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Asymptotic boundary element methods for thin conducting sheets

Schmidt, Kersten and Hiptmair, Ralf :
Asymptotic boundary element methods for thin conducting sheets.
In: Discrete Contin. Dyn. Syst. Ser. S, 8 (3) pp. 619-647.
[Article] , (2015)

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.

Item Type: Article
Erschienen: 2015
Creators: Schmidt, Kersten and Hiptmair, Ralf
Title: Asymptotic boundary element methods for thin conducting sheets
Language: English
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.

Journal or Publication Title: Discrete Contin. Dyn. Syst. Ser. S
Volume: 8
Number: 3
Divisions: 04 Department of Mathematics
04 Department of Mathematics > Numerical Analysis and Scientific Computing
Date Deposited: 19 Nov 2018 21:22
DOI: 10.3934/dcdss.2015.8.619
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