Fast Algorithms for Optimal Control, Anisotropic Front Propagation and Multiple Arrivals

We review some recent work in fast, efficient and accurate methods to compute viscosity solutions and non-viscosity solutions to static HamiltonJacobi equations which arise in optimal control, anisotropic front propagation, and multiple arrivals in wave propagation. For viscosity solutions, the class of algorithms are known as “Ordered Upwind Methods”, and rely on a systematic ordering inherent in the characteristic flow of information. For non-viscosity multiple arrivals, the techniques hinge on a static boundary value phase-space formulation which again can be solved through a systematic ordering.