Evolution, implementation, and application of level set and fast marching methods for advancing fronts

By James A. Sethian. 2001

555 citations recorded by the source corpus.

Subfields: Computational Mechanics, Geophysics, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/32392f18630872b1e5477a436c07adb01744d37a

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Citations in the corpus

LEVEL SET METHODS FOR FLUID INTERFACES (2003, background): “Here, we follow closely the discussion in Sethian (2001).”
A hybrid particle level set method for improved interface capturing (2002, methodology): “The application of level set methods to a wide variety of problems including fluid mechanics, combustion, computer vision, and materials science is discussed in the recent review articles by Osher and Fedkiw [20] and Sethian [34] as well as the recent books of Osher and Fedkiw [21] and Sethian [33].”
A Lagrangian particle level set method. (2005, methodology): “Techniques such as fast marching methods [31,5,3] and re-distancing algorithms [32] have been introduced in order to maintain this property by reinitializing the level set function.”
The Fast Marching Method: An Effective Tool for Tomographic Imaging and Tracking Multiple Phases in Complex Layered Media (2005, methodology): “To date, FMM has been applied to a wide variety of problems including optimal path planning, medical imaging, geodesics, and photolithographic development ( Sethian, 1999, 2001 ).”
Wave front evolution in strongly heterogeneous layered media using the fast marching method (2004, methodology): “To date, FMM has been applied to a wide variety of problems including photolithographic development, geodesics, deposition of sediments, medical imaging and optimal path planning ( Sethian 1996, 1999, 2001 ).”
A mixed markers and volume-of-fluid method for the reconstruction and advection of interfaces in two-phase and free-boundary flows (2003, background): “Other popular Eulerian front-capturing schemes, able to capture or define in some way an interface, include the level set [16,29] and phase-field approaches [12,13].”
Seismic ray tracing and wavefront tracking in laterally heterogeneous media (2008, background): “…in the field of computational mathematics for solving various types of interface evolution problems, and to date has been applied in numerous areas of the physical sciences including optimal path planning, medical imaging, geodesics, and photolithographic development (Sethian, 1999, 2001).”
Extended Voronoi cell finite element model for multiple cohesive crack propagation in brittle materials (2006, methodology): “Level set methods, introduced by Adalsteinsson and Sethian [45] and Sethian [46] for following the evolution of interfaces, is ideal for representing arbitrary contours.”
Simple and efficient relaxation methods for interfaces separating compressible fluids, cavitating flows and shocks in multiphase mixtures (2009, background): “It fulfills the equation of state and energy conservation on both sides of interfaces and guarantees correct transmission of shocks across them.”
Direct numerical simulations of gas/liquid multiphase flows (2011, methodology): “Other methods, based on similar ideas but advecting the marker function in a different way include the level set method (reviewed by Osher and Fedkiw, 2001; Sethian, 2001) and the CIP method of Yabe and collaborators (see Yabe et al., 2001, for a review).”
Transport and diffusion of material quantities on propagating interfaces via level set methods (2003, background): “As understood by many practitioners of level set methods (see [19, 22]), reinitialization every time step (or close to every time step) is a poor strategy, since each reinialization causes error in the position of the front.”