A Two-Scale Asymptotic Analysis of a Time-Harmonic Scattering Problem with a Multi Layered Thin Periodic Domain
Mounir Tlemcani 1*1 Universite des Sciences et de la Technologie d'Oran, U.S.T.O-M.B, BP 1505 El M'Naouer, Algeria.
Received 9 June 2008; Accepted (in revised version) 10 December 2008
Available online 5 March 2009
The scope of this paper is to show how a two-scale asymptotic analysis, based on a superposition principle, allows us to derive high order approximate boundary conditions for a scattering problem of a time-harmonic wave by a thin and tangentially periodic multi-layered domain. The periods are assumed of the same order of the thickness. New terms like memory effect and variance-covariance ones are observed contrarily to the laminar case. As a result, optimal error estimates are obtained.AMS subject classifications: 78A45, 35B27, 35B25, 35C20
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Key words: Two-scale asymptotic analysis, superposition principle, tangential periodicity, thin layer, approximate boundary condition, time-harmonic scattering.
Email: email@example.com (M. Tlemcani)