Geodesic
Optimization method in two-dimensional electrical cloaking problems
Dalʹnevostočnyj matematičeskij žurnal, Tome 19 (2019) no. 1, pp. 31-42 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper, we study control problems for the two-dimensional electrical cloaking model in the case when the cloaking device has shape of a ring filled with an inhomogeneous anisotropic medium. These problems arise while developing technologies of design of electrical cloaking devices using an optimization method for solving inverse problems. The solvability of the direct and control problems for considered electrical transmission model is proved. The optimality system that describes the necessary conditions for an extremum is derived, and its properties are investigated. The possibility of implementing two types of numerical algorithms that are used to find approximate solutions is discussed. 
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A. V. Lobanov; Yu. E. Spivak. Optimization method in two-dimensional electrical cloaking problems. Dalʹnevostočnyj matematičeskij žurnal, Tome 19 (2019) no. 1, pp. 31-42. http://geodesic.mathdoc.fr/item/DVMG_2019_19_1_a5/

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

[2] S. A. Cummer, B. I. Popa, D. Shurig, D. R. Smith, J. Pendry, M. Rahm, A. Starr, “Scattering theory derivation of a 3D acoustic cloaking shell”, Phys. Rev. Lett., 100 (2008), 024301 | DOI

[3] A. Sanchez, C. Navau, J. Prat-Camps, D. X. Chen, “Antimagnets: controlling magnetic fields with superconductormetamaterial hybrids”, New J. Phys., 13 (2011), 093034 | DOI

[4] W. Jiang, C. Luo, H. F. Ma, Z. L. Mei, T. J. Cui, “Enhancement of current density by dc electric concentrator”, Sci. Rep., 2 (2012), 956 | DOI

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

[6] G. V. Alekseev, Problema nevidimosti v akustike, optike i teploperenose, Dalnauka, Vladivostok, 2016

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

[8] R. V. Brizitskii, Zh. Yu. Saritskaya, “Obratnye koeffitsientnye zadachi dlya nelineinogo uravneniya konvektsii-diffuzii-reaktsii”, Izv. RAN (Seriya Matematicheskaya)., 82:1 (2018), 17–33 | DOI | MR | Zbl

[9] R. V. Brizitskii, Zh. Yu. Saritskaya, “Zadacha granichnogo upravleniya dlya nelineinogo uravneniya konvektsii–diffuzii–reaktsii”, Zh. vychisl. matem. i matem. fiz., 58:12 (2018), 2139–2152 | DOI | MR | Zbl

[10] D. A. Tereshko, “Chislennoe vosstanovlenie granichnogo potoka tepla dlya statsionarnykh uravnenii teplovoi konvektsii”, Sib. zhurn. industr. matem., 17:4 (2014), 111–119 | Zbl

[11] S. Xu, Y. Wang, B. Zhang, H. Chen, “Invisibility cloaks from forward design to inverse design”, Science China Information Sciences, 56 (2013), 120408

[12] B. I. Popa, S. A. Cummer, “Cloaking with optimized homogeneous anisotropic layers”, Phys. Rev. A., 79 (2009), 023806 | DOI

[13] S. Xi, H. Chen, B. Zhang, B.-I. Wu, J.A. Kong, “Route to low-scattering cylindrical cloaks with finite permittivity and permeability”, Phys. Rev. B., 79 (2009), 155122 | DOI

[14] G. V. Alekseev, “Upravlenie granichnym impedansom v dvumernoi zadache maskirovki materialnykh tel metodom volnovogo obtekaniya”, Zhurn. vych. matem. i matem. fiz., 53:12 (2013), 98–115

[15] G. V. Alekseev, A. V. Lobanov, “Otsenki ustoichivosti v dvumernoi zadache maskirovki materialnykh tel”, Dalnevost. matem. zhurn., 14:2 (2014), 127–140 | MR | Zbl

[16] G. V. Alekseev, “Analiz i optimizatsiya v zadachakh maskirovki materialnykh tel dlya uravnenii Maksvella”, Differentsialnye uravneniya, 52:3 (2016), 366–377 | DOI | MR | Zbl

[17] G. V. Alekseev Yu. E. Spivak, “Analysis of the 3D acoustic cloaking problems using optimization method”, J. Phys.: Conf. Ser., 722 (2016), 012002 | DOI

[18] G. V. Alekseev, A. V. Lobanov, Yu. E. Spivak, “Optimizatsionnyi metod v zadachakh akusticheskoi maskirovki materialnykh tel”, Zhurn. vych. matem. i matem. fiz., 57:9 (2017), 79–95

[19] G. V. Alekseev, “Analiz dvumernoi zadachi teplovoi maskirovki na osnove optimizatsionnogo metoda”, Zh. vychisl. matem. i matem. fiz., 58:4 (2018), 504–519 | DOI | Zbl

[20] G. V. Alekseev, Yu. E. Spivak, “Teoreticheskii analiz zadachi magnitnoi maskirovki na osnove optimizatsionnogo metoda”, Differentsialnye uravneniya, 54:9 (2018), 1155–1166 | DOI | Zbl

[21] G. V. Alekseev, V. A. Levin, D. A. Tereshko, “Optimizatsionnyi analiz zadachi teplovoi maskirovki tsilindricheskogo tela”, Dokl. AN., 472:4 (2017), 398–402 | DOI | MR

[22] G. V. Alekseev, D. A. Tereshko, “Optimizatsionnyi metod v osesimmetrichnykh zadachakh elektricheskoi maskirovki materialnykh tel”, Zh. vychisl. matem. i matem. fiz, 59:2 (2019), 217–234 | DOI | MR

[23] G. Alekseev, D. Tereshko, “Particle swarm optimization-based algorithms for solving inverse problems of designing thermal cloaking and shielding devices”, International Journal of Heat and Mass Transfer, 135 (2019), 1269–1277 | DOI

[24] H. Han, X. Wu, Artificial Boundary Method, Springer-Verlag (Tsinghua University Press), Berlin (Beijing), 2013 | MR | Zbl

[25] A. D. Ioffe, V. M. Tikhomirov, Teoriya ekstremalnykh zadach, Nauka, M., 1974 | MR