Assessment of an isogeometric approach with Catmull-Clark subdivision surfaces using the Laplace-Beltrami problems

Liu, Z. , McBride, A. , Saxena, P. and Steinmann, P. (2020) Assessment of an isogeometric approach with Catmull-Clark subdivision surfaces using the Laplace-Beltrami problems. Computational Mechanics, (doi: 10.1007/s00466-020-01877-3) (Early Online Publication)

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Abstract

An isogeometric approach for solving the Laplace–Beltrami equation on a two-dimensional manifold embedded in three-dimensional space using a Galerkin method based on Catmull–Clark subdivision surfaces is presented and assessed. The scalar-valued Laplace–Beltrami equation requires only C0 continuity and is adopted to elucidate key features and properties of the isogeometric method using Catmull–Clark subdivision surfaces. Catmull–Clark subdivision bases are used to discretise both the geometry and the physical field. A fitting method generates control meshes to approximate any given geometry with Catmull–Clark subdivision surfaces. The performance of the Catmull–Clark subdivision method is compared to the conventional finite element method. Subdivision surfaces without extraordinary vertices show the optimal convergence rate. However, extraordinary vertices introduce error, which decreases the convergence rate. A comparative study shows the effect of the number and valences of the extraordinary vertices on accuracy and convergence. An adaptive quadrature scheme is shown to reduce the error.

Item Type:Articles
Status:Early Online Publication
Refereed:Yes
Glasgow Author(s) Enlighten ID:McBride, Dr Andrew and Saxena, Dr Prashant and Steinmann, Professor Paul and Liu, Dr Zhaowei
Authors: Liu, Z., McBride, A., Saxena, P., and Steinmann, P.
College/School:College of Science and Engineering > School of Engineering > Infrastructure and Environment
Journal Name:Computational Mechanics
Publisher:Springer
ISSN:0178-7675
ISSN (Online):1432-0924
Published Online:15 July 2020
Copyright Holders:Copyright © The Author(s) 2020
First Published:First published in Computational Mechanics 2020
Publisher Policy:Reproduced under a Creative Commons license

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