The tetrahedral finite cell method: Higher-order immersogeometric analysis on adaptive non-boundary-fitted meshes

Vasco Varduhn, Ming Chen Hsu, Martin Ruess, Dominik Schillinger

Research output: Contribution to journalArticlepeer-review

31 Scopus citations

Abstract

The finite cell method (FCM) is an immersed domain finite element method that combines higher-order non-boundary-fitted meshes, weak enforcement of Dirichlet boundary conditions, and adaptive quadrature based on recursive subdivision. Because of its ability to improve the geometric resolution of intersected elements, it can be characterized as an immersogeometric method. In this paper, we extend the FCM, so far only used with Cartesian hexahedral elements, to higher-order non-boundary-fitted tetrahedral meshes, based on a reformulation of the octree-based subdivision algorithm for tetrahedral elements. We show that the resulting TetFCM scheme is fully accurate in an immersogeometric sense, that is, the solution fields achieve optimal and exponential rates of convergence for h-refinement and p-refinement, if the immersed geometry is resolved with sufficient accuracy. TetFCM can leverage the natural ability of tetrahedral elements for local mesh refinement in three dimensions. Its suitability for problems with sharp gradients and highly localized features is illustrated by the immersogeometric phase-field fracture analysis of a human femur bone.

Original languageEnglish (US)
Pages (from-to)1054-1079
Number of pages26
JournalInternational Journal for Numerical Methods in Engineering
Volume107
Issue number12
DOIs
StatePublished - Sep 21 2016

Bibliographical note

Publisher Copyright:
Copyright © 2016 John Wiley & Sons, Ltd.

Keywords

  • adaptive tetrahedral meshes
  • finite cell method
  • higher-order finite element methods
  • immersogeometric analysis

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