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

Fractured Meshes

by M. Averseng and X. Claeys and R. Hiptmair

(Report number 2022-14)

Abstract
This work introduces a concept of ``generalized meshes", similar to simplicial meshes, but allowing for overlapping elements, and with adjacency relations that are defined independently from the number of shared vertices. This additional flexibility allows for the representation of complex geometries such as fractured meshes and two sided complex surfaces. The generalized mesh is then a convenient object to accompany a numerical method, as its so-called ``generalized subfacets" play naturally the role of degrees of freedom for finite/boundary element methods. Our emphasis is on precise definitions and proofs, as well as numerical implementation especially for the boundary element applications.

Keywords: Fractures, Meshes, Finite Elements, Boundary Elements

@Techreport{ACH22_1002,
  author = {M. Averseng and X. Claeys and R. Hiptmair},
  title = {Fractured Meshes},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2022-14},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2022/2022-14.pdf },
  year = {2022}
}

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).