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Main Title: Asymptotic boundary element methods for thin conducting sheets
Author(s): Schmidt, Kersten
Hiptmair, Ralf
Type: Research Paper
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.
Subject(s): boundary element method
asymptotic expansions
transmission condition
thin conducting sheets
Issue Date: 24-Jun-2013
Date Available: 17-Dec-2021
Language Code: en
DDC Class: 510 Mathematik
MSC 2000: 65N30 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
35C20 Asymptotic expansions
Series: Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin
Series Number: 2013, 15
ISSN: 2197-8085
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik
Appears in Collections:Technische Universität Berlin » Publications

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