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Stability of thin layer approximation of electromagnetic waves scattering by linear and nonlinear coatings. (English) Zbl 0998.78008
Summary: We consider first the scattering problem of electromagnetic waves by thin coatings that are formed by linear materials. We describe, through an asymptotic study, the formal derivation of thin layer approximations, called effective boundary conditions. We then discuss the stability in time of the new initial boundary value problems. We give in the last part a generalization to nonlinear coatings of ferromagnetic type.

78A45 Diffraction, scattering
Full Text: DOI
[1] Ammari, H.; Latiri-Grouz, C., Conditions aux limites approchés pour LES couches minces périodiques en électromagnétisme, M2AN math. model. numer. anal., 33, 4, 673-693, (1999) · Zbl 0944.35008
[2] Bendali, A.; Lemrabet, K., The effect of a thin coating on the scattering of a time-harmonic wave for the Helmholtz equation, SIAM J. appl. math., 58, 6, 1664-1693, (1996) · Zbl 0869.35068
[3] Choquet-Bruhat, Y., Géométrie différentielle et système extérieur, (1968), DUNOD Paris
[4] Engquist, B.; Majda, A., Absorbing boundary conditions for the numerical simulation of waves, Math. comp., 31, 139, 629-651, (1977) · Zbl 0367.65051
[5] B. Engquist, J.C. Nedelec, Effective boundary conditions for acoustic and electromagnetic scattering in thin layers, Technical Report 278, Ecole Polytechnique-CMAP, France, 1993.
[6] H. Haddar, Modèles asymptotiques en ferromagnétisme: couches minces et homogénéisation, Ph.D. Thesis, Ecole Nationales de Ponts et Chaussées, 2000.
[7] H. Haddar, P. Joly, Effective boundary conditions for thin ferromagnetic coatings, asymptotic analysis of the 1d model, Asympt. Anal. 27 (2001) 127-160. · Zbl 0995.35072
[8] H. Haddar, P. Joly, Effective boundary conditions for thin ferromagnetic layers; the one dimensional model, SIAM J. Appl. Math. 61 (2000) 1386-1417. · Zbl 0973.78011
[9] Hoppe, D.J.; Rahmat-Sami, Y., Impedance boundary conditions in electromagnetics, (1995), Taylor & Francis, cop London
[10] P. Joly, O. Vacus, Mathematical and numerical studies of non-linear ferromagnetic materials, M2AN, 1997. · Zbl 0960.78003
[11] Kreiss, H., Initial boundary value problems for hyperbolic systems, Comm. pure appl. math., 13, 277-298, (1970) · Zbl 0193.06902
[12] T.B.A. Senior, J.L. Volakis, Approximate Boundary Conditions in Electromagnetics, Vol. 41. IEE Electromagnetic Waves Series, 1995.
[13] I. Terrasse, Résolution mathématique des équations de Maxwell instationnaires par une méthode de potentiels retardés, Ph.D. Thesis, Ecole polytechnique, France, 1993.
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