Free Access
Issue |
ESAIM: M2AN
Volume 40, Number 1, January-February 2006
|
|
---|---|---|
Page(s) | 63 - 97 | |
DOI | https://doi.org/10.1051/m2an:2006008 | |
Published online | 23 February 2006 |
- 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. [Google Scholar]
- 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. [Google Scholar]
- 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] [Google Scholar]
- J. Beale, Scattering frequencies of reasonators. Comm. Pure Appl. Math. 26 (1973) 549–563. [Google Scholar]
- 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] [Google Scholar]
- A. Bensoussan, J.-L. Lions and G. Papanicolaou, Asymptotic analysis for periodic structures. North-Holland Publishing Co., Amsterdam. Stud. Math. Appl. 5 (1978). [Google Scholar]
- 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] [Google Scholar]
- C. Butler and D. Wilton, General analysis of narrow strips and slots. IEEE Trans Ant. and Propag. 28 (1980). [Google Scholar]
- P.G. Ciarlet, Plates and junctions in elastic multi-structures, 14 Recherches en Mathématiques Appliquées [Res. Appl. Math.], Masson, Paris (1990). An asymptotic analysis. [Google Scholar]
- 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). [Google Scholar]
- 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. [Google Scholar]
- C. Conca and E. Zuazua, Asymptotic analysis of a multidimensional vibrating structure. SIAM J. Math. Anal. 25 (1994) 836–858. [CrossRef] [MathSciNet] [Google Scholar]
- 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. [Google Scholar]
- R. Dautray and J.-L. Lions, Analyse mathématique et calcul numérique pour les sciences et les techniques. Tome 3. Masson, Paris (1985). [Google Scholar]
- 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). [Google Scholar]
- J. Gilbert and R. Holland, Implementation of the thin-slot formalism in the finite-difference code threedii. IEEE Trans. Nuc. Sci. 28 (1981). [Google Scholar]
- 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] [Google Scholar]
- P. Grisvard, Elliptic problems in nonsmooth domains 24, Pitman (Advanced Publishing Program), Boston, MA, Monographs Stud. Math. (1985). [Google Scholar]
- P. Grisvard, Singularities in boundary value problems 22, Recherches en Mathématiques Appliquées [Res. Appl. Math.], Masson, Paris (1992). [Google Scholar]
- D. Guiney, B. Noye and E. Tuck, Transmission of water waves through small apertures. J. Fluid Mech. 55 (1972) 149–161. [CrossRef] [Google Scholar]
- I. Harari, I. Patlashenko and D. Givoli, Dirichlet-to-Neumann maps for unbounded wave guides. J. Comput. Phys. 143 (1998) 200–223. [CrossRef] [MathSciNet] [Google Scholar]
- P. Harrington and D. Auckland, Electromagnetic transmission through narrow slots in thick conducting screens. IEEE Trans. Antenna Propagation 28 (1980) 616–622. [CrossRef] [Google Scholar]
- R. Holland and L. Simpson, Finite-difference analysis EMP coupling to thin struts and wires. IEEE Trans. Electromagn. Compat. 23 (1981). [Google Scholar]
- 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). [Google Scholar]
- J. Keller and D. Givoli, Exact nonreflecting boundary conditions. J. Comput. Phys. 82 (1989) 172–192. [CrossRef] [MathSciNet] [Google Scholar]
- G. Kriegsmann, The flanged waveguide antenna: discrete reciprocity and conservation. Wave Motion 29 (1999) 81–95. [CrossRef] [MathSciNet] [Google Scholar]
- 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]. [Google Scholar]
- N. Lebedev, Special functions and their applications, Revised English edition. Translated and edited by Richard A. Silverman, Prentice-Hall Inc., Englewood Cliffs, NJ (1965). [Google Scholar]
- 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. [Google Scholar]
- D. Martin, Documentation de la librairie éléments finis melina. http://perso.univ-rennes1.fr/daniel.martin/melina, 1996–2003. [Google Scholar]
- 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] [Google Scholar]
- J.C. Nédélec, Acoustic and electromagnetic equations. Springer-Verlag, New York. Appl. Math. Sci. 144 (2001). Integral representations for harmonic problems. [Google Scholar]
- 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). [Google Scholar]
- E. Sánchez-Palencia, Nonhomogeneous media and vibration theory. Lect. Notes Phys. 127 (1980). [Google Scholar]
- T. Senior and J. Volakis, Approximate Boundary Conditions in Electromagnetics. IEE Pres, New York and London (1995). [Google Scholar]
- A. Taflove, Computational electrodynamics. Artech House Inc., Boston, MA (1995). The finite-difference time-domain method. [Google Scholar]
- 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] [Google Scholar]
- 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] [Google Scholar]
- 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). [Google Scholar]
- S. Tordeux, Méthodes asymptotiques pour la propagation des ondes dans les milieux comportant des fentes. Ph.D. thesis, Université de Versailles (2005). [Google Scholar]
- E. Tuck, Matching problems involving flow through small holes. Academic Press, New York Adv. Appl. Mechanics 15 (1975) 89–158. [Google Scholar]
- G. Watson, Bessel functions and Kapteyn series. Proc. London Math. Soc. (April 1916) 150–174. [Google Scholar]
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.