Asymptotic boundary element methods for thin conducting sheets

Kersten Schmidt; Ralf Hiptmair

doi:10.3934/dcdss.2015.8.619

Article Contents

2015, Volume 8, Issue 3: 619-647. Doi: 10.3934/dcdss.2015.8.619

This issue Previous Article On Maxwell's and Poincaré's constants Next Article

Asymptotic boundary element methods for thin conducting sheets

Kersten Schmidt^1, and
Ralf Hiptmair^2,

1.
Research Center MATHEON, Institut für Mathematik, Technische Universität Berlin, 10623 Berlin
2.
Seminar for Applied Mathematics, ETH Zurich, 8092 Zürich

Received: November 2013

Revised: June 2014

Published: July 2015

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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.

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Mathematics Subject Classification: 65N38, 35C20, 35J25, 41A60, 35B40, 78M30, 78M35.

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