Transmission Conditions for the Helmholtz-Equation in Perforated Domains

Autor:	Ben Schweizer, Christina Dörlemann, Martin Heida
Rok vydání:	2016
Předmět:	Helmholtz equation General Mathematics 010102 general mathematics Perforation (oil well) Mathematical analysis Open set Order (ring theory) 01 natural sciences Omega Domain (mathematical analysis) Manifold 010101 applied mathematics Jump 0101 mathematics Mathematics
Zdroj:	Vietnam Journal of Mathematics. 45:241-253
ISSN:	2305-2228 2305-221X
DOI:	10.1007/s10013-016-0222-y
Popis:	We study the Helmholtz equation in a perforated domain Ω e . The domain Ω e is obtained from an open set $\phantom {\dot {i}\!}{\Omega }\subset \mathbb {R}^{3}$ by removing small obstacles of typical size e>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 e→0. We obtain that, to leading order O(e 0), the perforation is invisible. On the other hand, at order O(e 1), inhomogeneous jump conditions for the pressure and the flux appear. The form of the jump conditions is derived.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::f813a7df34255802a9a1c226ac36465a https://doi.org/10.1007/s10013-016-0222-y Zobrazit plný text záznamu Full text from SpringerLink