meshstruktuurid

Meshstruktuurid, or mesh structures, are discrete representations of a geometric or physical domain created by connecting a set of vertices with edges and higher‑dimensional faces. They are used to discretize continuous spaces for numerical simulation, visualization, and analysis. In two dimensions they commonly consist of polygons (often triangles) and, in three dimensions, polyhedra (often tetrahedra or hexahedra).

Meshes are classified as structured or unstructured, and as simplicial (based on triangles or tetrahedra) or polyhedral (based on general polygons or polyhedra). Structured meshes have regular connectivity, while unstructured meshes adapt to complex geometries. Meshes may be 2D or 3D, and may incorporate boundary constraints to match the geometry of the domain.

Generation and refinement: Meshes are produced by algorithms such as Delaunay triangulation, Voronoi-based methods, advancing front techniques, or octree-based approaches. Quality measures, like element aspect ratio, minimum angle, and positive Jacobians, are used to assess and improve mesh quality; poor‑quality elements can degrade simulation accuracy or stability.

Applications: In science and engineering, meshes underpin the finite element method, finite volume methods, and other numerical schemes for solving partial differential equations. In computer graphics and visualization, they represent surfaces and volumes for rendering and analysis. In geosciences and medical simulation, meshes model complex structures and processes.

Adaptivity and challenges: Adaptive mesh refinement selectively increases resolution where needed, using error estimators. Challenges include generating meshes for complex geometries, maintaining mesh quality under refinement, and balancing computational cost with accuracy.