Transmission Conditions for the Helmholtz-Equation in Perforated Domains

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• 作者：Christina Dörlemann ; Martin Heida ; Ben Schweizer
• 关键词：Helmholtz equation ; Perforated domain ; Transmission conditions ; Neumann sieve ; Acoustics
• 刊名：Vietnam Journal of Mathematics
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：45
• 期：1-2
• 页码：241-253
• 全文大小：
• 刊物主题：Mathematics, general;
• 出版者：Springer Singapore
• ISSN：2305-2228
• 卷排序：45

文摘

We study the Helmholtz equation in a perforated domain Ω_ε. The domain Ω_ε is obtained from an open set \(\phantom {\dot {i}\!}{\Omega }\subset \mathbb {R}^{3}\) 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→0. We obtain that, to leading order O(ε0), the perforation is invisible. On the other hand, at order O(ε1), inhomogeneous jump conditions for the pressure and the flux appear. The form of the jump conditions is derived.