An unstructured grid or irregular grid is a

tessellation A tessellation or tiling is the covering of a surface, often a plane, using one or more geometric shapes, called ''tiles'', with no overlaps and no gaps. In mathematics, tessellation can be generalized to higher dimensions and a variety of ...

of a part of the

Euclidean plane In mathematics, the Euclidean plane is a Euclidean space of dimension two. That is, a geometric setting in which two real quantities are required to determine the position of each point ( element of the plane), which includes affine notions ...

Euclidean space Euclidean space is the fundamental space of geometry, intended to represent physical space. Originally, that is, in Euclid's ''Elements'', it was the three-dimensional space of Euclidean geometry, but in modern mathematics there are Euclidea ...

by simple shapes, such as

triangle A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices ''A'', ''B'', and ''C'' is denoted \triangle ABC. In Euclidean geometry, any three points, when non- colline ...

s or

tetrahedra In geometry, a tetrahedron (plural: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertex corners. The tetrahedron is the simplest of all th ...

, in an irregular pattern. Grids of this type may be used in

finite element analysis The finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical problem areas of interest include the traditional fields of structural analysis, heat ...

when the input to be analyzed has an irregular shape. Unlike

structured 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 volu ...

s, unstructured grids require a list of the

connectivity Connectivity may refer to: Computing and technology * Connectivity (media), the ability of the social media to accumulate economic capital from the users connections and activities * Internet connectivity, the means by which individual terminal ...

which specifies the way a given set of vertices make up individual elements (see

graph (data structure) In computer science, a graph is an abstract data type that is meant to implement the undirected graph and directed graph concepts from the field of graph theory within mathematics. A graph data structure consists of a finite (and possibly mutabl ...

). Ruppert's algorithm is often used to convert an irregularly shaped polygon into an unstructured grid of triangles. In addition to triangles and tetrahedra, other commonly used elements in finite element simulation include quadrilateral (4-noded) and hexahedral (8-noded) elements in 2D and 3D, respectively. One of the most commonly used algorithms to generate unstructured quadrilateral grid is "Paving". However, there is no such commonly used algorithm for generating unstructured hexahedral grid on a general 3D solid model. "Plastering" is a 3D version of Paving, but it has difficulty in forming hexahedral elements at the interior of a solid.

External links

*{{cite web , url=https://visualization.hpc.mil/wiki/Types_of_Grids , title=Types of Grids , quote=Unstructured Grid , archiveurl=https://web.archive.org/web/20130325151312/https://visualization.hpc.mil/wiki/Types_of_Grids , archivedate=2013-03-25 Mesh generation fr:Maillage

See also

External links