Geometrically accurate, efficient, and flexible quadrature techniques for the tetrahedral finite cell method

Atanas Stavrev, Lam H. Nguyen, Ruyi Shen, Vasco Varduhn, Marek Behr, Stefanie Elgeti, Dominik Schillinger

Research output: Contribution to journalArticlepeer-review

26 Scopus citations


We illustrate the importance of geometrically accurate volume quadrature for obtaining optimal accuracy with non-boundary-fitted finite element discretizations, when the problem domain is defined by sharp boundaries. We consider the tetrahedral finite cell method (TetFCM) and replace its recursive subdivision based integration approach with geometrically accurate quadrature rules that emanate from higher-order geometric parametrizations of cut tetrahedral elements. The element-wise parametrization procedure relies on the identification of the intersection topology and a series of higher-order mappings based on Lagrange polynomials. We demonstrate with several 3D examples that geometrically faithful local parametrization ensures optimal accuracy, while significantly reducing the number of quadrature points with respect to recursive subdivision. On the other hand, we highlight the strength of subdivision quadrature in the context of a patient-specific workflow for the simulation-based performance analysis of coupled bone/implant configurations. In particular, we show that accuracy, flexibility and computational efficiency of the TetFCM critically depend on flexibly applying the two different quadrature variants for fuzzy imaging data and sharp boundary representations, respectively.

Original languageEnglish (US)
Pages (from-to)646-673
Number of pages28
JournalComputer Methods in Applied Mechanics and Engineering
StatePublished - Oct 1 2016

Bibliographical note

Funding Information:
The first author gratefully acknowledges support from the German Research Foundation (DFG) program GSC 111 (AICES Graduate School). The Minnesota group gratefully acknowledges support from the National Science Foundation (grant no. ACI-1565997 ) and the Internship Opportunities Program (IOP) run by the Department of Civil, Environmental, and Geo-Engineering at the University of Minnesota . The authors also acknowledge the Minnesota Supercomputing Institute (MSI) of the University of Minnesota for providing computing resources that have contributed to the research results reported within this paper ( ).

Publisher Copyright:
© 2016 Elsevier B.V.

Copyright 2016 Elsevier B.V., All rights reserved.


  • Higher-order geometric parametrization
  • Non-boundary-fitted discretization
  • Numerical integration
  • Tetrahedral finite cell method


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