Fast algorithms for optimal control, anisotropic front propagation and multiple arrivals

Details Fast algorithms for optimal control, anisotropic front propagation and multiple arrivals Fast algorithms for optimal control, anisotropic front propagation and multiple arrivals

2003-05-08

arxiv.org/abs/math/0305130v1

Proceedings of the ICM, Beijing 2002, vol. 3, 735--746

Mathematics

Numerical Analysis

Scientific paper

We review some recent work in fast, efficient and accurate methods to compute viscosity solutions and non-viscosity solutions to static Hamilton-Jacobi 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.

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