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

Authors:
Sonia Fliss;Patrick Joly
Affiliations:
POems (UMR 2706 CNRS-INRIA-ENSTA), France and CTO/IW/SE/AM EADS Innovation Works, France;POems (UMR 2706 CNRS-INRIA-ENSTA), France
Venue:
Applied Numerical Mathematics
Year:
2009

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Abstract

We consider the solution of the Helmholtz equation with absorption -@Du(x)-n(x)^2(@w^2+i@e)u(x)=f(x), x=(x,y), in a 2D periodic medium @W=R^2. We assume that f(x) is supported in a bounded domain @W^i and that n(x) is periodic in the two directions in @W^e=@W@?@W^i. We show how to obtain exact boundary conditions on the boundary of @W^i, @S"S that will enable us to find the solution on @W^i. Then the solution can be extended in @W in a straightforward manner from the values on @S"S. The particular case of medium with symmetries is exposed. The exact boundary conditions are found by solving a family of waveguide problems.