Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
Journal of Computational Physics
High-order essentially nonsocillatory schemes for Hamilton-Jacobi equations
SIAM Journal on Numerical Analysis
A viscosity solutions approach to shape-from-shading
SIAM Journal on Numerical Analysis
A level set formulation for the solution of the Dirichlet problem for Hamilton-Jacobi equations
SIAM Journal on Mathematical Analysis
The Runge-Kutta discontinuous Galerkin method for conservation laws V multidimensional systems
Journal of Computational Physics
Numerical schemes for the Hamilton-Jacobi and level set equations on triangulated domains
Journal of Computational Physics
SIAM Journal on Numerical Analysis
The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
SIAM Journal on Numerical Analysis
A PDE-based fast local level set method
Journal of Computational Physics
A Discontinuous Galerkin Finite Element Method for Hamilton--Jacobi Equations
SIAM Journal on Scientific Computing
Weighted ENO Schemes for Hamilton--Jacobi Equations
SIAM Journal on Scientific Computing
High-Resolution Nonoscillatory Central Schemes for Hamilton--Jacobi Equations
SIAM Journal on Scientific Computing
Computer Vision and Image Understanding
High Order Numerical Discretization for Hamilton–Jacobi Equations on Triangular Meshes
Journal of Scientific Computing
Runge–Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems
Journal of Scientific Computing
Paraxial eikonal solvers for anisotropic quasi-P travel times
Journal of Computational Physics
Journal of Computational Physics
SIAM Journal on Numerical Analysis
A Local Discontinuous Galerkin Method for KdV Type Equations
SIAM Journal on Numerical Analysis
Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
SIAM Journal on Numerical Analysis
High-Order WENO Schemes for Hamilton-Jacobi Equations on Triangular Meshes
SIAM Journal on Scientific Computing
Ordered Upwind Methods for Static Hamilton--Jacobi Equations: Theory and Algorithms
SIAM Journal on Numerical Analysis
High-Order Central WENO Schemes for Multidimensional Hamilton--Jacobi Equations
SIAM Journal on Numerical Analysis
Numerical methods for high dimensional Hamilton-Jacobi equations using radial basis functions
Journal of Computational Physics
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
Short note: O(N) implementation of the fast marching algorithm
Journal of Computational Physics
High Order Fast Sweeping Methods for Static Hamilton---Jacobi Equations
Journal of Scientific Computing
A discontinuous Galerkin finite element method for directly solving the Hamilton-Jacobi equations
Journal of Computational Physics
A Fast Sweeping Method for Static Convex Hamilton-Jacobi Equations
Journal of Scientific Computing
Fast Sweeping Methods for Eikonal Equations on Triangular Meshes
SIAM Journal on Numerical Analysis
Journal of Scientific Computing
Some Improvements for the Fast Sweeping Method
SIAM Journal on Scientific Computing
A boundary-only meshless method for numerical solution of the Eikonal equation
Computational Mechanics
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
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In this paper, we construct a second order fast sweeping method with a discontinuous Galerkin (DG) local solver for computing viscosity solutions of a class of static Hamilton-Jacobi equations, namely the Eikonal equations. Our piecewise linear DG local solver is built on a DG method developed recently [Y. Cheng, C.-W. Shu, A discontinuous Galerkin finite element method for directly solving the Hamilton-Jacobi equations, Journal of Computational Physics 223 (2007) 398-415] for the time-dependent Hamilton-Jacobi equations. The causality property of Eikonal equations is incorporated into the design of this solver. The resulting local nonlinear system in the Gauss-Seidel iterations is a simple quadratic system and can be solved explicitly. The compactness of the DG method and the fast sweeping strategy lead to fast convergence of the new scheme for Eikonal equations. Extensive numerical examples verify efficiency, convergence and second order accuracy of the proposed method.