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

Spurious Quasi-Resonances in Boundary Integral Equationsfor the Helmholtz Transmission Problem

by R. Hiptmair and A. Moiola and E. A. Spence

(Report number 2021-28)

Abstract
We consider the Helmholtz transmission problem with piecewise-constant material coefficients, and the standard associated direct boundary integral equations. For certain coefficients and geometries, the norms of the inverses of the boundary integral operators grow rapidly through an increasing sequence of frequencies, even though this is not the case for the solution operator of the transmission problem; we call this phenomenon that of spurious quasiresonances. We give a rigorous explanation of why and when spurious quasi-resonances occur, and propose modified boundary integral equations that are not affected by them.

Keywords: Helmholtz equation, boundary integral equations, transmission problem, quasiresonance

@Techreport{HMS21_970,
  author = {R. Hiptmair and A. Moiola and E. A. Spence},
  title = {Spurious Quasi-Resonances in Boundary Integral Equationsfor the Helmholtz Transmission Problem},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2021-28},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2021/2021-28.pdf },
  year = {2021}
}

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).