unstructuredgrid

An unstructured grid, or unstructured mesh, is a discretization in which nodes are placed irregularly in space and elements connect these nodes in an arbitrary topology rather than a regular lattice. In two dimensions, common elements are triangles and quadrilaterals; in three dimensions, tetrahedra, hexahedra (cubes), prisms, pyramids, or general polyhedra may be used. This flexibility makes unstructured grids well suited to modeling complex geometries and enabling local refinement where needed.

Data organization typically consists of a list of points (nodes) and a list of cells (elements). Each cell is defined by a set of point indices, and mixed-element meshes (containing different cell shapes in the same mesh) are routine. Additional structures may track edges or faces, orientation, and boundary markers for applying boundary conditions.

Unstructured grids are usually generated by mesh generation algorithms that create a conforming mesh to a given geometry, such as Delaunay-based methods, advancing-front techniques, or octree-influenced approaches. They support adaptive refinement, local mesh coarsening, and hp-adaptivity, which adjust element size and polynomial order to balance accuracy and cost.

Applications include finite element analysis, finite volume methods for fluid flow, and other numerical simulations that require accurate representation of irregular domains. Advantages include geometric flexibility, the ability to represent complex boundaries, and local refinement; drawbacks include more complex data management, higher memory use, and potential degradation of numerical accuracy if mesh quality is poor.

In the Visualization Toolkit and related software, UnstructuredGrid denotes a data structure capable of storing arbitrary cell types and their connectivity along with associated field data on points or cells.