Matched Asymptotic Expansions of the Eigenvalues of a 3-D Boundary-Value Problem Relative to Two Cavities Linked by a Hole of Small Size

Abstract

In this article, we consider a domain consisting of two cavities linked by a hole of small size. We derive a numerical method to compute an approximation of the eigenvalues of an elliptic operator without refining in the neighborhood of the hole. Several convergence rates are obtained and illustrated by numerical simulations.