Journal of Computational Physics
A Fast Sweeping Method for Static Convex Hamilton-Jacobi Equations
Journal of Scientific Computing
A second order discontinuous Galerkin fast sweeping method for Eikonal equations
Journal of Computational Physics
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Journal of Scientific Computing
Journal of Computational Physics
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Computer Aided Geometric Design
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Fast sweeping method for the factored eikonal equation
Journal of Computational Physics
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Some Improvements for the Fast Sweeping Method
SIAM Journal on Scientific Computing
Journal of Computational Physics
Uniformly Accurate Discontinuous Galerkin Fast Sweeping Methods for Eikonal Equations
SIAM Journal on Scientific Computing
A Third Order Accurate Fast Marching Method for the Eikonal Equation in Two Dimensions
SIAM Journal on Scientific Computing
Computers & Mathematics with Applications
The Chebyshev spectral viscosity method for the time dependent Eikonal equation
Mathematical and Computer Modelling: An International Journal
Fast Two-scale Methods for Eikonal Equations
SIAM Journal on Scientific Computing
Lax-Friedrichs fast sweeping methods for steady state problems for hyperbolic conservation laws
Journal of Computational Physics
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Journal of Scientific Computing
A uniformly second order fast sweeping method for eikonal equations
Journal of Computational Physics
Journal of Computational Physics
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We propose a new sweeping algorithm which discretizes the Legendre transform of the numerical Hamiltonian using an explicit formula. This formula yields the numerical solution at a grid point using only its immediate neighboring grid values and is easy to implement numerically. The minimization that is related to the Legendre transform in our sweeping scheme can either be solved analytically or numerically. We illustrate the efficiency and accuracy approach with several numerical examples in two and three dimensions.