Fast algorithms for optimal control, anisotropic front propagation and multiple arrivals
Numerical Analysis
2025-10-20 v1 Numerical Analysis
Abstract
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.
Cite
@article{arxiv.math/0305130,
title = {Fast algorithms for optimal control, anisotropic front propagation and multiple arrivals},
author = {J. A. Sethian},
journal= {arXiv preprint arXiv:math/0305130},
year = {2025}
}