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Ordered upwind methods for static Hamilton–Jacobi equations

2001; National Academy of Sciences; Volume: 98; Issue: 20 Linguagem: Inglês

10.1073/pnas.201222998

1091-6490

James A. Sethian, Ajeet Kumar,

Computational Geometry and Mesh Generation

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.