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

Compact Equivalent Inverse of the Electric Field Integral Operator on Screens

by R. Hiptmair and C. Urzua-Torres

(Report number 2018-46)

Abstract
We study explicit inverses of the variational electric field boundary integral operator on orientable topologically simple Lipschitz screens. We describe them as solution operators of variational problems set in low-regularity standard trace spaces. On flat disks these variational problems do not involve the inversion of any non-local operators and supply an inverse up to a compact perturbation. This result lays the foundation for operator preconditioning for the discretized electric field integral equation.

Keywords: Boundary integral operators; Electric field integral equation; Screens; Hodge decomposition

@Techreport{HU18_800,
  author = {R. Hiptmair and C. Urzua-Torres},
  title = {Compact Equivalent Inverse of the Electric Field Integral
Operator on Screens},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2018-46},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2018/2018-46.pdf },
  year = {2018}
}

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).