We propose an effective stopping criterion for higher-order fast sweeping schemes for static Hamilton-Jacobi equations based on ratios of three consecutive iterations. To design the new stopping criterion we analyze the convergence of the first-order Lax-Friedrichs sweeping scheme by using the theory of nonlinear iteration. In addition, we propose a fifth-order Weighted Power ENO sweeping scheme for static Hamilton-Jacobi equations with convex Hamiltonians and present numerical examples that validate the effectiveness of the new stopping criterion. © 2010 by AMSS, Chinese Academy of Sciences.
- Eikonal equations
- Fast sweeping methods
- Gauss-Seidel iteration
- High order accuracy
- Static Hamilton-Jacobi equations