%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 %~ ENSTA %~ CNRS %~ INRIA %~ INRIA-SACLAY %~ INSMI %~ INRIA_TEST %~ TESTALAIN1 %~ UMA_ENSTA %~ INRIA2 %~ TDS-MACS