M. Arlen and . Il-in, Matching of asymptotic expansions of solutions of boundary value problems, volume 102 of Translations of Mathematical Monographs, 1992.

P. Joly and A. Semin, Construction and analysis of improved Kirchoff conditions for acoustic wave propagation in a junction of thin slots, ESAIM Proceedings, 2008.
DOI : 10.1051/proc:082504

URL : https://hal.archives-ouvertes.fr/hal-00976404

P. Joly and S. Tordeux, Matching of Asymptotic Expansions for Wave Propagation in Media with Thin Slots I: The Asymptotic Expansion, Multiscale Modeling & Simulation, vol.5, issue.1, pp.304-336, 2006.
DOI : 10.1137/05064494X

URL : https://hal.archives-ouvertes.fr/inria-00527588

B. Joseph, D. Keller, and . Givoli, Exact nonreflecting boundary conditions, J. Comput. Phys, vol.82, issue.1, pp.172-192, 1989.

P. Kuchment, Graph models for waves in thin structures. Waves Random Media, pp.1-24, 2002.

V. Maz-ya, S. Nazarov, and B. Plamenevskij, Asymptotic theory of elliptic boundary value problems in singularly perturbed domains Advances and Applications, 2000.

J. Rubinstein and M. Schatzman, Variational Problems??on Multiply Connected Thin Strips I:??Basic Estimates and Convergence??of the Laplacian Spectrum, Archive for Rational Mechanics and Analysis, vol.160, issue.4, pp.271-308, 2001.
DOI : 10.1007/s002050100164

J. Rubinstein and M. Schatzman, Variational Problems??on Multiply Connected Thin Strips II:??Convergence of the Ginzburg-Landau, Archive for Rational Mechanics and Analysis, vol.160, issue.4, pp.309-324, 2001.
DOI : 10.1007/s002050100165

[. Tordeux, G. Vial, and M. Dauge, Matching and multiscale expansions for a model singular perturbation problem, Comptes Rendus Mathematique, vol.343, issue.10, pp.343637-642, 2006.
DOI : 10.1016/j.crma.2006.10.010

URL : https://hal.archives-ouvertes.fr/hal-00453366

M. Van-dyke, Perturbation Method in Fluid Mechanics, Journal of Applied Mechanics, vol.43, issue.1, 1964.
DOI : 10.1115/1.3423785

A. Overlaping-domain-decomposition and .. , 10 2.2 Local expansions and basic equations, 12 2.3.1 Modal expansion of solutions of embeddeb Laplace equations . . . . . 13 2.3.2 Derivation of the matching conditions . . . . . . . . . . . . . . . . . . 18

U. Existence and .. Of-the-formal-expansion, 21 3.1.1 Restriction to a bounded domain of the problems for the, p.24

I. Unité-de-recherche and . Lorraine, Technopôle de Nancy-Brabois -Campus scientifique 615, rue du Jardin Botanique -BP 101 -54602 Villers-lès-Nancy Cedex (France) Unité de recherche INRIA Rennes : IRISA, Campus universitaire de Beaulieu -35042 Rennes Cedex (France) Unité de recherche INRIA Rhône-Alpes : 655, avenue de l'Europe -38334 Montbonnot Saint-Ismier (France) Unité de recherche, 2004.

I. De-voluceau-rocquencourt, BP 105 -78153 Le Chesnay Cedex (France) http://www.inria.fr ISSN, pp.249-6399