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Thin Layer Models for Electromagnetism

  • Marc Duruflé (a1), Victor Péron (a2) and Clair Poignard (a3)


We present a review on the accuracy of asymptotic models for the scattering problem of electromagnetic waves in domains with thin layer. These models appear as first order approximations of the electromagnetic field. They are obtained thanks to a multiscale expansion of the exact solution with respect to the thickness of the thin layer, that makes possible to replace the thin layer by approximate conditions. We present the advantages and the drawbacks of several approximations together with numerical validations and simulations. The main motivation of this work concerns the computation of electromagnetic field in biological cells. The main difficulty to compute the local electric field lies in the thinness of the membrane and in the high contrast between the electrical conductivities of the cytoplasm and of the membrane, which provides a specific behavior of the electromagnetic field at low frequencies.


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[1]Caloz, G., Dauge, M., Faou, E., and Péron, V.On the influence of the geometry on skin effect in electromagnetism. Computer Methods in Applied Mechanics and Engineering, 200(9-12): 10531068, 2011.
[2]Chun, S., Haddar, H., and Hesthaven, J. S.High-order accurate thin layer approximations for time-domain electromagnetics, Part II: transmission layers. J. Comput. Appl. Math., 234(8): 25872608, 2010.
[3]Cohen, C. and Duruflé, M.Non spurious spectral-like element methods for Maxwell’s equations. Journal of Computational Mathematics, 25: 282304, 2007.
[4]Delourme, B., Haddar, H., and Joly, P.On the Well-Posedness, Stability And Accuracy Of An Asymptotic Model For Thin Periodic Interfaces In Electromagnetic Scattering Problems. Mathematical Models and Methods in Applied Sciences, 2013.
[5]Duruflé, M.Integration numerique et elements finis d’ordre eleve appliques aux equations de Maxwell en regime harmonique. PhD thesis, Universite Paris IX-Dauphine, 2006.
[6]Duruflé, M., Péron, V., and Poignard, C.Thin Layer Models for Electromagnetism. In Waves 2011: The 10th International Conference on Mathematical and Numerical Aspects of Waves, pages 687690, Vancouver, Canada, July 2011.
[7]Duruflé, M., Péron, V., and Poignard, C.Time-harmonic Maxwell equations in biological cells—the differential form formalism to treat the thin layer. Confluentes Math., 3(2): 325357, 2011.
[8]Fear, E.C. and Stuchly, M.A.Modelling assemblies of biological cells exposed to electric fields. IEEE Trans Biomed Eng, 45(10): 12591271, 0ct 1998.
[9]Fear, E.C. and Stuchly, M.A.A novel equivalent circuit model for gap-connected cells. Phys Med Biol, 43(6): 14391448, Jun 1998.
[10]Foster, K.R. and Schwan, H.P.Dielectric properties of tissues and biological materials: a critical review. CRC in Biomedical Engineering, 17(1): 25104, 1989.
[11]Kavian, O., Leguebe, M., Poignard, C., and Weynans, L.“Classical” Electropermeabilization Modeling at the Cell Scale. Journal of Mathematical Biology, 2012.
[12]Muñoz, S., Sebastián, J.L., Sancho, M., and Miranda, J.M.Transmembrane voltage induced on altered erythrocyte shapes exposed to RF fields. Bioelectromagnetics, 25(1): 631633 (electronic), 2004.
[13]Nédélec, J.-C.Acoustic and electromagnetic equations, volume 144 of Applied Mathematical Sciences. Springer-Verlag, New York, 2001. Integral representations for harmonic problems.
[14]Perrussel, R. and Poignard, C.Asymptotic expansion of steady-state potential in a high contrast medium with a thin resistive layer. Applied Mathematics and Computation, to appear, 2013.
[15]Poignard, C.Asymptotics for steady-state voltage potentials in a bidimensional highly contrasted medium with thin layer. Math. Methods Appl. Sci., 31(4): 443479, 2008.
[16]Poignard, C.About the transmembrane voltage potential of a biological cell in time-harmonic regime. ESAIM: Proceedings, 26: 162179, 2009.
[17]Poignard, C.Approximate transmission conditions through a weakly oscillating thin layer. Math. Meth. App. Sci., 32(4): 435453, 2009.
[18]Poignard, C., Dular, P., Perrussel, R., Krähenbühl, L., Nicolas, L., and Schatzman, M.Approximate conditions replacing thin layer. IEEE Trans. on Mag., 44(6): 11541157, 2008.
[19]Pucihar, G., Kotnik, T., Valič, B., and Miklavčič, D.Numerical determination of transmembrane voltage induced on irregularly shaped cells. Ann Biomed Eng, 34(4):642652, Apr 2006.
[20]Sebastián, J.L., Muñoz, S., Sancho, M., and Miranda, J.M.Analysis of the influence of the cell geometry and cell proximity effects on the electric field distribution from direct rf exposure. Phys. Med. Biol., 46:213225 (electronic), 2001.
[21]Teissié, J., Golzio, M., and Rols, M.P.Mechanisms of cell membrane electropermeabilization: A minireview of our present (lack of?) knownledge. Biochimica et Biophysica Acta, 1724: 270280, 2005.
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Communications in Computational Physics
  • ISSN: 1815-2406
  • EISSN: 1991-7120
  • URL: /core/journals/communications-in-computational-physics
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