NDLI: Another Look at Velocity Extensions in the Level Set Method

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Chopp, David L.
Copyright Year	2009
Abstract	The level set method [S. Osher and J. A. Sethian, J. Comput. Phys., 79 (1988), pp. 1249] has become a widely used numerical method for moving interfaces; e.g., see the many examples in [J. Sethian, Level Set Methods: Evolving Interfaces in Geometry, Fluid Mechanics, Computer Vision and Material Science, Cambridge University Press, London, 1996; S. Osher and R. Fedkiw, Level Set Methods and Dynamic Implicit Surfaces, Springer Verlag, Heidelberg, 2002]. For many applications, the velocity of the interface is known only on the interface, while the level set method requires information about the interface speed at least in a neighborhood of grid points near the interface. To address this issue, velocity extensions are used to map the velocity information on the interface into the rest of the computational domain [D. Adalsteinsson and J. Sethian, J. Comput. Phys., 118 (1995), pp. 269277]. This allows the level set method to proceed. The velocity extension method presented in [D. Adalsteinsson and J. Sethian, J. Comput. Phys., 118 (1995), pp. 269277] uses the fast marching method [J. Sethian, Proc. Natl. Acad. Sci., 93 (1996), pp. 15911595; J. Sethian, SIAM Rev., 41 (1999), pp. 199235], and is only a first-order approximation for the velocity field near the interface. Furthermore, it can lead to unexpected behavior in some cases. This is primarily due to the strictly local solution for the characteristics of the flow near the interface. In this paper, we look more closely at the characteristics near the interface, and then present a modified velocity extension method, also based on the fast marching method, which handles the characteristcs more accurately. In turn, this new method will lead to some interesting new possibilities for the fast marching method.
Starting Page	3255
Ending Page	3273
Page Count	19
File Format	PDF
ISSN	10648275
DOI	10.1137/070686329
e-ISSN	10957197
Issue Number	5
Volume Number	31
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2009-08-05
Access Restriction	Subscribed
Subject Keyword	fast marching method Interpolation bicubic interpolation Smoothing, curve fitting velocity extension level set method Finite difference methods
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Computational Mathematics

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

Some Improvements of the Fast Marching Method

Another look at velocity extensions in the level set method (2007)

A Fast-marching Algorithm for Nonmonotonically Evolving Fronts

A Curvature-Augmented, REA Approach to the Level Set Method

A Third Order Accurate Fast Marching Method for the Eikonal Equation in Two Dimensions

A Finite Element Level Set Redistancing Method Based on Gradient Recovery

The Fast Construction of Extension Velocities in Level Set Methods (1997)

Characteristic Fast Marching Method for Monotonically Propagating Fronts in a Moving Medium

Convergence of a Generalized Fast-Marching Method for an Eikonal Equation with a Velocity-Changing Sign

Another Look at Velocity Extensions in the Level Set Method

Similar Documents

Some Improvements of the Fast Marching Method

Another look at velocity extensions in the level set method (2007)

A Fast-marching Algorithm for Nonmonotonically Evolving Fronts

A Curvature-Augmented, REA Approach to the Level Set Method

A Third Order Accurate Fast Marching Method for the Eikonal Equation in Two Dimensions

A Finite Element Level Set Redistancing Method Based on Gradient Recovery

The Fast Construction of Extension Velocities in Level Set Methods (1997)

Characteristic Fast Marching Method for Monotonically Propagating Fronts in a Moving Medium

Convergence of a Generalized Fast-Marching Method for an Eikonal Equation with a Velocity-Changing Sign

Another Look at Velocity Extensions in the Level Set Method