MeshErzeugung

MeshErzeugung, or mesh generation, is the process of creating a discrete mesh over a geometric domain to support numerical simulation or rendering. The mesh defines elements and their connectivity and aims to approximate geometry while satisfying computational needs.

In two dimensions, common elements are triangles and quadrilaterals; in three dimensions, tetrahedra, hexahedra, prisms, and pyramids. A boundary-conforming mesh respects the domain boundary; graded meshes vary element size to capture features or changes inSolution behavior.

Core approaches include Delaunay-based triangulation, constrained Delaunay triangulation for fixed boundaries, and advancing-front methods. For 3D, tetrahedralization often uses Delaunay approaches; hex-mesh generation is more complex and uses hexahedral or mixed elements. Modern techniques combine local refinement, smoothing (e.g., Laplacian smoothing), and optimization to improve element quality. Adaptive mesh refinement uses error estimates to refine where more resolution is needed.

Quality metrics include minimum and maximum angles, aspect ratio, radius ratio, and shape quality measures; good meshes avoid poorly shaped elements to ensure stability in simulations.

Applications include finite element analysis in engineering, computational fluid dynamics, heat transfer, and computer graphics for rendering and physical simulation. MeshErzeugung is also used in geophysics and architectural modeling.

History and terminology: the field originated in the 1960s and expanded with Delaunay triangulation in the 1980s; many software libraries implement mesh generation algorithms. The English term is mesh generation; German literature often uses Mesh-Erzeugung or Netzbildung.