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(pattern of input to numerical solutions at a point)

A stencil (in numerical analysis, i.e., methods to solve mathematical problems through computation) is a pattern indicating the choice of data used to calculate data at a "point". Stencils are used in solving partial differential equations (PDEs).

In the case of PDE variables referring to space dimensions, e.g., where something across space is changing over time, it can be thought of as the surrounding points in space from which data is used to update the data for a given point. For example, in a cubical grid, it might be the points above, below, on each side, and in front of and behind the point in question. A different stencil, for example, would be one that includes all 26 points, that form a cube surrounding the point in question.

The concept is also used when the "space" being handle includes a time dimension and/or other dimensions (e.g., momentum), i.e., any variables which the specific problem can be treat in a similar way to space. The concept has also been adapted to non-regular grids, and for methods using something other than points, e.g., volumes.

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