We develop a family of fast methods for approximating the solutions to a wide class of static
Hamilton--Jacobi PDEs; these fast methods include both semi-Lagrangian and fully Eulerian
versions. Numerical solutions to these problems are typically obtained by solving large
systems of coupled nonlinear discretized equations. Our techniques, which we refer to as"
Ordered Upwind Methods"(OUMs), use partial information about the characteristic directions
to decouple these nonlinear systems, greatly reducing the computational labor. Our …

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 …