A method for calculating effective electromagnetic parameters of a periodic medium

Kondrashov S.V., Shashkeev K.A., Popkov O.V.
UDC
66.017
DOI
10.18577/2307-6046-2017-0-6-9-9
Article PDF (Russian) (593.25 KB)
How to cite
Kondrashov S.V., Shashkeev K.A., Popkov O.V. A method for calculating effective electromagnetic parameters of a periodic medium // Proceedings of VIAM. 2017. No. 6. DOI: 10.18577/2307-6046-2017-0-6-9-9. URL: https://test.viam.ru/en/journal/2017/6/9
Keywords
effective electromagnetic parameters, permittivity, permeability, periodic medium, disordered medium, parallel computations.
Abstract

This paper describes a method for computing effective electrodynamic parameters (susceptibility tensors) of a partially disordered periodic medium with a rectangular cell; the cell must be considerably smaller that the electromagnetic wave length in the medium. The computational complexity of the suggested iterative algorithm is O(NxNyNzlnNxlnNylnNz) per iteration, and the required memory size is Θ(NxNyNz), where Nx, Ny and Nz stand for the grid size in the respective directions. The algorithm can be extended so that it will also support periodic media with non-rectangular cells, which only requires a few additional linear transforms.

Reference list
  1. Kablov E.N. Konstrukcionnye i funkcionalnye materialy – osnova ekonomicheskogo i nauchno-tehnicheskogo razvitiya Rossii [Constructional and functional materials are the base of economic and scientific and technical development of Russia] // Voprosy materialovedeniya. 2006. №1. S. 64–67.
  2. Kablov E.N. Innovacionnye razrabotki FGUP «VIAM» GNC RF po realizacii «Strategicheskih napravlenij razvitiya materialov i tehnologij ih pererabotki na period do 2030 goda» [Innovative developments of FSUE «VIAM» SSC of RF on realization of «Strategic directions of the development of materials and technologies of their processing for the period until 2030»] // Aviacionnye materialy i tehnologii. 2015. №1 (34). S. 3–33. DOI: 10.18577/2071-9140-2015-0-1-3-33.
  3. Kondrashov S.V., Gurevich Ya.M., Popkov O.V., Shashkeev K.A. i dr. Shirokopolosnye radiopogloshhayushhie materialy na osnove poristyh kompozitov s uglerodnymi nanotrubkami [Broadband radio absorbing materials on the basis of porous composites with carbon nanotubes] // Vse materialy: Enciklopedicheskij spravochnik (v pechati).
  4. Qinand F., Brosseau C. A review and analysis of microwave absorption in polymer composites filled with carbonaceous particles // J. Appl. Phys. 2012. Vol. 111. Paper No. 061301. DOI: 10.1063/1.3688435.
  5. Kondrashov S.V., Shashkeev K.A., Popkov O.V., Solovyanchik L.V. Perspektivnye tehnologii polucheniya funkcionalnyh materialov konstrukcionnogo naznacheniya na osnove nanokompozitov s UNT (obzor) [Prospective producing methods for functional structural materials based on CNT-filled nanocomposites (review)] // Trudy VIAM: elektron. nauch.-tehnich. zhurn. 2016. №3. St. 07. Available at: http://www.viam-works.ru (accessed: July 05, 2016). DOI: 10.18577/2307-6046-2016-0-3-7-7.
  6. Kondrashov S.V., Shashkeev K.A., Popkov O.V., Solovyanchik L.V. Fiziko-mehanicheskie svojstva nanokompozitov s UNT (obzor) [Mechanical properties of CNT nanocomposites (review)] // Trudy VIAM: elektron. nauch.-tehnich. zhurn. 2016. №5. St. 08. Available at: http://www.viam-works.ru (accessed: July 05, 2016). DOI: 10.18577/2307-6046-2016-0-5-8-8.
  7. Kablov E.N., Kondrashov S.V., Yurkov G.Yu. Perspektivy ispolzovaniya uglerodsoderzhashhih nanochastic v svyazuyushhih dlya polimernyh kompozicionnyh materialov [Perspectives of use of carbon-containing nanoparticles in binding for polymeric composite materials] // Rossijskie nanotehnologii. 2013. T. 8. №3–4. S. 28–42.
  8. Kondrashov S.V., Gunyaeva A.G., Shashkeev K.A., Barinov D.Ya., Soldatov M.A., Shevchenko V.G., Muzafarov A.M. Elektroprovodyashhie gibridnye polimernye kompozicionnye materialy na osnove nekovalentno funkcionalizirovannyh uglerodnyh nanotrubok [Electrically-conductive hybrid polymer composite materials on the basis of noncovalent functional carbon nanotubes] // Trudy VIAM: elektron. nauch.-tehnich. zhurn. 2016. №2. St. 10. Available at: http://www.viam-works.ru (accessed: July 05, 2016). DOI: 10.18577/2307-6046-2016-0-2-10-10.
  9. Akatenkov R.V., Anoshkin I.V., Belyaev A.A., Bitt V.V., Bogatov V.A., Dyachkova T.P., Kutsevich K.E., Kondrashov S.V., Romanov A.M., Shirokov V.V., Horobrov N.V. Vliyanie strukturnoj organizacii uglerodnyh nanotrubok na radiojekraniruyushhie i elektroprovodyashhie svojstva nanokompozitov [Influence of the structural organization of carbon nanotubes on radio shielding and electrocarrying-out properties of nanocomposites] // Aviacionnye materialy i tehnologii. 2011. №1. S. 35–42.
  10. Challa R.K., Kajfez D., Demir V., Gladden J.R., Elsherbeni A.Z. Characterization of Multiwalled Carbon Nanotube (MWCNT) Composites in a of Square Cross Section Waveguide // IEEE Microwave and Wireless Components Letters. 2008. Vol. 18. No. 3. P. 161–163. http://ieeexplore.ieee.org/document/4459260/ (accessed: December 23, 2017). DOI: 10.1109/LMWC.2008.916776.
  11. De Vivo B., Guagno L., Lamberti P. et al. Electromagnetic properties of Carbon NanoTube/epoxy nanocomposites // International Symposium on Electromagnetic Compatibility – EMC Europe. Athens, 2009. P. 1–4. http://ieeexplore.ieee.org/document/5189674/ (accessed: December 23, 2017). DOI: 10.1109/EMCEUROPE.2009.5189674.
  12. Huang Q., Holland T.B., Mukherjee A.K. et al. Carbon nanotube RF absorbing materials // Proc. SRF2009. Berlin, 2009. P. 648–651.
  13. Huang Yi., Li N., Ma Y. et al. The influence of single-walled carbon nanotube structure on the electromagnetic interference shielding efficiency of its epoxy composites // Carbon. 2007. Vol. 45. P. 1614–1621. DOI: 10.1016/j.carbon.2007.04.016.
  14. Liu Z.F., Bai G., Huang Y. et al. Microwave Absorption of Single-Walled Carbon Nanotubes/Soluble Cross-Linked Polyurethane Composites // J. Phys. Chem. C. 2007. Vol. 111. No. 37. P. 13696–13700. DOI: 10.1021/jp0731396.
  15. Fan Z., Luo G., Zhang Z. et al. Electromagnetic and microwave absorbing properties of multi-walled carbon nanotubes/polymer composites // Materials Science and Engineering B. 2006. Vol. 132. P. 85–89.
  16. Zhang Y., Zhang A., Ding L. et al. The effect of polymer spatial configuration on the microwave absorbing properties of non-covalent modified MWNTs // Composites. Part A. 2016. Vol. 81. P. 264–270.
  17. Che R.C., Liang C.Y., Shi H.L. et al. Electron energy-loss spectroscopy characterization and microwave absorption of iron-filled carbon-nitrogen nanotubes// Nanotechnology. Vol. 18. No. 35. Paper No. 355705.
  18. Qi X., Hu Q., Xu J. et al. Enhanced microwave absorption properties and mechanism of core/shell structured magnetic nanoparticles/carbon-based nanohybrids // Materials Science and Engineering B. 2016. Vol. 211. P. 53–60.