An unstructured grid or irregular grid is a
tessellation
A tessellation or tiling is the covering of a surface, often a plane (mathematics), plane, using one or more geometric shapes, called ''tiles'', with no overlaps and no gaps. In mathematics, tessellation can be generalized to high-dimensional ...
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 of ...
or
Euclidean space
Euclidean space is the fundamental space of geometry, intended to represent physical space. Originally, that is, in Euclid's Elements, Euclid's ''Elements'', it was the three-dimensional space of Euclidean geometry, but in modern mathematics ther ...
by simple shapes, such as
triangle
A triangle is a polygon with three Edge (geometry), edges and three Vertex (geometry), 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, an ...
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 the o ...
, 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 grids, 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 terminals, ...
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 mutab ...
).
Ruppert's algorithm In mesh generation, Delaunay refinement are algorithms for mesh generation based on the principle of adding Steiner points to the geometry of an input to be meshed, in a way that causes the Delaunay triangulation or constrained Delaunay triangulat ...
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.
See also
*
*
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*
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
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