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A parabolic level set reinitialisation method using a discontinuous Galerkin discretisation [figure data] Open Access

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 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 $L^2$ norm decreases proportionally to $h^{p+1}$ and the error in the DG norm decreases proportionally to $h^p$.

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Resource type
Dataset
Contributors
Creator: Adams, Thomas 1
Contact person: Adams, Thomas 1
Creator: McLeish, Nicholas 1
Creator: Giani, Stefano 1
Creator: Coombs, William M 1
1 University of Durham, UK
Funder
Engineering and Physical Sciences Research Council
Research methods
Other description
Keyword
Level set method
Reinitialisation
Discontinuous Galerkin
Subject
Galerkin methods
Location
Language
Cited in
10.1016/j.camwa.2019.01.032
Identifier
ark:/32150/r2x346d417r
doi:10.15128/r2x346d417r
Rights
Creative Commons Attribution 4.0 International (CC BY)

Publisher
Durham University
Date Created

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T.D. Adams
Date Uploaded
Date Modified
10 June 2019, 11:06:28
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File format: zip (ZIP Format)
Mime type: application/zip
File size: 4875
Last modified: 2018:12:13 12:53:29+00:00
Filename: FigureData.zip
Original checksum: 4bef13c3048efe0fd9241571cec8d9a6
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