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Optimization Analysis of a 2D Magnetic Cloaking Problem for Bilayer Structure

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Nonlinear and Inverse Problems in Electromagnetics (PIERS 2017, PIERS 2017)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 243))

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Abstract

We consider the control problems for the 2D model of magnetic scattering by a permeable isotropic obstacle having the form of a cylindrical bilayer. These problems arise while developing the design technologies of magnetic cloaking bilayer devices using the optimization method for solving the corresponding inverse problems. The solvability of direct and optimization problems for the magnetic scattering model under study is proved. The optimality system which describes the necessary conditions of extremum is derived. Based on its analysis the sufficient conditions to the data are established which provide local uniqueness and stability of optimal solutions. Also numerical aspects of applying the optimization approach are discussed.

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Acknowledgements

The first author was supported by the Russian Science Foundation (project no. 14-11-00079). The second author acknowledge the support by the Russian Foundation for Basic Research (project no. 16-01-00365-a).

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Authors and Affiliations

  1. Institute of Applied Mathematics Far Eastern Branch of RAS, 7, Radio Street, Vladivostok, Russia

    G. V. Alekseev & Y. E. Spivak

  2. Far Eastern Federal University, 8, Sukhanova Street, Vladivostok, Russia

    G. V. Alekseev & Y. E. Spivak

Authors
  1. G. V. Alekseev
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  2. Y. E. Spivak
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Corresponding author

Correspondence to G. V. Alekseev .

Editor information

Editors and Affiliations

  1. Department of Mathematical Sciences, Chalmers University of Technology and University of Gothenburg, Gothenburg, Sweden

    L. Beilina

  2. Penza State University, Penza, Russia

    Yu. G. Smirnov

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Alekseev, G.V., Spivak, Y.E. (2018). Optimization Analysis of a 2D Magnetic Cloaking Problem for Bilayer Structure. In: Beilina, L., Smirnov, Y. (eds) Nonlinear and Inverse Problems in Electromagnetics. PIERS PIERS 2017 2017. Springer Proceedings in Mathematics & Statistics, vol 243. Springer, Cham. https://doi.org/10.1007/978-3-319-94060-1_1

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