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

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

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


Authors

T. Adams



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.

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
Public URL https://durham-repository.worktribe.com/output/1341707

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