Transmission conditions for the Helmholtzequation in perforated domains
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Date
2015-04-07
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Abstract
We study the Helmholtz equation in a perforated domain . The domain Ωε. The domain Ωε is obtained from an open set
Ω⊂ℝ³ by removing small obstacles of typical size ε > 0, the obstacles are located along a 2-dimensional manifold Γ0 ⊂Ω, We derive
effective transmission conditions across Γ0 that characterize solutions in the limit
ε→0O. We obtain that, to leading order O(ε0)=O(1), the perforation is invisible.
On the other hand, at order O(ε1)=O(ε), inhomogeneous jump conditions for the
pressure and the flux appear. The jumps can be characterized without cell problems
by elementary expressions that contain the ε0-order limiting pressure function and
the volume of the obstacles.
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Keywords
Helmholtz equation, perforated domain, transmission conditions, acoustic properties