Far Eastern Mathematical Journal

To content of the issue


Economical method for solving two-dimensional problems of electrostatic cloaking


Alekseev G.V., Lobanov A.V., Silchenko V.I.

2020, issue 2, P. 127-134
DOI: https://doi.org/10.47910/FEMJ202013


Abstract
An economical numerical algorithm for solving a two-dimensional problem of electrostatic cloaking is proposed and implemented. The algorithm is based on the use of an $M$-layer shell, each layer of which is filled with one of two specified materials, while the material of the last layer is determined by minimizing a special quality functional associated with the cloaking efficiency of the desired shell.

Keywords:
inverse problems, electrostatic cloaking, optimization method, particle swarm optimization method, alternating design scheme

Download the article (PDF-file)

References

[1] S. Narayana, V. Sato, “Heat ?ux manipulation with engineered thermal materials”, Phys. Rev. Lett., 108, (2012), 214303.
[2] F. Yang, Z. L. Mei, T. Z. Jin, T. J. Cui, “DC electric invisibility cloak”, Phys. Review Lett., 5, (2012), 053902.
[3] S. Guenneau, C. Amra, D. Veynante, “Transformation thermodynamics: cloaking and concentrating heat ?ux”, Opt. Express, 20:7, (2012), 8207–8218.
[4] C. W. Lan, Y. Yang, J. Zhou, B. Li, “Electrostatic ?eld invisibility cloak”, Sci Rep., 5, (2015), 16416.
[5] J. B. Pendry, D. Shurig, D. R. Smith, “Controlling electromagnetic ?eld”, Science, 312, (2006), 1780–1782.
[6] U. Leonhardt, “Optical conformal mapping”, Science, 312, (2006), 1777–1780.
[7] G. V. Alekseev, V. A. Levin, D. A. Tereshko, “ Optimizatsionnyi analiz zadachi teplovoi maskirovki tsilindricheskogo tela” , Dokl. Akad. nauk, 472:4, (2017), 398–402.
[8] 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.
[9] G. V. Alekseev, D. A. Tereshko, “ Optimizatsionnyi metod v osesimmetrichnykh zadachakh elektricheskoi maskirovki material'nykh tel” , Zhurn. vychisl. matematiki i mat. fiziki, 59:2, (2019), 217–234.
[10] G. V. Alekseev, D. A. Tereshko, “Optimization method in material bodies cloaking with respect to static physical ?elds”, J. Inv. Ill-posed Problems, 27:6, (2019), 845–857.
[11] A. V. Lobanov, Iu. E. Spivak, “ Optimizatsionnyi metod v dvumernykh zadachakh elektricheskoi maskirovki” , Dal'nevost. matem. zhurn., 19, (2019), 31–42.
[12] Iu. E. Spivak, “ Optimizatsionnyi metod v dvumernykh zadachakh magnitnoi maskirov ki” , Sib. elektron. matem. izv., 16, (2019), 812–825.
[13] F. Gomory, M. Solovyov, J. Souc, C. Navau, J. Prat-Camps, A. Sanchez, “Experimental realization of a magnetic cloak”, Science, 335, (2012), 1466–1468.
[14] A. N. Tikhonov, V. Ia. Arsenin, Metody resheniia nekorrektnykh zadach, Nauka, M., 1986.
[15] R. Poli, J. Kennedy, T. Blackwell, “Particle swarm optimization: an overview”, Swarm Intel, 1, (2007), 33–57.

To content of the issue