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
Weighted essentially non-oscillatory schemes
Journal of Computational Physics
The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
SIAM Journal on Numerical Analysis
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
Paraxial eikonal solvers for anisotropic quasi-P travel times
Journal of Computational Physics
Journal of Computational Physics
Rapid and accurate computation of the distance function using grids
Journal of Computational Physics
SIAM Journal on Numerical Analysis
Ordered Upwind Methods for Static Hamilton--Jacobi Equations: Theory and Algorithms
SIAM Journal on Numerical Analysis
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
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 Computational Physics
Fast sweeping method for the factored eikonal equation
Journal of Computational Physics
A local discontinuous Galerkin method for directly solving Hamilton-Jacobi equations
Journal of Computational Physics
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
Hi-index | 31.45 |
A uniformly second order method with a local solver based on the piecewise linear discontinuous Galerkin formulation is introduced to solve the eikonal equation with Dirichlet boundary conditions. The method utilizes an interesting phenomenon, referred as the superconvergence phenomenon, that the numerical solution of monotone upwind schemes for the eikonal equation is first order accurate on both its value and gradient when the solution is smooth. This phenomenon greatly simplifies the local solver based on the discontinuous Galerkin formulation by reducing its local degrees of freedom from two (1-D) (or three (2-D), or four (3-D)) to one with the information of the gradient frozen. When considering the eikonal equation with point-source conditions, we further utilize a factorization approach to resolve the source singularities of the eikonal by decomposing it into two parts, either multiplicatively or additively. One part is known and captures the source singularities; the other part serves as a correction term that is differentiable at the sources and satisfies the factored eikonal equations. We extend the second order method to solve the factored eikonal equations to compute the correction term with second order accuracy, then recover the eikonal with second order accuracy. Numerical examples are presented to demonstrate the performance of the method.