Level set methods: an overview and some recent results

By Stanley J. Osher, Ronald Fedkiw. 2001

2,024 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/4e4210d40eb97c03b87260c613abe404e926a82e

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In Computational Mechanics

In Computational Theory and Mathematics

Citations in the corpus

The extended/generalized finite element method: An overview of the method and its applications (2010, methodology): “The level-set method [138, 137, 159] has proven to be an ideal complement to the XFEM.”
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].”
An unsteady single‐phase level set method for viscous free surface flows (2007, methodology): “Since the introduction of the level set method by Osher & Sethian [2], a large amount of bibliography on the subject has been published and several types of problems have been tackled with this method; see for instance the cited review by Sethian & Smereka [1] and the work by Osher & Fedkiw [3].”
Structural Shape and Topology Optimization Using an Implicit Free Boundary Parametrization Method (2006, methodology): “In the present shape and topology optimization, choosing the normal velocity field vn is equivalent to choosing a descent direction for the objective function, which can be easily implemented by using a steepest gradient method [Osher and Santosa (2001); Wang, Wang, and Guo (2003); Allaire, Jouve, a”
Topology optimization of thermoelastic structures using level set method (2008, methodology): “Then, such extension velocity V e n is utilized as the advection velocity in the following Hamilton–Jacobi equation in the level set method [ 31 ,32,34]:”
Filling holes in complex surfaces using volumetric diffusion (2002, methodology): “Diffusion processes and level set methods are very general computational frameworks [Sethian96, Osher01 ], so our algorithm can be extended in several ways.”
Simple and efficient relaxation methods for interfaces separating compressible fluids, cavitating flows and shocks in multiphase mixtures (2009, methodology): “Another class of popular Eulerian methods is based on the level-set equation [13,34,36,47] to locate the interface.”
A level set‐based parameterization method for structural shape and topology optimization (2008, background): “As mentioned previously, the CFL condition seriously hampers convergent efficiency especially when confronting with a finer mesh that means a smaller time step is applied to satisfy the CFL condition, because the time step-size is determined by the minimum grid size [62].”
Using a signed distance function for the simulation of metal forming processes: Formulation of the contact condition and mesh adaptation. From a Lagrangian approach to an Eulerian approach (2009, background): “[2] to have an overview on the level set methods and of their applications.”
Modeling three-dimensional multiphase flow using a level contour reconstruction method for front tracking without connectivity (2002, methodology): “However, we direct the interested reader to recent comprehensive reviews of numerical developments and capabilities of these and other methods in Scardovelli and Zaleski [22], Osher and Fedkiw [17], Jamet et al. [11], Tryggvason et al. [28], and Glimm et al. [7, 8].”
Level set based shape prior segmentation (2005, background): “and is a parameter that describes how large the length of the boundaries is permitted, since the term just represents the length of zero level set of ( see [14] ).”
Integrated topology optimization with embedded movable holes based on combined description by material density and level sets (2013, background): “The level set approach was originally developed for tracking the motion of dynamic interfaces with topological changes of merging and breaking naturally [31].”
Electrical impedance tomography using level set representation and total variational regularization (2005, neutral): “See also [1] [13] [14] [32] for some related studies for the same problem.”
A level set method for structural topology optimization with multi-constraints and multi-materials (2004, methodology): “The reader is referred to references for detailed formulae [21, 22 ].”