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 a part of the
Euclidean plane
In mathematics, a Euclidean plane is a Euclidean space of Two-dimensional space, dimension two, denoted \textbf^2 or \mathbb^2. It is a geometric space in which two real numbers are required to determine the position (geometry), position of eac ...
or
Euclidean space
Euclidean space is the fundamental space of geometry, intended to represent physical space. Originally, in Euclid's ''Elements'', it was the three-dimensional space of Euclidean geometry, but in modern mathematics there are ''Euclidean spaces ...
by simple shapes, such as
triangle
A triangle is a polygon with three corners and three sides, one of the basic shapes in geometry. The corners, also called ''vertices'', are zero-dimensional points while the sides connecting them, also called ''edges'', are one-dimension ...
s or
tetrahedra
In geometry, a tetrahedron (: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular Face (geometry), faces, six straight Edge (geometry), edges, and four vertex (geometry), vertices. The tet ...
, in an irregular pattern. Grids of this
type
Type may refer to:
Science and technology Computing
* Typing, producing text via a keyboard, typewriter, etc.
* Data type, collection of values used for computations.
* File type
* TYPE (DOS command), a command to display contents of a file.
* ...
may be used in
finite element analysis
Finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical models, mathematical modeling. Typical problem areas of interest include the traditional fields of structural ...
when the input to be analyzed has an irregular shape.
Unlike
structured grids, unstructured grids require a list of the
connectivity 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 mut ...
).
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.
See also
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References
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