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

Varduhn, V., Hsu, M.-C., Ruess, M. and Schillinger, D. (2016) The tetrahedral finite cell method: higher-order immersogeometric analysis on adaptive non-boundary-fitted meshes. International Journal for Numerical Methods in Engineering, 107(12), pp. 1054-1079. (doi: 10.1002/nme.5207)

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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. Due to 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- 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.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Ruess, Dr Martin
Authors: Varduhn, V., Hsu, M.-C., Ruess, M., and Schillinger, D.
College/School:College of Science and Engineering > School of Engineering > Infrastructure and Environment
Journal Name:International Journal for Numerical Methods in Engineering
Publisher:Wiley
ISSN:0029-5981
ISSN (Online):1097-0207
Published Online:05 February 2016
Copyright Holders:Copyright © 2016 John Wiley & Sons Ltd.
First Published:First published in International Journal for Numerical Methods in Engineering 107(12):1054-1079
Publisher Policy:Reproduced in accordance with the copyright policy of the publisher.

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