Abstract
Under consideration are the inverse problems of electrostatics which 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.
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REFERENCES
S. Guenneau, C. Amra, and D. Veynante, “Transformation Thermodynamics: Cloaking and Concentrating Heat Flux,” Opt. Express. 20 (7), 8207–8218 (2012).
S. Narayana and V. Sato, “Heat Flux Manipulation with Engineered Thermal Materials,” Phys. Rev. Lett. 108, 214303 (2012).
F. Yang, Z. L. Mei, T. Z. Jin, and T. J. Cui, “DC Electric Invisibility Cloak,” Phys. Review Lett. 109, 053902 (2012).
C. W. Lan, Y. Yang, J. Zhou, and B. Li, “Electrostatic Field Invisibility,” Cloak. Sci Rep. 5, 16416 (2015).
J. B. Pendry, D. Shurig, and D. R. Smith, “Controlling Electromagnetic Fields,” Science 312, 1780–1782 (2006).
U. Leonhardt, “Optical Conformal Mapping,” Science 312, 1777–1780 (2006).
A. N. Tikhonov and V. Ya. Arsenin, Methods of Solution of Ill-Posed Problems (Nauka, Moscow, 1986) [in Russian].
E. M. Dede, T. Nomura, and J. Lee, “Thermal-Composite Design Optimization for Heat Flux Shielding, Focusing, and Reversal,” Struct. Multidisc. Optim. 49, 59–68 (2014).
G. V. Alekseev, V. A. Levin, and D. A. Tereshko, “Optimization Analysis of the Thermal Cloaking Problem for a Cylindrical Body,” Dokl. Physics 62 (2), 71–75 (2017).
G. V. Alekseev, V. A. Levin, and D. A. Tereshko, “The Optimization Method in Design Problems on Spherical Layered Thermal Shells,” Dokl. Physics 62 (10), 465–469 (2017).
I. Peralta, V. D. Fachinotti, and A. A. Ciarbonetti, “Optimization-Based Design of a Heat Flux Concentrator,” Sci. Rep. 7, 40591 (2017).
V. D. Fachinotti, A. A. Ciarbonetti, I. Peralta, and I. Rintoul, “Optimization-Based Design to Easy-to-Make Devices for Heat Flux Manipulation,” Internat. J. Therm. Sci. 28, 38–48 (2018).
G. V. Alekseev and D. A. Tereshko, “Optimization Method for Axisymmetric Problems of Electric Cloaking of Material Bodies,” Comp. Math. Math. Phys. 59 (2), 207–223 (2019).
G. V. Alekseev and D. A. Tereshko, “Particle Swarm Optimization-Based Algorithms for Solving Inverse Problems of Designing Thermal Cloaking and Shielding Devices,” Internat. J. Heat Mass Transf. 135, 1269–1277 (2019).
G. V. Alekseev and D. A. Tereshko, “Optimization Method in Material Bodies Cloaking with Respect to Static Physical Fields,” J. Inverse Ill-Posed Probl. 27 (6), 845–857 (2019).
V. G. Romanov, “The Inverse Diffraction Problem for Acoustic Equations,” Dokl. Math. 81 (2), 238–240 (2010).
V. G. Romanov and Yu. A. Chirkunov, “Nonscattering Acoustic Objects in an Anisotropic Medium of a Special Form,” Dokl. Akad. Nauk 448 (4), 396–398 (2013).
Yu. A. Chirkunov, “Nonscattering Acoustic Objects in a Medium with a Spherical Stratification,” Acta Mechanica 228 (7), 2533–2539 (2017).
G. V. Alekseev and A. V. Lobanov, “Stability Estimates of the Solutions to Inverse Extremal Problems for the Helmholtz Equations,” J. Appl. Ind. Math. 7 (3), 302–312 (2013).
G. V. Alekseev, “Analysis and Optimization in Problems of Cloaking of Material Bodies for the Maxwell Equations,” Differential Equations 52 (3), 361–372 (2016).
A. V. Lobanov and Yu. E. Spivak, “Optimization Method in Two-Dimensional Electrical Cloaking Problems,” Dal’nevost. Mat. Zh. 19, 31–42 (2019).
Yu. E. Spivak, “Optimization Method in 2D Magnetic Cloaking Problems,” Sibir. Elektron. Mat. Izv. 16, 812–825 (2019).
F. Gomory, M. Solovyov, J. Souc, C. Navau, J. Prat-Camps, and A. Sanchez, “Experimental Realization of a Magnetic Cloak,” Science 335, 1466–1468 (2012).
R. Poli, J. Kennedy, and T. Blackwell, “Particle Swarm Optimization: An Overview,” Swarm Intel. 1, 33–57 (2007).
Funding
The authors were supported by the State Task to the Institute of Applied Mathematics of the Far-Eastern Branch of the Russian Academy of Sciences (project no. 075–01095–20–00) and the Ministry of Education and Science of the Russian Federation (Additional Agreement no. 075–02–2020–1482–1 on April 21, 2020).
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Alekseev, G.V., Lobanov, A.V. Optimization Analysis of Electrostatic Cloaking Problems. J. Appl. Ind. Math. 14, 599–609 (2020). https://doi.org/10.1134/S1990478920040018
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DOI: https://doi.org/10.1134/S1990478920040018