Automatic conformal decomposition of elements cut by NURBS

Jakob W. Steidl, Thomas Peter Fries

Research output: Chapter in Book/Report/Conference proceedingConference contributionResearch

Abstract

In fictitious domain and extended finite element methods, elements cut by boundaries or interfaces are frequently present. They pose challenges with respect to the application of boundary and interface conditions, numerical integration, and the conditioning of the system of equations. A different path is the automatic decomposition of cut elements into smaller, conforming finite elements. Herein, we propose a concept for the automatic decomposition of elements cut by (curved) NURBS which automatically generates higher-order Lagrange elements on the two sides of the interfaces. The NURBS data, defining boundaries and interfaces in two dimensions, is converted into implicit level-set data by evaluating signed distance computations at all nodes in the background mesh. Based on the findings in [1] this data is then used for the decomposition into sub-elements. First numerical results are achieved as a proof-of-concept.

Original languageEnglish
Title of host publicationECCOMAS Congress 2016 - Proceedings of the 7th European Congress on Computational Methods in Applied Sciences and Engineering
PublisherNational Technical University of Athens
Pages2591-2600
Number of pages10
Volume2
ISBN (Electronic)9786188284401
Publication statusPublished - 2016
Event7th European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS Congress 2016 - Crete, Greece
Duration: 5 Jun 201610 Jun 2016

Conference

Conference7th European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS Congress 2016
CountryGreece
CityCrete
Period5/06/1610/06/16

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Keywords

  • Conformal decomposition
  • Fictitious domain method
  • Level set method
  • NURBS
  • Signed distance

ASJC Scopus subject areas

  • Applied Mathematics

Cite this

Steidl, J. W., & Fries, T. P. (2016). Automatic conformal decomposition of elements cut by NURBS. In ECCOMAS Congress 2016 - Proceedings of the 7th European Congress on Computational Methods in Applied Sciences and Engineering (Vol. 2, pp. 2591-2600). National Technical University of Athens .