|Title:||Effective Helmholtz problem in a domain with a Neumann sieve perforation|
|Abstract:||A first order model for the transmission of waves through a sound-hard perforation along an interface is derived. Mathematically, we study the Neumann problem for the Helmholtz equation in a complex geometry, the domain contains a periodic array of inclusions of size ε > 0 along a co-dimension 1 manifold. We derive effective equations that describe the limit as ε → 0. At leading order, the Neumann sieve perforation has no effect; the corrector is given by a Helmholtz equation on the unperturbed domain with jump conditions across the interface. The corrector equations are derived with unfolding methods in L^1-based spaces.|
|Subject Headings:||Helmholtz equation|
|Appears in Collections:||Schweizer, Ben Prof. Dr.|
Preprints der Fakultät für Mathematik
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