A fast sweeping method for Eikonal equations

By Hongkai Zhao. Mathematics of Computation, 2004

1,155 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/921b248c1c101d758914ff4a333cdbeb74b21a5f

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In Computational Theory and Mathematics

In Numerical Analysis

Citations in the corpus

An adjoint state method for three-dimensional transmission traveltime tomography using first-arrivals (2006, methodology): “Therefore, in synthetic experiment the boundary measurements can be obtained by solving the equation (2.1) directly using the Fast Sweeping Method together with the exact velocity c.”
On utilizing topology optimization to design support structure to prevent residual stress induced build failure in laser powder bed metal additive manufacturing (2019, methodology): “Alternatively, another method to remove the support structure is by using dissolvable support technique [62, 63], which utilizes a self-terminating chemical process to clean the support structure without destroying the original design.”
An efficient discontinuous Galerkin method on triangular meshes for a pedestrian flow model (2008, methodology): “The fast marching method [23, 24, 25] and the fast sweeping method [26, 27, 28, 29] are designed to solve a nonlinear discretized system directly and efficiently by exploiting the causality of the Eikonal equations.”
MultiStencils Fast Marching Methods: A Highly Accurate Solution to the Eikonal Equation on Cartesian Domains (2007, methodology): “TheFSM[17],[21],[22],[23],[24],[25]isaniterative algorithm with optimal complexity that finds the numerical solution by using a nonlinear upwind method and Gauss-Seidel type iterations with alternating sweepings in pre-determined directions.”
Animating sand as a fluid (2005, methodology): “We then construct a distance field φ(x) in the unmarked (non-fluid) part of the grid using fast sweeping[Zhao 2005] and use that to extend the velocity field outside the fluid with the PDE ∇u ·∇φ = 0 (also solved with fast sweeping).”
3D distance fields: a survey of techniques and applications (2006, methodology): “Zhao [ 140 ] uses a sweeping method to solve the Eikonal equation.”
A review of level-set methods and some recent applications (2018, methodology): “In [130], Detrixhe et al. proposed to consider sweeping directions that are not those used in the serial version of FSM. Defining the level as the set of grid points (i,j) such that i+j=level, the sweeps are performed along the ‘diagonals’ defined by level=constant (see figure 14).”
Bayesian inversion for finite fault earthquake source models I—theory and algorithm (2013, methodology): “This mapping can be done quickly and efficiently using the Fast Sweeping Algorithm (Zhao 2005), a level-set method which uses a Godunov upwind difference scheme (Rouy & Tourin 1992) for solving the eikonal equation.”
Multiple level set methods with applications for identifying piecewise constant functions (2004, methodology): “There are dierent methods available in the literature for reinitialize the level set functions, see [36, 44, 43, 50, 52 ].”
Thickness control in structural optimization via a level set method (2016, methodology): “For the reinitialization, different algorithms can be used (fast marching, fast sweeping, Hamilton-Jacobi equation, etc... Osher and Fedkiw 2003; Sethian 1999; Zhao 2005).”
Fast image and video colorization using chrominance blending (2006, methodology): “Geodesic distances of this type can be efficiently and accurately computed using recently developed fast numerical techniques [10], [14], [24], [25], [27], [29], [31].”
Exact imposition of boundary conditions with distance functions in physics-informed deep neural networks (2021, methodology): “For monotonically advancing fronts ( f > 0), the fast marching method [72] and the fast sweeping method [103] are highly efficient methods to solve (75).”
PolyMesher: a general-purpose mesh generator for polygonal elements written in Matlab (2012, methodology): “…a signed distance function can be obtained from the level sets of a given implicit function by solving a nonlinear system of equations (cf. Persson and Strang 2004) or more generally using marching algorithms (see, for example, (Sussman et al. 1998; Sethian 1999; Osher and Fedkiw 2003; Zhao 2004)).”