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First, assume that the ___domain has been discretized into a mesh. We will refer to meshpoints as nodes. Each node <math>x_i</math> has a corresponding value <math>U_i = U(x_i) \approx u(x_i)</math>.
The algorithm works just like Dijkstra's algorithm but differs in how the nodes' values are calculated. In Dijkstra's algorithm, a node's value is calculated using a single one of the neighboring nodes. However, in solving the [[Partial differential equation|PDE]] in <math>\mathbb{R}^n</math>, between <math>1</math> and <math>n</math> of the neighboring nodes [[Eikonal equation#Numerical Approximation|are used]].
Nodes are labeled as ''far'' (not yet visited), ''considered'' (visited and value tentatively assigned), and ''accepted'' (visited and value permanently assigned).
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