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) = pap2 + bq2 2 pq; 2 < ab: We combine our Godunov numerical fluxes with a simple GaussSeidel type iterations for solving the corresponding Hamilton-Jacobi Equations. The resulting algorithm is fast since it does not require a sorting strategy as does 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.