A viscosity solutions approach to shape-from-shading
SIAM Journal on Numerical Analysis
Numerical methods for stochastic control problems in continuous time
Numerical methods for stochastic control problems in continuous time
Parallel asynchronous label-correcting methods for shortest paths
Journal of Optimization Theory and Applications
SIAM Review
Algorithm 360: shortest-path forest with topological ordering [H]
Communications of the ACM
Dynamic Programming and Optimal Control
Dynamic Programming and Optimal Control
An $\cal O(N)$ Level Set Method for Eikonal Equations
SIAM Journal on Scientific Computing
SIAM Journal on Numerical Analysis
Ordered Upwind Methods for Hybrid Control
HSCC '02 Proceedings of the 5th International Workshop on Hybrid Systems: Computation and Control
Ordered Upwind Methods for Static Hamilton--Jacobi Equations: Theory and Algorithms
SIAM Journal on Numerical Analysis
Lax-Friedrichs sweeping scheme for static Hamilton-Jacobi equations
Journal of Computational Physics
Fast Sweeping Methods for Static Hamilton--Jacobi Equations
SIAM Journal on Numerical Analysis
Computational Study of Fast Methods for the Eikonal Equation
SIAM Journal on Scientific Computing
Short note: O(N) implementation of the fast marching algorithm
Journal of Computational Physics
A second order discontinuous Galerkin fast sweeping method for Eikonal equations
Journal of Computational Physics
A Fast Iterative Method for Eikonal Equations
SIAM Journal on Scientific Computing
Parallel algorithms for approximation of distance maps on parametric surfaces
ACM Transactions on Graphics (TOG)
Fast Marching Methods for Stationary Hamilton-Jacobi Equations with Axis-Aligned Anisotropy
SIAM Journal on Numerical Analysis
Some Improvements for the Fast Sweeping Method
SIAM Journal on Scientific Computing
Uniformly Accurate Discontinuous Galerkin Fast Sweeping Methods for Eikonal Equations
SIAM Journal on Scientific Computing
Applied Numerical Mathematics
Fast iterative graph computation with block updates
Proceedings of the VLDB Endowment
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Fast Marching and Fast Sweeping are the two most commonly used methods for solving the eikonal equation. Each of these methods performs best on a different set of problems. Fast Sweeping, for example, will outperform Fast Marching on problems where the characteristics are largely straight lines. Fast Marching, on the other hand, is usually more efficient than Fast Sweeping on problems where characteristics frequently change their directions and on domains with complicated geometry. In this paper we explore the possibility of combining the best features of both approaches by using Marching on a coarser scale and sweeping on a finer scale. We present three new hybrid methods based on this idea and illustrate their properties in several numerical examples with continuous and piecewise-constant speed functions in $R^2$.