[Conditions d'impédances généralisées d'ordre élevé pour les problèmes de diffraction en électromagnétisme]
Nous effectuons une revue succincte de l'obtention et l'utilisation des conditions d'impédances généralisées (GIBC) dans le cas de revêtements diélectriques minces et dans le cas d'objets fortement conducteurs. Nous nous plaçons dans le cadre des probèmes de diffraction d'ondes électromagnétiques en régime harmonique. Nous testons numériquement la validité et la précision de ces conditions aux limites pour le cas de forte conductivité. En présence de géométries comportant des coins, nous proposons un traitement numérique astucieux afin de garder la même précision que dans le cas de géométries régulières.
We briefly review the use and the derivation of Generalized Impedance Boundary Conditions (GIBC) in the case of thin dielectric coatings and in the case of strongly absorbing media, within the context of electromagnetic scattering problem at a fixed frequency. We then numerically test the validity and accuracy of these boundary conditions in the case of high absorption. A numerical treatment of the corner singularity is proposed to recover the accuracy of the GIBC for singular geometries.
Mot clés : Conditions d'impédances généralisées, Couches minces, Modèles asymptotiques, GIBC, Électromagnétisme
@article{CRPHYS_2006__7_5_533_0,
author = {Marc Durufl\'e and Houssem Haddar and Patrick Joly},
title = {Higher order generalized impedance boundary conditions in electromagnetic scattering problems},
journal = {Comptes Rendus. Physique},
pages = {533--542},
publisher = {Elsevier},
volume = {7},
number = {5},
year = {2006},
doi = {10.1016/j.crhy.2006.03.010},
language = {en},
}
TY - JOUR AU - Marc Duruflé AU - Houssem Haddar AU - Patrick Joly TI - Higher order generalized impedance boundary conditions in electromagnetic scattering problems JO - Comptes Rendus. Physique PY - 2006 SP - 533 EP - 542 VL - 7 IS - 5 PB - Elsevier DO - 10.1016/j.crhy.2006.03.010 LA - en ID - CRPHYS_2006__7_5_533_0 ER -
Marc Duruflé; Houssem Haddar; Patrick Joly. Higher order generalized impedance boundary conditions in electromagnetic scattering problems. Comptes Rendus. Physique, Volume 7 (2006) no. 5, pp. 533-542. doi : 10.1016/j.crhy.2006.03.010. https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/j.crhy.2006.03.010/
[1] Approximate boundary conditions in electromagnetics, IEE Electromagnetic Waves Series (1995)
[2] Effective boundary conditions for acoustic and electromagnetic scattering in thin layers, Ecole Polytechnique – CMAP (France), Volume 278 (1993)
[3] The effect of a thin coating on the scattering of a time-harmonic wave for the Helmholtz equation, SIAM J. Appl. Math., Volume 58 (1996), pp. 1664-1693
[4] Scattering of an electromagnetic wave by a slender composite slab in contact with a thick perfect conductor. II. Inclusions (or coated material) with high conductivity and high permeability, C. R. Acad. Sci. Paris Sér. I Math., Volume 313 (1991) no. 6, pp. 381-385
[5] Diffraction in the high frequency regime by a thin layer of dielectric material. I. The equivalent impedance boundary condition, SIAM J. Appl. Math., Volume 59 (1999) no. 3, pp. 1028-1052
[6] Diffraction at a curved grating. TM and TE cases, homogenization, J. Math. Anal. Appl., Volume 202 (1996), pp. 995-1026
[7] Conditions aux limites approchés pour les couches minces périodiques en électromagnétisme, Math. Model. Numer. Anal., Volume 4 (1999) no. 33, pp. 673-693
[8] Effective boundary conditions for thin ferromagnetic layers; the one-dimensional model, SIAM J. Appl. Math., Volume 61 (2001) no. 4, pp. 1386-1417
[9] Stability of thin layer approximation of electromagnetic waves scattering by linear and non linear coatings, J. Comp. Appl. Math., Volume 143 (2002) no. 2, pp. 201-236
[10] The Leontovich conditions in electromagnetism, Les grands systèmes des sciences et de la technologie, RMA Res. Notes Appl. Math., vol. 28, Masson, Paris, 1994, pp. 11-21
[11] Calcul du skin-effect par la méthode des perturbations, J. Physique USSR, Volume 2 (1940), pp. 233-242
[12] High-frequency asymptotic analysis of a dissipative transmission problem resulting in generalized impedance boundary conditions, Asymptot. Anal., Volume 26 (2001) no. 3–4, pp. 257-283
[13] Generalized impedance boundary conditions for scattering by strongly absorbing obstacles: the scalar case, Math. Models Meth. Appl. Sci., Volume 15 (2005) no. 8, pp. 1273-1300
[14] H. Haddar, P. Joly, H.M. Nguyen, Generalized impedance boundary conditions for scattering by strongly absorbing obstacles: the Maxwell case (2005), in preparation
[15] Boundary element solution of a scattering problem involving a generalized impedance boundary condition, Math. Methods Appl. Sci., Volume 22 (1999) no. 7, pp. 587-603
[16] M. Duruflé, Intégration numérique et éléments finis d'ordre élevé appliqués aux équations de Maxwell en régime harmonique, Thèse Université Paris IX – Dauphine (2006)
[17] V. Levillain, Couplage éléments finis-équations intégrales pour la résolution des équations de Maxwell en milieu hétérogène, Thèse École Polytechnique (1991)
[18] Singular Integrals and Differentiability Properties of Functions, Princeton Math. Ser., vol. 30, Princeton Univ. Press, Princeton, NJ, 1970
[19] Robust and high-order effective boundary conditions for perfectly conducting scatterers coated by a thin dielectric layer, IMA J. Appl. Math., Volume 67 (2002) no. 5, pp. 479-508
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