Actions

Download Analytics Citations

Export to: EndNote  |  Zotero  |  Mendeley

Collections

This file is not currently in any collections.

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 $h^p$.

Descriptions

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

File Details

Depositor

T.D. Adams

Date Uploaded

12 December 2018, 16:12:03

Date Modified

10 June 2019, 11:06:28

Audit Status

Audits have not yet been run on this file.

Characterization

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