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Asymptotic boundary element methods for thin conducting sheets

Schmidt, Kersten; Hiptmair, Ralf

Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin

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.