Asymptotic analysis of an approximate model for time harmonic waves in media with thin slots
Patrick Joly; Sébastien Tordeux
ESAIM: Mathematical Modelling and Numerical Analysis (2006)
- Volume: 40, Issue: 1, page 63-97
- ISSN: 0764-583X
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topJoly, Patrick, and Tordeux, Sébastien. "Asymptotic analysis of an approximate model for time harmonic waves in media with thin slots." ESAIM: Mathematical Modelling and Numerical Analysis 40.1 (2006): 63-97. <http://eudml.org/doc/249715>.
@article{Joly2006,
abstract = {
In this article, we derive a complete mathematical analysis of a
coupled 1D-2D model for 2D wave propagation in media including thin
slots. Our error estimates are illustrated by numerical results.
},
author = {Joly, Patrick, Tordeux, Sébastien},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Slit; slot; wave equation; Helmholtz equation; approximate model.; approximate model},
language = {eng},
month = {2},
number = {1},
pages = {63-97},
publisher = {EDP Sciences},
title = {Asymptotic analysis of an approximate model for time harmonic waves in media with thin slots},
url = {http://eudml.org/doc/249715},
volume = {40},
year = {2006},
}
TY - JOUR
AU - Joly, Patrick
AU - Tordeux, Sébastien
TI - Asymptotic analysis of an approximate model for time harmonic waves in media with thin slots
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2006/2//
PB - EDP Sciences
VL - 40
IS - 1
SP - 63
EP - 97
AB -
In this article, we derive a complete mathematical analysis of a
coupled 1D-2D model for 2D wave propagation in media including thin
slots. Our error estimates are illustrated by numerical results.
LA - eng
KW - Slit; slot; wave equation; Helmholtz equation; approximate model.; approximate model
UR - http://eudml.org/doc/249715
ER -
References
top- 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.
- 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.
- 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.
- J. Beale, Scattering frequencies of reasonators. Comm. Pure Appl. Math.26 (1973) 549–563.
- 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.
- A. Bensoussan, J.-L. Lions and G. Papanicolaou, Asymptotic analysis for periodic structures. North-Holland Publishing Co., Amsterdam. Stud. Math. Appl.5 (1978).
- A. Buffa and S.H. Christiansen, The electric field integral equation on Lipschitz screens: definitions and numerical approximation. Numer. Math. 94 (2003) 229–267.
- C. Butler and D. Wilton, General analysis of narrow strips and slots. IEEE Trans Ant. and Propag.28 (1980).
- P.G. Ciarlet, Plates and junctions in elastic multi-structures, 14 Recherches en Mathématiques Appliquées [Res. Appl. Math.], Masson, Paris (1990). An asymptotic analysis.
- 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, (Août 1998). URIhttp://www.inria.fr
- 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.
- C. Conca and E. Zuazua, Asymptotic analysis of a multidimensional vibrating structure. SIAM J. Math. Anal.25 (1994) 836–858.
- 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.
- R. Dautray and J.-L. Lions, Analyse mathématique et calcul numérique pour les sciences et les techniques. Tome 3. Masson, Paris (1985).
- 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).
- J. Gilbert and R. Holland, Implementation of the thin-slot formalism in the finite-difference code threedii. IEEE Trans. Nuc. Sci.28 (1981).
- 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).
- P. Grisvard, Elliptic problems in nonsmooth domains 24, Pitman (Advanced Publishing Program), Boston, MA, Monographs Stud. Math. (1985).
- P. Grisvard, Singularities in boundary value problems22, Recherches en Mathématiques Appliquées [Res. Appl. Math.], Masson, Paris (1992).
- D. Guiney, B. Noye and E. Tuck, Transmission of water waves through small apertures. J. Fluid Mech.55 (1972) 149–161.
- I. Harari, I. Patlashenko and D. Givoli, Dirichlet-to-Neumann maps for unbounded wave guides. J. Comput. Phys.143 (1998) 200–223.
- P. Harrington and D. Auckland, Electromagnetic transmission through narrow slots in thick conducting screens. IEEE Trans. Antenna Propagation28 (1980) 616–622.
- R. Holland and L. Simpson, Finite-difference analysis EMP coupling to thin struts and wires. IEEE Trans. Electromagn. Compat.23 (1981).
- P. Joly and S. Tordeux, Modèles asymptotiques pour la propagation des ondes dans les milieux comportant des fentes, Tech. Report RR-5568, INRIA, (May 2005). URIhttp://www.inria.fr
- J. Keller and D. Givoli, Exact nonreflecting boundary conditions. J. Comput. Phys.82 (1989) 172–192.
- G. Kriegsmann, The flanged waveguide antenna: discrete reciprocity and conservation. Wave Motion29 (1999) 81–95.
- H. Le Dret, Problèmes variationnels dans les multi-domaines19, Recherches en Mathématiques Appliquées [Res. Appl. Math.], Masson, Paris (1991). Modélisation des jonctions et applications. [Modeling of junctions and applications].
- N. Lebedev, Special functions and their applications, Revised English edition. Translated and edited by Richard A. Silverman, Prentice-Hall Inc., Englewood Cliffs, NJ (1965).
- 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.
- D. Martin, Documentation de la librairie éléments finis melina. , 1996–2003. URIhttp://perso.univ-rennes1.fr/daniel.martin/melina
- P. McIver and A.D. Rawlins, Two-dimensional wave-scattering problems involving parallel-walled ducts. Quart. J. Mech. Appl. Math.46 (1993) 89–116.
- J.C. Nédélec, Acoustic and electromagnetic equations. Springer-Verlag, New York. Appl. Math. Sci.144 (2001). Integral representations for harmonic problems.
- 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).
- E. Sánchez-Palencia, Nonhomogeneous media and vibration theory. Lect. Notes Phys.127 (1980).
- T. Senior and J. Volakis, Approximate Boundary Conditions in Electromagnetics. IEE Pres, New York and London (1995).
- A. Taflove, Computational electrodynamics. Artech House Inc., Boston, MA (1995). The finite-difference time-domain method.
- 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.
- 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.
- 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).
- S. Tordeux, Méthodes asymptotiques pour la propagation des ondes dans les milieux comportant des fentes. Ph.D. thesis, Université de Versailles (2005).
- E. Tuck, Matching problems involving flow through small holes. Academic Press, New York Adv. Appl. Mechanics15 (1975) 89–158.
- G. Watson, Bessel functions and Kapteyn series. Proc. London Math. Soc. (April 1916) 150–174.
Citations in EuDML Documents
top- Patrick Joly, Sébastien Tordeux, Matching of asymptotic expansions for waves propagation in media with thin slots II: The error estimates
- Kersten Schmidt, Sébastien Tordeux, High order transmission conditions for thin conductive sheets in magneto-quasistatics
- Kersten Schmidt, Sébastien Tordeux, High order transmission conditions for thin conductive sheets in magneto-quasistatics
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