Free access
Issue
ESAIM: M2AN
Volume 40, Number 1, January-February 2006
Page(s) 63 - 97
DOI http://dx.doi.org/10.1051/m2an:2006008
Published online 23 February 2006
  1. T. Abboud and F. Starling, Scattering of an electromagnetic wave by a screen, in Boundary value problems and integral equations in nonsmooth domains (Luminy, 1993), Dekker, New York. Lect. Notes Pure Appl. Math. (1995) 167 1–17.
  2. M. Artola and M. Cessenat, Diffraction d'une onde électromagnétique par une couche composite mince accolée à un corps conducteur épais. I. Cas des inclusions fortement conductrices. C. R. Acad. Sci. Paris Sér. I Math. 313 (1991) 231–236.
  3. F. Assous, P. Ciarlet, Jr., and J. Segré, Numerical solution to the time-dependent Maxwell equations in two-dimensional singular domains: the singular complement method. J. Comput. Phys. 161 (2000) 218–249. [CrossRef] [MathSciNet]
  4. J. Beale, Scattering frequencies of reasonators. Comm. Pure Appl. Math. 26 (1973) 549–563. [CrossRef] [MathSciNet]
  5. A. Bendali and K. Lemrabet, The effect of a thin coating on the scattering of a time-harmonic wave for the Helmholtz equation. SIAM J. Appl. Math. 56 (1996) 1664–1693. [CrossRef] [MathSciNet]
  6. A. Bensoussan, J.-L. Lions and G. Papanicolaou, Asymptotic analysis for periodic structures. North-Holland Publishing Co., Amsterdam. Stud. Math. Appl. 5 (1978).
  7. A. Buffa and S.H. Christiansen, The electric field integral equation on Lipschitz screens: definitions and numerical approximation. Numer. Math. 94 (2003) 229–267. [CrossRef] [MathSciNet]
  8. C. Butler and D. Wilton, General analysis of narrow strips and slots. IEEE Trans Ant. and Propag. 28 (1980).
  9. P.G. Ciarlet, Plates and junctions in elastic multi-structures, 14 Recherches en Mathématiques Appliquées [Res. Appl. Math.], Masson, Paris (1990). An asymptotic analysis.
  10. F. Collino and F. Millot, Fils et méthodes d'éléments finis pour les équations de Maxwell. Le modèle de Holland revisité. Tech. Report 3472, INRIA, http://www.inria.fr (Août 1998).
  11. D. Colton and R. Kress, Integral equation methods in scattering theory, John Wiley & Sons Inc., New York, Pure Appl. Math. (1983). A Wiley-Interscience Publication.
  12. C. Conca and E. Zuazua, Asymptotic analysis of a multidimensional vibrating structure. SIAM J. Math. Anal. 25 (1994) 836–858. [CrossRef] [MathSciNet]
  13. D. Crighton, A. Dowling, J.F. Williams, M. Heckl and F. Leppington, Modern Methods in Analytical acoustics. Lect. Notes, Springer-Verlag, London (1992). An asymptotic analysis.
  14. R. Dautray and J.-L. Lions, Analyse mathématique et calcul numérique pour les sciences et les techniques. Tome 3. Masson, Paris (1985).
  15. B. Engquist and J.C. Nédélec, Effective boundary conditions for acoustic and electromagnetic scattering in thin layers. Tech. Report 278, École Polytechnique CMAP (France) (1993).
  16. J. Gilbert and R. Holland, Implementation of the thin-slot formalism in the finite-difference code threedii. IEEE Trans. Nuc. Sci. 28 (1981).
  17. D. Givoli, I. Patlashenko and J. Keller, Discrete Dirichlet-to-Neumann maps for unbounded domains. Comput. Methods Appl. Mech. Engrg. 164 (1998) 173–185. Exterior problems of wave propagation (Boulder, CO, 1997; San Francisco, CA, 1997). [CrossRef] [MathSciNet]
  18. P. Grisvard, Elliptic problems in nonsmooth domains 24, Pitman (Advanced Publishing Program), Boston, MA, Monographs Stud. Math. (1985).
  19. P. Grisvard, Singularities in boundary value problems 22, Recherches en Mathématiques Appliquées [Res. Appl. Math.], Masson, Paris (1992).
  20. D. Guiney, B. Noye and E. Tuck, Transmission of water waves through small apertures. J. Fluid Mech. 55 (1972) 149–161. [CrossRef]
  21. I. Harari, I. Patlashenko and D. Givoli, Dirichlet-to-Neumann maps for unbounded wave guides. J. Comput. Phys. 143 (1998) 200–223. [CrossRef] [MathSciNet]
  22. P. Harrington and D. Auckland, Electromagnetic transmission through narrow slots in thick conducting screens. IEEE Trans. Antenna Propagation 28 (1980) 616–622. [CrossRef]
  23. R. Holland and L. Simpson, Finite-difference analysis EMP coupling to thin struts and wires. IEEE Trans. Electromagn. Compat. 23 (1981).
  24. P. Joly and S. Tordeux, Modèles asymptotiques pour la propagation des ondes dans les milieux comportant des fentes, Tech. Report RR-5568, INRIA, http://www.inria.fr (May 2005).
  25. J. Keller and D. Givoli, Exact nonreflecting boundary conditions. J. Comput. Phys. 82 (1989) 172–192. [CrossRef] [MathSciNet]
  26. G. Kriegsmann, The flanged waveguide antenna: discrete reciprocity and conservation. Wave Motion 29 (1999) 81–95. [CrossRef] [MathSciNet]
  27. H. Le Dret, Problèmes variationnels dans les multi-domaines 19, Recherches en Mathématiques Appliquées [Res. Appl. Math.], Masson, Paris (1991). Modélisation des jonctions et applications. [Modeling of junctions and applications].
  28. N. Lebedev, Special functions and their applications, Revised English edition. Translated and edited by Richard A. Silverman, Prentice-Hall Inc., Englewood Cliffs, NJ (1965).
  29. J.-L. Lions and E. Magenes, Non-homogeneous boundary value problems and applications. Vol. I, Springer-Verlag, New York (1972). Translated from the French by P. Kenneth, Die Grundlehren der mathematischen Wissenschaften, Band 181.
  30. D. Martin, Documentation de la librairie éléments finis melina. http://perso.univ-rennes1.fr/daniel.martin/melina, 1996–2003.
  31. P. McIver and A.D. Rawlins, Two-dimensional wave-scattering problems involving parallel-walled ducts. Quart. J. Mech. Appl. Math. 46 (1993) 89–116. [CrossRef] [MathSciNet]
  32. J.C. Nédélec, Acoustic and electromagnetic equations. Springer-Verlag, New York. Appl. Math. Sci. 144 (2001). Integral representations for harmonic problems.
  33. F. Rogier, Problèmes mathématiques et numériques liés à l'approximation de la géométrie d'un corps diffractant dans les équations de l'électromagnétisme, Ph.D. thesis, Université de Paris 6 (1989).
  34. E. Sánchez-Palencia, Nonhomogeneous media and vibration theory. Lect. Notes Phys. 127 (1980).
  35. T. Senior and J. Volakis, Approximate Boundary Conditions in Electromagnetics. IEE Pres, New York and London (1995).
  36. A. Taflove, Computational electrodynamics. Artech House Inc., Boston, MA (1995). The finite-difference time-domain method.
  37. A. Taflove, K. Umashankar and B. Becker, Calculation and experimental validation of induced currents on coupled wires in an arbitrary shaped cavity. IEEE Trans Antenna Propag. 35 (1987) 1248–1257. [CrossRef]
  38. A. Taflove, K. Umashankar, B. Becker, F. Harfoush and K. Yee, Detailed fdtd analysis of electromagnetic fields penetrating narrow slots ans lapped joints in thick conducting screens. IEEE Trans Antenna Propag. 36 (1988) 247–257. [CrossRef]
  39. F. Tatout, Propagation d'une onde électromagnétique dans une fente mince. Propagation et réflexion d'ondes en élasticité. Application au contrôle. Ph.D. thesis, École normale supérieure de Cachan (Dec. 1996).
  40. S. Tordeux, Méthodes asymptotiques pour la propagation des ondes dans les milieux comportant des fentes. Ph.D. thesis, Université de Versailles (2005).
  41. E. Tuck, Matching problems involving flow through small holes. Academic Press, New York Adv. Appl. Mechanics 15 (1975) 89–158.
  42. G. Watson, Bessel functions and Kapteyn series. Proc. London Math. Soc. (April 1916) 150–174.

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