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 quadrilateral edge element scheme with minimum dispersion

by R. Hiptmair and P. Ledger

(Report number 2003-17)

Abstract
This paper describes a novel quadrilateral edge element discretisation of Maxwell's equations in which the effects of dispersion are minimised. A modified edge finite element stencil is proposed and it is subsequently shown how this can be expressed in terms of new material coefficients thus allowing us to incorporate both Dirchlet and Neumann boundary conditions in a natural fashion. To demonstrate the success of the proposed procedure, we include a series numerical examples. First we apply the approach to plane and circular wave propagation problems. Secondly, we apply the approach to a series of electromagnetic scattering problems. For the electromagnetic scattering computations, we monitor the effect of the modified edge finite element stencil on the scattering width output. We use a hp-edge element code as a benchmark for all our electromagnetic scattering computations.

Keywords:

@Techreport{HL03_44,
  author = {R. Hiptmair and P. Ledger},
  title = {A quadrilateral edge element scheme with minimum dispersion},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2003-17},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2003/2003-17.pdf },
  year = {2003}
}

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).