Meshing

Meshing is the process of discretizing a complex geometric domain into a network of elements that can be used for numerical computation or digital representation. A mesh divides the domain into nodes, edges, faces, and cells, forming the computational grid on which equations are approximated.

Meshes are classified by element type and topology. In two dimensions, common elements are triangles and quadrilaterals; in three dimensions, tetrahedra, hexahedra (cubes), prisms, and pyramids are typical. A mesh may be structured, with regular connectivity like a grid, or unstructured, with irregular connectivity. Surface meshes describe boundaries, while volume meshes fill the interior of the domain.

Mesh generation aims to create a faithful and efficient discretization. Common approaches include Delaunay triangulation and its refinements, advancing-front methods, and octree-based techniques. Hybrid and multi-part meshes combine different element types. Adaptive meshing uses error estimates or size functions to refine or coarsen locally, concentrating effort where it is most needed.

Mesh quality influences accuracy and numerical stability. Metrics such as minimum angle, element aspect ratio, skewness, and Jacobian determinant are used to assess and improve quality. Poor-quality or inverted elements can undermine simulations, so quality control and smoothing are often employed to enhance the mesh before solving.

Applications of meshing span finite element analysis, finite volume methods, computational fluid dynamics, and computer graphics. It also supports tasks in medical imaging, geosciences, and 3D printing preparation, where a suitable discretization enables efficient and accurate computation or rendering.