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Journal Articles Applied Numerical Mathematics Year : 2009

Exact boundary conditions for time-harmonic wave propagation in locally perturbed periodic media

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Abstract

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.
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Dates and versions

hal-00873067 , version 1 (16-10-2013)

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Sonia Fliss, Patrick Joly. Exact boundary conditions for time-harmonic wave propagation in locally perturbed periodic media. Applied Numerical Mathematics, 2009, 59 (9), pp.2155-2178. ⟨10.1016/j.apnum.2008.12.013⟩. ⟨hal-00873067⟩
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