%0 Journal Article
%T Exact boundary conditions for time-harmonic wave propagation in locally perturbed periodic media
%+ Propagation des Ondes : Étude Mathématique et Simulation (POEMS)
%+ EADS Innovation Works [Suresnes] (EADS IW)
%A Fliss, Sonia
%A Joly, Patrick
%< avec comité de lecture
%@ 0168-9274
%J Applied Numerical Mathematics
%I Elsevier
%V 59
%N 9
%P 2155-2178
%8 2009
%D 2009
%R 10.1016/j.apnum.2008.12.013
%K Periodic media
%K Helmholtz equation
%K Transparent Boundary Conditions
%K DtN operator
%Z Mathematics [math]/Numerical Analysis [math.NA]Journal articles
%X We consider the solution of the Helmholtz equation with absorption − u(x)−n(x)2(ω2 + ıε)u(x) = f (x), x = (x, y), in a 2D periodic medium Ω = R2. We assume that f (x) is supported in a bounded domain Ωi and that n(x) is periodic in the two directions in Ωe = Ω \ Ωi . We show how to obtain exact boundary conditions on the boundary of Ωi ,ΣS that will enable us to find the solution on Ωi . Then the solution can be extended in Ω in a straightforward manner from the values on ΣS . The particular case of medium with symmetries is exposed. The exact boundary conditions are found by solving a family of waveguide problems. © 2008 IMACS.
%G English
%L hal-00873067
%U https://ensta-paris.hal.science/hal-00873067
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