Fast sweeping algorithms for a class of Hamilton-Jacobi equations

We derive a Godunov-type numerical flux for the class of strictly convex, homogeneous Hamiltonians that includes H(p, q) = root ap(2) + bq(2) - 2cpq, c(2) < ab. We combine our Godunov numerical fluxes with simple Gauss - Seidel- type iterations for solving the corresponding Hamilton-Jacobi (HJ) equations. The resulting algorithm is fast since it does not require a sorting strategy as found, e. g., in the fast marching method. In addition, it provides a way to compute solutions to a class of HJ equations for which the conventional fast marching method is not applicable. Our experiments indicate convergence after a few iterations, even in rather difficult cases.