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

Convergence of natural hp-BEM for the electric field integral equation on polyhedral surfaces

by A. Bespalov and N. Heuer and R. Hiptmair

(Report number 2009-24)

Abstract
We consider the variational formulation of the electric field integral equation (EFIE) on bounded polyhedral open or closed surfaces. We employ a conforming Galerkin discretization based on $Div_\Gamma$-conforming Raviart-Thomas boundary elements (BEM) of locally variable polynomial degree on shape-regular surface meshes. We establish asymptotic quasi-optimality of Galerkin solutions on sufficiently fine meshes or for sufficiently high polynomial degree.

Keywords: electromagnetic scattering, electric field integral equation (EFIE), Galerkin discretization, boundary element method (BEM), hp-refinement, non-coercive variational problems, smoothed Poincaré mapping, projection based interpolation

@Techreport{BHH09_36,
  author = {A. Bespalov and N. Heuer and R. Hiptmair},
  title = {Convergence of natural hp-BEM for the electric field integral equation on polyhedral surfaces},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2009-24},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2009/2009-24.pdf },
  year = {2009}
}

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).