A high-order elliptic PDE based level set reinitialisation method using a discontinuous Galerkin discretisation

Adams, T.; Giani, S.; Coombs, W.M.

doi:10.1016/j.jcp.2018.12.003

A high-order elliptic PDE based level set reinitialisation method using a discontinuous Galerkin discretisation

Adams, T.; Giani, S.; Coombs, W.M.

Authors

T. Adams

Dr Stefano Giani stefano.giani@durham.ac.uk
Associate Professor

Professor William Coombs w.m.coombs@durham.ac.uk
Professor

Abstract

In this paper, an efficient, high-order accurate, level set reinitialisation method is proposed, based on the elliptic reinitialisation method (Basting and Kuzmin, 2013 [1]), which is discretised spatially using the discontinuous Galerkin (DG) symmetric interior penalty method (SIPG). In order to achieve this a number of improvements have been made to the elliptic reinitialisation method including; reformulation of the underlying minimisation problem driving the solution; adoption of a Lagrange multiplier approach for enforcing a Dirichlet boundary condition on the implicit level set interface; and adoption of a narrow band approach. Numerical examples confirm the high-order accuracy of the resultant method by demonstrating experimental orders of convergence congruent with optimal convergence rates for the SIPG method, that is and in the and DG norms respectively. Furthermore, the degree to which the level set function satisfies the Eikonal equation improves proportionally to , and the often ignored homogeneous Dirichlet boundary condition on the interface is shown to be satisfied accurately with a rate of convergence of at least for all polynomial orders.

Citation

Adams, T., Giani, S., & Coombs, W. (2019). A high-order elliptic PDE based level set reinitialisation method using a discontinuous Galerkin discretisation. Journal of Computational Physics, 379, 373-391. https://doi.org/10.1016/j.jcp.2018.12.003

Journal Article Type	Article
Acceptance Date	Dec 5, 2018
Online Publication Date	Dec 12, 2018
Publication Date	Feb 15, 2019
Deposit Date	Dec 6, 2018
Publicly Available Date	Dec 12, 2019
Journal	Journal of Computational Physics
Print ISSN	0021-9991
Publisher	Elsevier
Peer Reviewed	Peer Reviewed
Volume	379
Pages	373-391
DOI	https://doi.org/10.1016/j.jcp.2018.12.003
Keywords	Level set, Reinitialisation, Discontinuous Galerkin

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http://creativecommons.org/licenses/by-nc-nd/4.0/

Copyright Statement
© 2019 The Authors. Published by Elsevier Inc. This is an open access article under the CC
BY license (http://creativecommons.org/licenses/by/4.0/).