The fast marching method is introduced by James A. Sethian as a numerical method for solving boundary value problems of the Eikonal equation:
Typically, such a problem describes the evolution of a closed curve as a function of time with speed in the normal direction at a point on the curve. The speed function is specified, and the time at which the contour crosses a point is obtained by solving the equation.
The algorithm is similar to Dijkstra's algorithm and uses the fact that information only flows outward from the seeding area.
This problem is a special case of level set methods. More general algorithms exist but are normally slower.
Extensions to non-flat (triangulated) domains solving:
was introduced by Ron Kimmel and Sethian.