[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.
Mots-clés : Conditions d'impédances généralisées, Couches minces, Modèles asymptotiques, GIBC, Électromagnétisme
Marc Duruflé 1 ; Houssem Haddar 1 ; Patrick Joly 1
@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, Electromagnetic modelling, 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
- Bg waves in a piezo–flexo-magnetic layered model with impedance boundary and imperfect interface, Acta Mechanica, Volume 235 (2024) no. 7, p. 4339 | DOI:10.1007/s00707-024-03916-z
- Jointly determining the point sources and obstacle from Cauchy data, Inverse Problems, Volume 40 (2024) no. 1, p. 015014 | DOI:10.1088/1361-6420/ad10c8
- Numerical study of a D-shaped optical fiber SPR biosensor for monitoring refractive index variations in biological tissue via a thin layer of gold coated with titanium dioxide, Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy, Volume 304 (2024), p. 123358 | DOI:10.1016/j.saa.2023.123358
- Acoustic waveguide with a dissipative inclusion, ESAIM: Mathematical Modelling and Numerical Analysis, Volume 57 (2023) no. 6, p. 3585 | DOI:10.1051/m2an/2023070
- Numerical analysis for electromagnetic scattering with nonlinear boundary conditions, Mathematics of Computation, Volume 93 (2023) no. 348, p. 1529 | DOI:10.1090/mcom/3914
- Inverse time-dependent source problem for the heat equation with a nonlocal Wentzell-Neumann boundary condition, Networks and Heterogeneous Media, Volume 18 (2023) no. 4, p. 1747 | DOI:10.3934/nhm.2023076
- Reverse time migration for inverse obstacle scattering with a generalized impedance boundary condition, Applicable Analysis, Volume 101 (2022) no. 1, p. 48 | DOI:10.1080/00036811.2020.1727894
- Time-dependent acoustic scattering from generalized impedance boundary conditions via boundary elements and convolution quadrature, IMA Journal of Numerical Analysis, Volume 42 (2022) no. 1, p. 1 | DOI:10.1093/imanum/draa091
- Numerical solution of a generalized boundary value problem for the modified Helmholtz equation in two dimensions, Mathematics and Computers in Simulation, Volume 190 (2021), p. 181 | DOI:10.1016/j.matcom.2021.05.013
- An Inverse Parameter Problem with Generalized Impedance Boundary Condition for Two-Dimensional Linear Viscoelasticity, SIAM Journal on Applied Mathematics, Volume 81 (2021) no. 4, p. 1668 | DOI:10.1137/20m1383422
- Asymptotic modelling of Skin-effects in coaxial cables, SN Partial Differential Equations and Applications, Volume 1 (2020) no. 6 | DOI:10.1007/s42985-020-00043-x
- , 2019 IEEE Conference on Antenna Measurements Applications (CAMA) (2019), p. 113 | DOI:10.1109/cama47423.2019.8959709
- A Discontinuous Galerkin Self-Dual Integral Equation Method for Scattering From IBC Objects, IEEE Transactions on Antennas and Propagation, Volume 67 (2019) no. 7, p. 4708 | DOI:10.1109/tap.2019.2905670
- Direct Acoustic Obstacle Scattering, Inverse Acoustic and Electromagnetic Scattering Theory, Volume 93 (2019), p. 43 | DOI:10.1007/978-3-030-30351-8_3
- Integral Equation Methods in Inverse Obstacle Scattering with a Generalized Impedance Boundary Condition, Contemporary Computational Mathematics - A Celebration of the 80th Birthday of Ian Sloan (2018), p. 721 | DOI:10.1007/978-3-319-72456-0_32
- , 2017 International Symposium on Electromagnetic Compatibility - EMC EUROPE (2017), p. 1 | DOI:10.1109/emceurope.2017.8094767
- Transfer and approximation of the impedance for time-harmonic Maxwell’s system in a planar domain with thin contrasted multi-layers, Asymptotic Analysis, Volume 101 (2017) no. 1-2, p. 1 | DOI:10.3233/asy-161391
- Scattering of a scalar time-harmonic wave by a penetrable obstacle with a thin layer, European Journal of Applied Mathematics, Volume 27 (2016) no. 2, p. 264 | DOI:10.1017/s095679251500056x
- Reconstruction of discontinuous parameters in a second order impedance boundary operator, Inverse Problems, Volume 32 (2016) no. 10, p. 105004 | DOI:10.1088/0266-5611/32/10/105004
- Electromagnetic inverse shape problem for coated obstacles, Advances in Computational Mathematics, Volume 41 (2015) no. 6, p. 1179 | DOI:10.1007/s10444-015-9406-3
- APPROXIMATE TRANSMISSION CONDITIONS FOR A POISSON PROBLEM AT MID-DIFFUSION, Mathematical Modelling and Analysis, Volume 20 (2015) no. 1, p. 53 | DOI:10.3846/13926292.2015.1000988
- Reconstruction of thickness variation of a dielectric coating through the generalized impedance boundary conditions, ESAIM: Mathematical Modelling and Numerical Analysis, Volume 48 (2014) no. 4, p. 1011 | DOI:10.1051/m2an/2013131
- Simultaneous reconstruction of shape and generalized impedance functions in electrostatic imaging, Inverse Problems, Volume 30 (2014) no. 10, p. 105009 | DOI:10.1088/0266-5611/30/10/105009
- Reconstruction of Complex Obstacles with Generalized Impedance Boundary Conditions from Far-Field Data, SIAM Journal on Applied Mathematics, Volume 74 (2014) no. 1, p. 106 | DOI:10.1137/130921350
- A Unified Analysis of Transmission Conditions for Thin Conducting Sheets in the Time-Harmonic Eddy Current Model, SIAM Journal on Applied Mathematics, Volume 73 (2013) no. 6, p. 1980 | DOI:10.1137/120901398
- High order transmission conditions for thin conductive sheets in magneto-quasistatics, ESAIM: Mathematical Modelling and Numerical Analysis, Volume 45 (2011) no. 6, p. 1115 | DOI:10.1051/m2an/2011009
- Stable reconstruction of generalized impedance boundary conditions, Inverse Problems, Volume 27 (2011) no. 9, p. 095002 | DOI:10.1088/0266-5611/27/9/095002
- Generalized impedance boundary conditions for thin dielectric coatings with variable thickness, Wave Motion, Volume 48 (2011) no. 7, p. 681 | DOI:10.1016/j.wavemoti.2011.06.002
- Asymptotic models for scattering from unbounded media with high conductivity, ESAIM: Mathematical Modelling and Numerical Analysis, Volume 44 (2010) no. 6, p. 1295 | DOI:10.1051/m2an/2010029
- Asymptotic modelling of conductive thin sheets, Zeitschrift für angewandte Mathematik und Physik, Volume 61 (2010) no. 4, p. 603 | DOI:10.1007/s00033-009-0043-x
- GENERALIZED IMPEDANCE BOUNDARY CONDITIONS FOR SCATTERING PROBLEMS FROM STRONGLY ABSORBING OBSTACLES: THE CASE OF MAXWELL'S EQUATIONS, Mathematical Models and Methods in Applied Sciences, Volume 18 (2008) no. 10, p. 1787 | DOI:10.1142/s0218202508003194
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