Research reports

Years: 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

Coupled Surface and Volume Integral Equations for Electromagnetism

by I. Labarca and R. Hiptmair

(Report number 2023-35)

Abstract
We study frequency domain electromagnetic scattering at a bounded, penetrable, and inhomogeneous obstacle. By defining constant reference coefficients, a new representation formula for interior and exterior vector fields is proposed, based on the general form of the Stratton-Chu integral representation. The final integral equation system consists of surface integral operators arising from a Poggio-Miller-Chang-Harrington-Wu-Tsai (PMCHWT) formulation and compact volume integral operators with weakly singular kernels. The problem is solved with a Galerkin approach with usual Curl-conforming and Div-conforming finite elements on the surface and in the volume. Compression techniques and special quadrature rules for singular integrands are required for an efficient and accurate solution. Numerical experiments provide evidence that our new formulation enjoys promising properties.

Keywords: volume integral equations, boundary integral operators, boundary elements, finite elements, electromagnetic waves

@Techreport{LH23_1072,
  author = {I. Labarca and R. Hiptmair},
  title = {Coupled Surface and Volume Integral Equations for Electromagnetism},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2023-35},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2023/2023-35.pdf },
  year = {2023}
}

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).