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

A scalar boundary integrodifferential equation for eddy current problems using an impedance boundary condition

by O. Sterz and Ch. Schwab

(Report number 2000-10)

Abstract
At low frequencies the time harmonic electromagnetic fields exterior to a lossy, highly conducting and possibly magnetic body can be described by the eddy current approximation of Maxwell's equations with impedance or Leontovich [18] boundary conditions if the so called penetration depth is small. We show how to reduce this problem to a scalar, hypersingular boundary integral equation (BIE) on the surface $\Gamma$ of the conductor. Strong ellipticity of the associated nonsymmetric, hypersingular operator is established. Convergence of ${\cal \Omega}(^{\frac{\nabla}{\epsilon}})}$ of the Ohmic losses for piecewise linear, continuous boundary elements is established theoretically and numerically.

Keywords: Boundary elements, eddy currents, impedance boundary condition, scalar potential formulation, single layer ansatz, hypersingular operator

@Techreport{SS00_269,
  author = {O. Sterz and Ch. Schwab},
  title = {A scalar boundary integrodifferential equation for eddy current problems using an impedance boundary condition},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2000-10},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2000/2000-10.pdf },
  year = {2000}
}

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).