(untitled) (Communications in Computational Physics, 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.