In numerical mathematics, a non-compact
stencil
Stencilling produces an image or pattern on a surface, by applying pigment to a surface through an intermediate object, with designed holes in the intermediate object, to create a pattern or image on a surface, by allowing the pigment to reach ...
is a type of
discretization
In applied mathematics, discretization is the process of transferring continuous functions, models, variables, and equations into discrete counterparts. This process is usually carried out as a first step toward making them suitable for numerical ...
method, where any node surrounding the node of interest may be used in the calculation. Its
computational time
In computer science, the time complexity is the computational complexity that describes the amount of computer time it takes to run an algorithm. Time complexity is commonly estimated by counting the number of elementary operations performed by ...
grows with an increase of layers of nodes used. Non-compact stencils may be compared to
Compact stencil
In mathematics, especially in the areas of numerical analysis called numerical partial differential equations, a compact stencil is a type of stencil that uses only nine nodes for its discretization method in two dimensions. It uses only the cent ...
s.
[Communications in Numerical Methods in Engineering, Copyright © 2008 John Wiley & Sons, Ltd.]
See also
*
Nine-point stencil
*
Five-point stencil
In numerical analysis, given a square grid in one or two dimensions, the five-point stencil of a point in the grid is a stencil made up of the point itself together with its four "neighbors". It is used to write finite difference approximations to ...
References
Numerical differential equations
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