Paper Info
Title
A parabolic level set reinitialisation method using a discontinuous Galerkin discretisation.
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 L2 norm decreases proportionally to hp+1 and the error in the DG norm decreases proportionally to hp.
Year
DOI
Venue
2019
10.1016/j.camwa.2019.01.032
Computers & Mathematics with Applications
Keywords
Field
DocType
Level set,Reinitialisation,Discontinuous Galerkin
Convergence (routing),Discontinuous Galerkin method,Signed distance function,Mathematical analysis,Level set,Norm (mathematics),Backward Euler method,Mathematics,Numerical stability,Penalty method
Journal
Volume
Issue
ISSN
78
9
0898-1221
Citations 
PageRank 
References 
0
0.34
0
Authors
4
Name
Order
Citations
PageRank
Thomas Adams100.34
Nicholas McLeish200.34
Stefano Giani3369.55
William M. Coombs402.37