Meshgenerator

Meshgenerator refers to algorithms and software that create meshes of geometric domains for simulations, rendering, or analysis. A mesh partitions a domain into simple elements, typically triangles or quadrilaterals in 2D, tetrahedra, pentahedra, or hexahedra in 3D. Meshes support numerical methods such as finite element, finite volume, or finite difference methods by providing a discretization of the domain. Mesh generation can be categorized as structured or unstructured. Structured meshes use regular grids; unstructured meshes allow arbitrary connectivity and flexibly fit complex geometries. 2D meshes often rely on Delaunay triangulation or constrained Delaunay triangulation to respect boundaries; 3D meshes commonly use Delaunay-based tetrahedralization or advancing-front strategies, sometimes combined with octree or Voronoi concepts. Anisotropic meshing seeks element shapes that align with solution features by using a size or metric field.

Input to a mesh generator typically includes a geometric model with boundary representations, region labels, and a size function or error tolerance. Optional constraints preserve geometric features. Output consists of node coordinates and element connectivities, often with quality metrics. Common quality goals include avoiding slender elements and ensuring shape regularity, measured by angles, aspect ratios, and Jacobians. Post-processing may involve smoothing, refinement, coarsening, or mesh optimization.

Applications span finite element analysis in structural, fluid, and thermal simulations; computational geometry, computer graphics, and geographic information systems. Notable methods and tools include Delaunay-based approaches, advancing-front algorithms, constrained Delaunay, and software libraries such as TetGen and Gmsh.