A Toolbox of Level Set Methods

By Ian M. Mitchell. 2005

332 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/f7f4aa142f6beff42a95d6254289400a6038774e

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Citations in the corpus

A level set method for shape and topology optimization of large‐displacement compliant mechanisms (2008, background): “However, in applying these conventional level set methods to shape and topology optimization, several unfavorable numerical features arise during numerical implementation, such as the need for explicit schemes, reinitialization, and velocity extension [23, 28], in which many complicated PDEs are inv”
Structural Shape and Topology Optimization Using an Implicit Free Boundary Parametrization Method (2006, methodology): “In general, it is well known that the PDEs are rarely easy to implement [Mitchell (2004)], though some robust and accurate upwind schemes [Osher and Sethian (1988); Osher and Shu (1991); Jiang and Peng (2000)], fast marching methods [Sethian (1999)] and fast local level set methods [Peng, Merriman,…”
The Flexible, Extensible and Efficient Toolbox of Level Set Methods (2008, methodology): “The Toolbox has a lengthy, indexed user manual [18], and users interested in applying level set methods to applications will probably nd this manual a good place to get started.”
Reachability-based safe learning with Gaussian processes (2014, methodology): “We use the Level Set Toolbox [16] to compute the discriminating kernel and the optimal safety-preserving control laws.”
A time-dependent Hamilton-Jacobi formulation of reachable sets for continuous dynamic games (2005, unknown): “We describe only the key features of those implementations here, but more details are available in [8] and [21].”
Guaranteed Safe Online Learning via Reachability: tracking a ground target using a quadrotor (2012, methodology): “Pre τ ( K ) is then calculated using the method described in Section II-A, via the Level Set Toolbox [13], and is partially pictured in Figure 4.”
Radial basis functions and level set method for structural topology optimization (2006, methodology): “where u is the displacement field, ε(u) the strain field, H(Φ) the Heaviside step function of the implicit function Φ(x) [35], l a positive Lagrange multiplier, and the volume V of the admissible design can be written as”
Multiplayer reach-avoid games via low dimensional solutions and maximum matching (2014, methodology): “The setup for using HJ reachability to solve differential games can be found in [15], [22], [5].”
Reach-avoid problems with time-varying dynamics, targets and constraints (2014, methodology): “Construct signed distance functions with the zero level set corresponding to the boundary of the numerically computed reach-avoid set (for instance using [15]).”
Multiplayer Reach-Avoid Games via Pairwise Outcomes (2016, methodology): “The HJI approach for solving differential games is outlined in [2], [11], [17].”
A level set method for structural shape and topology optimization using radial basis functions (2009, background): “However, these PDEs are seldom easy to implement [22] because the mathematically meaningful solutions can only be obtained under some strict conditions [16,17,23].”