Skip to Content
No preview available

Actions

Download Analytics Citations

Export to: EndNote  |  Zotero  |  Mendeley

Collections

This file is not currently in any collections.

A high-order elliptic PDE based level set reinitialisation method using a discontinuous Galerkin discretisation [figure data] Open Access

Abstract from paper: In this paper, an efficient, high-order accurate, level set reinitialisation method is proposed, based on the elliptic reinitialisation method (Basting and Kuzmin, 2013), 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 $h^{p+1}$ and $h^p$ in the $L^2$ and DG norms respectively. Furthermore, the degree to which the level set function satisfies the Eikonal equation improves proportionally to $h^p$, 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 $h^2$ for all polynomial orders.

Descriptions

Resource type
Dataset
Contributors
Creator: Adams, Thomas 1
Contact person: Adams, Thomas 1
Creator: Giani, Stefano 1
Creator: Coombs, William M 1
1 Durham University, 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
Identifier
ark:/32150/r1cn69m412x
doi:10.15128/r1cn69m412x
Rights
Creative Commons Attribution 4.0 International (CC BY)

All rights reserved All rights reserved
Publisher
Durham University
Date Created

File Details

Depositor
T.D. Adams
Date Uploaded
Date Modified
18 September 2018, 09:09:56
Audit Status
Audits have not yet been run on this file.
Characterization
File format: x-rar (RAR archive data, v80, flags: Archive volume, os: OS/2, Rar)
Mime type: application/x-rar
File size: 5572518
Filename: FigureData.rar
Original checksum: f065af244b8e9e1a5f0c33704e8bb442
Activity of users you follow
User Activity Date
User T.D. Adams has added a new version of A high-order elliptic PDE based level set reinitialisation method using a discontinuous Galerkin discretisation [figure data] 1 day ago
User N. Syrotiuk has updated A high-order elliptic PDE based level set reinitialisation method using a discontinuous Galerkin discretisation [figure data] 6 months ago
User N. Syrotiuk has updated A high-order elliptic PDE based level set reinitialisation method using a discontinuous Galerkin discretisation [figure data] 6 months ago
User T.D. Adams has updated Figure Data: A high-order elliptic PDE based level set reinitialisation method using a discontinuous Galerkin discretisation 6 months ago
User T.D. Adams has updated Figure Data: A high-order elliptic PDE based level set reinitialisation method using a discontinuous Galerkin discretisation 6 months ago
User T.D. Adams has deposited FigureData-A_high_order_elliptic_PDE_based_level_set_reinitialisation_method_using_a_discontinuous_Galerkin_discretisation-ThomasAdams-2018.rar 6 months ago