 512–517 (in Russian) | MR

[11] I. Peralta, V. D. Fachinotti, A. A. Ciarbonetti, “Optimization-based design of a heat flux concentrator”, Sci. Rep., 7 (2017), 40591 | DOI

[12] V. D. Fachinotti, A. A. Ciarbonetti, I. Peralta, I. Rintoul, “Optimization-based design to easy-to-make devices for heat flux manipulation”, Int. J. Therm. Sci, 28 (2018), 38–48 | DOI

[13] G. V. Alekseev, D. A. Tereshko, “Optimization method for axisymmetric problems of electric cloaking of material bodies”, Comp. Math. Math. Phys., 59:2 (2019), 207–223 | DOI | MR | Zbl

[14] G. V. Alekseev, D. A. Tereshko, “Particle swarm optimization-based algorithms for solving inverse problems of designing thermal cloaking and shielding devices”, Int. J. Heat Mass Transf., 135 (2019), 1269–1277 | DOI

[15] G. V. Alekseev, D. A. Tereshko, “Optimization method in material bodies cloaking with respect to static physical fields”, J. Inverse Ill-Posed Probl., 27:6 (2019), 845–857 | DOI | MR | Zbl

[16] V. G. Romanov, “The inverse diffraction problem for acoustic equations”, Dokl. Akad. Nauk, 431:3 (2010), 319–322 (in Russian) | Zbl

[17] V. G. Romanov, Yu. A. Chirkunov, “Nonscattering acoustic objects in an anisotropic medium of a special form”, Dokl. Akad. Nauk, 448:4 (2013), 396–398 (in Russian) | MR | Zbl

[18] Yu. A. Chirkunov, “Nonscattering acoustic objects in a medium with a spherical stratification”, Acta Mechanica, 228:7 (2017), 2533–2539 | DOI | MR | Zbl

[19] G. V. Alekseev, A. V. Lobanov, “Stability estimates of the solutions to inverse extremal problems for the Helmholtz equations”, J. Appl. Ind. Math., 7:3 (2013), 302–312 | DOI | MR | Zbl

[20] G. V. Alekseev, “Analysis and optimization in problems of cloaking of material bodies for the Maxwell equations”, Differential Equations, 52:3 (2016), 361–372 | DOI | MR | Zbl

[21] A. V. Lobanov, Yu. E. Spivak, “Optimization method in two-dimensional electrical cloaking problems”, Dal'nevost. Mat. Zhurn., 19 (2019), 31–42 (in Russian) | MR | Zbl

[22] Yu. E. Spivak, “Optimization method in 2D magnetic cloaking problems”, Sibir. Elektron. Mat. Izv, 16 (2019), 812–825 (in Russian) | MR | Zbl

[23] F. Gomory, M. Solovyov, J. Souc, C. Navau, J. Prat-Camps, A. Sanchez, “Experimental realization of a magnetic cloak”, Science, 335 (2012), 1466–1468 | DOI

[24] R. Poli, J. Kennedy, T. Blackwell, “Particle swarm optimization: an overview”, Swarm Intel, 1 (2007), 33–57 | DOI