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Mathematics Group

Fast Marching and Ordered Upwind Methods for Wave Propagation and Control

Fast Marching Methods, and the more general class of Ordered Upwind Methods, are fast methods to solve Eikonal and Hamilton-Jacobi equations which arise in control and anisotropic front propagation. They exploit a fundamental ordering in Dijkstra’s method for the cheapest path on network graphs, and couple this to upwind entropy-satisfying weak viscosity solutions to the gradient and derivative operators. The resulting methods are used in path planning, fast simulations in phololithography, calculations of void spaces and channel structures in proposed zeolites and metal organic frameworks (MOFs) for gas separation and carbon sequestration, and first-arrivals in seismic imaging and beam propagation.