Curvilinear mesh generation using a variational framework
© 2017 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
We aim to tackle the challenge of generating unstructured high-order meshes of complex three-dimensional bodies, which remains a significant bottleneck in the wider adoption of high-order methods. In particular we show that by adopting a variational approach to the generation process, many of the current popular high-order generation methods can be encompassed under a single unifying framework. This allows us to compare the effectiveness of these methods and to assess the quality of the meshes they produce in a systematic fashion. We present a detailed overview of the theory and formulation of the variational framework, and we highlight how such formulation can be effectively exploited to yield a highly-efficient parallel implementation. The effectiveness of this approach is examined by considering a number of two- and three-dimensional examples, where we show how the proposed approach can be used for both mesh quality optimisation and untangling of invalid high-order meshes.
MT acknowledges Airbus and EPSRC for funding under anindustrial CASE studentship. DM acknowledges support from the EU Horizon 2020 project ExaFLOW (grant 671571) and the PRISM project under EPSRC grant EP/L000407/1. JP would like to acknowledge discussions with Prof. Javier Bonet on the problem of existence in hyperelasticity that led us to this direction of research in mesh generation. We also thank Jan Eichstädt for assistance in proofreading and validating the numerical code underpinning this work.
This is the final version of the article. Available from Elsevier via the DOI in this record.
Available online 14 November 2017