Regular grid

A regular grid is a <a href="/facts/Tessellation/7BWDywXC">tessellation</a> of n-dimensional <a href="/facts/Euclidean_space/R2UbzmzM">Euclidean space</a> by <a href="/facts/Congruence_(geometry)/2tKJ6AhB">congruent</a> <a href="/facts/Parallelepiped/Qn7cDgSr">parallelotopes</a> (e.g. <a href="/facts/Brick/2CBPgDIK">bricks</a>). Its opposite is <a href="/facts/Unstructured_grid/2CxbbbFx">irregular grid</a>.
Grids of this type appear on <a href="/facts/Graph_paper/NKJBaxCS">graph paper</a> and may be used in <a href="/facts/Finite_element_analysis/eUcfP1vn">finite element analysis</a>, <a href="/facts/Finite_volume_method/6JfQMucX">finite volume methods</a>, <a href="/facts/Finite_difference_method/EoG81Qn9">finite difference methods</a>, 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. <a href="/facts/Unstructured_grid/2CxbbbFx">Unstructured grids</a> offer more flexibility than structured grids and hence are very useful in finite element and finite volume methods.
Each cell in the grid can be addressed by index (i, j) in two <a href="/facts/Dimension/0ktmUyac">dimensions</a> or (i, j, k) in three dimensions, and each <a href="/facts/Vertex_(geometry)/ID3cea9z">vertex</a> has <a href="/facts/Coordinate/Mtd0q4SP">coordinates</a> 
 
 
 
 (
 i
 ⋅
 d
 x
 ,
 j
 ⋅
 d
 y
 )
 
 
 {\displaystyle (i\cdot dx,j\cdot dy)}
 
 in 2D or 
 
 
 
 (
 i
 ⋅
 d
 x
 ,
 j
 ⋅
 d
 y
 ,
 k
 ⋅
 d
 z
 )
 
 
 {\displaystyle (i\cdot dx,j\cdot dy,k\cdot dz)}
 
 in 3D for some real numbers dx, dy, and dz representing the grid spacing.

Regular grid open-in-new

Regular grid