The eikonal equation (from German Eikonal, which is from Greek εἰκών, image ) is a non-linear partial differential equation encountered in problems of wave propagation, when the wave equation is approximated using the WKB theory. It is derivable from Maxwell's equations of electromagnetics, and provides a link between physical (wave) optics and geometric (ray) optics.
The eikonal equation is of the form
subject to, where is an open set in with well-behaved boundary, is a function with positive values, denotes the gradient and |·| is the Euclidean norm. Here, the right-hand side is typically supplied as known input. Physically, the solution is the shortest time needed to travel from the boundary to inside with being the time cost (not speed) at .
One fast computational algorithm to approximate the solution to the eikonal equation is the fast marching method. In the special case when, the solution gives the signed distance from .
Read more about Eikonal Equation: Physical Interpretation, Mathematical Description, Applications
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