Definition:Stencil

Definition
A quintuple $\tuple {X, S_X, \map S 0, \Delta, \delta}$ defines a stencil :

By means of the update sweep $\forall \vec x \in X: \map {\map S {n + 1} } {\vec x} = \ds \map \delta {\prod_{i \mathop = 1}^{\size \Delta} \map {\map S n} {\vec x + \Delta_i} }$ this induces a stencil evolution $\N \ni n \mapsto \map S n \in \paren {X \to S_X}$ from the initial state $\map S 0$.