A parabolic level set reinitialisation method using a discontinuous Galerkin discretisation

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

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: Oct 10, 2019
• 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
• Public URL: https://durham-repository.worktribe.com/output/1304213