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A parabolic level set reinitialisation method using a discontinuous Galerkin discretisation

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

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Authors

T. Adams

N. McLeish



Abstract

Level set reinitialisation is a part of the level set methodology which allows one to generate, at any point during level set evolution, a level set function which is a signed distance function to its own zero isocontour. Whilst not in general a required condition, maintaining the level set function as a signed distance function is often desirable as it removes a known source of numerical instability. This paper presents a novel level set reinitialisation method based on the solution of a nonlinear parabolic PDE. The PDE is discretised using a symmetric interior penalty discontinuous Galerkin method in space, and an implicit Euler method in time. Also explored are explicit and semi-implicit time discretisations, however, numerical experiments demonstrate that such methods suffer from severe time step restrictions, leading to prohibitively large numbers of iterations required to achieve convergence. The proposed method is shown to be high-order accurate through a number of numerical examples. More specifically, the presented experimental orders of convergence align with the well established optimal convergence rates for the symmetric interior penalty method; that is the error in the norm decreases proportionally to and the error in the DG norm decreases proportionally to .

Citation

Adams, T., McLeish, N., Giani, S., & Coombs, W. (2019). A parabolic level set reinitialisation method using a discontinuous Galerkin discretisation. Computers and Mathematics with Applications, 78(9), 2944-2960. https://doi.org/10.1016/j.camwa.2019.01.032

Journal Article Type Article
Acceptance Date Jan 29, 2019
Online Publication Date Mar 7, 2019
Publication Date Nov 1, 2019
Deposit Date Jan 30, 2019
Publicly Available Date Mar 28, 2024
Journal Computers and Mathematics with Applications
Print ISSN 0898-1221
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 78
Issue 9
Pages 2944-2960
DOI https://doi.org/10.1016/j.camwa.2019.01.032
Keywords Level set, Reinitialisation, Discontinuous Galerkin

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