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Preprint 15-2013

Asymptotic boundary element methods for thin conducting sheets

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Author(s) : Kersten Schmidt , Ralf Hiptmair

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 15-2013

MSC 2000

65N30 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
35C20 Asymptotic expansions

Abstract :
Various asymptotic models for thin conducting sheets in computational electromagnetics describe them as closed hyper-surfaces equipped with linear local transmission conditions for the traces of electric and magnetic fields. The transmission conditions turn out to be singularly perturbed with respect to limit values of parameters depending on sheet thickness and conductivity. We consider the reformulation of the resulting transmission problems into boundary integral equations (BIE) and their Galerkin discretization by means of low-order boundary elements. We establish stability of the BIE and provide a priori $h$-convergence estimates, with the dependence on model parameters made explicit throughout. This is achieved by a novel technique harnessing truncated asymptotic expansions of Galerkin discretization errors.

Keywords : Boundary element method, Asymptotic Expansions, Transmission Condition, Thin Conducting Sheets

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