Research reports

Years: 2025 2024 2023 2022 2021 2020 2019 2018 2017 2016 2015 2014 2013 2012 2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001 2000 1999 1998 1997 1996 1995 1994 1993 1992 1991

Asymptotic Boundary Element Methods for Thin Conducting Sheets

by K. Schmidt and R. Hiptmair

(Report number 2013-19)

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.

@Techreport{SH13_515,
  author = {K. Schmidt and R. Hiptmair},
  title = {Asymptotic Boundary Element Methods for Thin Conducting Sheets},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2013-19},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2013/2013-19.pdf },
  year = {2013}
}

Disclaimer
© Copyright for documents on this server remains with the authors. Copies of these documents made by electronic or mechanical means including information storage and retrieval systems, may only be employed for personal use. The administrators respectfully request that authors inform them when any paper is published to avoid copyright infringement. Note that unauthorised copying of copyright material is illegal and may lead to prosecution. Neither the administrators nor the Seminar for Applied Mathematics (SAM) accept any liability in this respect. The most recent version of a SAM report may differ in formatting and style from published journal version. Do reference the published version if possible (see SAM Publications).