Scrabble?! EIKONS

Definitions of EIKONS in various dictionaries:

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 | ∇ u ( x ) | = 1 / f ( x ) , x ∈ Ω {\displaystyle |\nabla u(x)|=1/f(x),\ x\in \Omega } subject to u | ∂ Ω = 0 {\displaystyle u|_{\partial \Omega }=0} , where Ω {\displaystyle \Omega } is an open set in R n {\displaystyle \mathbb {R} ^{n}} with well-behaved boundary, f ( x ) {\displaystyle f(x)} is a function with positive values, ∇ {\displaystyle \nabla } denotes the gradient and | ⋅ | {\displaystyle |\cdot |} is the Euclidean norm. Here, the right-hand side f ( x ) {\displaystyle f(x)} is typically supplied as known input. Physically, the solution u ( x ) {\displaystyle u(x)} is the shortest time needed to travel from the boundary ∂ Ω {\displaystyle \partial \Omega } to x {\displaystyle x} inside Ω , {\displaystyle \Omega ,} with f ( x ) {\displaystyle f(x)} being the speed at x {\displaystyle x} . In the special case when f = 1 {\displaystyle f=1} , the solution gives the signed distance from ∂ Ω {\displaystyle \partial \Omega } . One fast computational algorithm to approximate the solution to the eikonal equation is the fast marching method.