Ordered Upwind Methods: Computing Viscosity Solutions to Optimal Control and Non-Viscosity Solutions to Wave Propagation
Wednesday, October 31, 2001 - 2:00pm - 3:00pm
James Sethian (University of California, Berkeley)
Ordered Upwind Methods are techniques for computing solutions of static Hamilton-Jacobi equations; they use partial information about characteristic directions as the computation unfolds to greatly reduce the computational labor. The methods are O(N log N) where N is the number of points in the computational domain. In this talk, we show how to design and build these schemes to find viscosity solutions to problems in optimal control, and non-viscosity multiple arrival solutions to problems in wave propagation. Applications include anisotropic front propagation in semiconductor manufacturing, computing multiple arrivals in seismic imaging, and finding local geodesic paths on complex manifolds. The work on optimal control is joint with A. Vladimirsky, and the work on multiple arrivals is joint with S. Fomel.