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Concept
Types of mesh
Summary
A mesh is a representation of a larger geometric domain by smaller discrete cells. Meshes are commonly used to compute solutions of partial differential equations and render computer graphics, and to analyze geographical and cartographic data. A mesh partitions space into elements (or cells or zones) over which the equations can be solved, which then approximates the solution over the larger domain. Element boundaries may be constrained to lie on internal or external boundaries within a model. Higher-quality (better-shaped) elements have better numerical properties, where what constitutes a "better" element depends on the general governing equations and the particular solution to the model instance.
There are two types of two-dimensional cell shapes that are commonly used. These are the triangle and the quadrilateral.
Computationally poor elements will have sharp internal angles or short edges or both.
This cell shape consists of 3 sides and is one of the simplest types of mesh. A triangular surface mesh is always quick and easy to create. It is most common in unstructured grids.
This cell shape is a basic 4 sided one as shown in the figure. It is most common in structured grids.
Quadrilateral elements are usually excluded from being or becoming concave.
The basic 3-dimensional element are the tetrahedron, quadrilateral pyramid, triangular prism, and hexahedron. They all have triangular and quadrilateral faces.
Extruded 2-dimensional models may be represented entirely by the prisms and hexahedra as extruded triangles and quadrilaterals.
In general, quadrilateral faces in 3-dimensions may not be perfectly planar. A nonplanar quadrilateral face can be considered a thin tetrahedral volume that is shared by two neighboring elements.
A tetrahedron has 4 vertices, 6 edges, and is bounded by 4 triangular faces. In most cases a tetrahedral volume mesh can be generated automatically.
A quadrilaterally-based pyramid has 5 vertices, 8 edges, bounded by 4 triangular and 1 quadrilateral face.
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