Regular grid in the context of Finite difference method


Regular grid in the context of Finite difference method

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⭐ Core Definition: Regular grid

A regular grid is a tessellation of n-dimensional Euclidean space by congruent parallelotopes (e.g. bricks). Its opposite is irregular grid.

Grids of this type appear on graph paper and may be used in finite element analysis, finite volume methods, finite difference methods, and in general for discretization of parameter spaces. Since the derivatives of field variables can be conveniently expressed as finite differences, structured grids mainly appear in finite difference methods. Unstructured grids offer more flexibility than structured grids and hence are very useful in finite element and finite volume methods.

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Regular grid in the context of Graph paper

Graph paper, coordinate paper, grid paper, or squared paper is writing paper that is printed with fine lines making up a regular grid. It is available either as loose leaf paper or bound in notebooks or graph books.

It is commonly found in mathematics and engineering education settings, exercise books, and in laboratory notebooks.

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Regular grid in the context of Blokus

Blokus (/ˈblɒkəs/ BLOK-əs) is an abstract strategy board game for two to four players, where players try to score points by occupying most of the board with pieces of their colour. The board is a square regular grid and the pieces are polyominoes. It was designed by French mathematician Bernard Tavitian and first released in 2000 by Sekkoïa, a French company. It has won several awards, including the Mensa Select award and the 2004 Teacher's Choice Award. In 2009, the game was sold to Mattel.

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Regular grid in the context of Text mode

Text mode is a computer display mode in which content is internally represented on a computer screen in terms of characters rather than individual pixels. Typically, the screen consists of a uniform rectangular grid of character cells, each of which contains one of the characters of a character set; at the same time, contrasted to graphics mode or other kinds of computer graphics modes.

Text mode applications communicate with the user by using command-line interfaces and text user interfaces. Many character sets used in text mode applications also contain a limited set of predefined semi-graphical characters usable for drawing boxes and other rudimentary graphics, which can be used to highlight the content or to simulate widget or control interface objects found in GUI programs. A typical example is the IBM code page 437 character set.

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Regular grid in the context of Voxel

In computing, a voxel is a representation of a value on a three-dimensional regular grid, akin to the two-dimensional pixel. Voxels are frequently used in the visualization and analysis of medical and scientific data (e.g. geographic information systems (GIS)). Voxels also have technical and artistic applications in video games, largely originating with surface rendering in Outcast (1999). Minecraft (2011) makes use of an entirely voxelated world to allow for a fully destructible and constructable environment. Voxel art, of the sort used in Minecraft and elsewhere, is a style and format of 3D art analogous to pixel art.

As with pixels in a 2D bitmap, voxels themselves do not typically have their position (i.e. coordinates) explicitly encoded with their values. Instead, rendering systems infer the position of a voxel based upon its position relative to other voxels (i.e., its position in the data structure that makes up a single volumetric image). Some volumetric displays use voxels to describe their resolution. For example, a cubic volumetric display might be able to show 512×512×512 (or about 134 million) voxels.

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