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Asymptotic modelling of conductive thin sheets. (English) Zbl 1235.78042

The authors derive and analyse models to reduce conducting sheets in two dimensions of small thickness \(\epsilon\) to an interface and to approximate the shielding behaviour by interface conditions. They investigate the asymptotics of constant shielding for \(\epsilon \to 0\) by scaling the conductivity as \(1/\epsilon\). Hierarchical coupled problems are derived which leads to well-defined expansions functions of each order for smooth sheets. The models of the first three orders are explicitly given. In numerical experiments for a domain with an ellipsoidal shield, the modelling error, the differences between the exact model and the asymptotic expansion models is investigated.

MSC:

78M35 Asymptotic analysis in optics and electromagnetic theory
35J25 Boundary value problems for second-order elliptic equations
78M30 Variational methods applied to problems in optics and electromagnetic theory
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35C20 Asymptotic expansions of solutions to PDEs
35B40 Asymptotic behavior of solutions to PDEs

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