High-order essentially non-oscillatory schemes for Hamilton-Jacobi equations

By Haibing Wang. 2006

476 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/5a2b9a94ce4a6fc855054f93a70eb175c59a1fca

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Citations in the corpus

A balanced force refined level set grid method for two-phase flows on unstructured flow solver grids (2008, methodology): “We use the fifthorder WENO scheme for Hamilton-Jacobi equations of Jiang and Peng [23] in conjunction with a Roe flux with local Lax-Friedrichs entropy correction [36,47] to advance the level set scalar.”
Spatially adaptive techniques for level set methods and incompressible flow (2006, unknown): “This work was generalized in [70].”
Radial basis functions and level set method for structural topology optimization (2006, methodology): “Usually, the robust upwind schemes [30,36,37] can be used to solve this equation accurately.”
An immersed boundary technique for simulating complex flows with rigid boundary (2007, methodology): “This accuracy of fluid calculations can be improved by employing high resolution schemes [1–3] or using adaptive or moving mesh techniques such as in [4–7] to resolve the small scale structures.”
A Toolbox of Level Set Methods (2005, methodology): “This function is based on the framework proposed in [26] and described in [24, chapter 5.”
Sub-pixel distance maps and weighted distance transforms (1996, methodology): “All the evolution rules presented here are implemented by numerical schemes that are consistent with the continuous propagation rule, and are motivated by numerical schemes that where developed in solving Hamilton Jacobi type of equations, [16, 21, 22].”
Hermite WENO schemes for Hamilton-Jacobi equations (2005, unknown): “For choices of two dimensional numerical ﬂuxes suitable for the HJ equations we again refer to, e.g. [21].”
The Flexible, Extensible and Efficient Toolbox of Level Set Methods (2008, methodology): “The test for the spinning rectangle was repeated with a third order accurate ENO spatial derivative approximation [30].”
Structural Shape and Topology Optimization Using an Implicit Free Boundary Parametrization Method (2006, methodology): “The upwind difference methods [Osher and Sethian (1988); Jiang and Peng (2000); Osher and Shu (1991)] popular in the conventional level set methods are not employed to advance the front in the present study since spatial derivatives of the level set function can be obtained analytically and a good…”
A time-dependent Hamilton-Jacobi formulation of reachable sets for continuous dynamic games (2005, unknown): “The spatial derivative Dxv(x, t) is computed with a fifth order accurate weighted essentially non-oscillatory approximation [43].”
Seismic ray tracing and wavefront tracking in laterally heterogeneous media (2008, background): “66 must exhibit reasonable behaviour in the presence of gradient discontinuities; fortunately, a large number of schemes, such as ENO and WENO, have been developed for solving differential equations of this type (e.g. Osher and Shu, 1991; Jiang and Peng, 2000).”
High Order Weighted Essentially Nonoscillatory Schemes for Convection Dominated Problems (2009, background): “, [121] for examples of monotone Hamiltonians in oneand multidimensional cases.”
Distributed shape derivative via averaged adjoint method and applications (2015, unknown): “We use the Local Lax-Friedrichs flux originally conceived in [36] and which reduces in our case to: Ĥ (p−, p, q−, q) = H ( p− + p+ 2 , q− + q+ 2 ) − 1 2 (p − p−)αx − 1 2 (p − p−)αy where αx = |θx|, αy = |θy|, θ = (θx, θy) and p− = D− x φij = φij − φi−1,j ∆x , p = D x φij = φi+1,j − φij ∆x , q− = D− ”
HIGH ORDER NUMERICAL METHODS FOR TIME DEPENDENT HAMILTON-JACOBI EQUATIONS (2007, methodology): “Numerical results obtained with these ENO schemes can be found in [31] and [32] and will be not be presented here.”
Hamilton-Jacobi Skeletons (2002, methodology): “Numerical thresholds are introduced, and high order accurate numerical schemes must be used (Osher and Shu, 1991; Siddiqi et al., 1997).”
Nonlocal Operators with Applications to Image Processing (2008, methodology): “See [44], [43] for classical approaches.”
Lax-Friedrichs sweeping scheme for static Hamilton-Jacobi equations (2004, methodology): “Even though our algorithm needs more iterations than the sweeping methods based on the Godunov Hamiltonian, it is still very fast.”
Numerical methods for high dimensional Hamilton-Jacobi equations using radial basis functions (2004, methodology): “The familiarity of polynomials and the ability to simply construct their derivatives using divided differences made the ENO methods for conservation laws and Hamilton-Jacobi equations very popular [16],[22],[26].”