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Ordered upwind methods for static Hamilton-Jacobi equations.

J A Sethian·A Vladimirsky
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Abstract

We introduce a family of fast ordered upwind methods for approximating solutions to a wide class of static Hamilton-Jacobi equations with Dirichlet boundary conditions. Standard techniques often rely on iteration to converge to the solution of a discretized version of the partial differential equation. Our fast methods avoid iteration through a careful use of information about the characteristic directions of the underlying partial differential equation. These techniques are of complexity O(M log M), where M is the total number of points in the domain. We consider anisotropic test problems in optimal control, seismology, and paths on surfaces.

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AlgorithmsMathematicsModels, TheoreticalSurface PropertiesViscosityJournal ArticleResearch Support, U.S. Gov't, Non-P.H.S.

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J A Sethian, A Vladimirsky. 2001-09-25. Ordered upwind methods for static Hamilton-Jacobi equations.. https://doi.org/10.1073/pnas.201222998

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