MeshDichte

MeshDichte, or mesh density, is a measure of how fine or coarse a computational mesh is, defined by the size, distribution, and sometimes the shape of its elements. In a mesh, density indicates how many elements occupy a domain and how their sizes vary spatially. It is influenced by the need to resolve geometric features and variations in the solution field in numerical simulations or rendering tasks.

In numerical methods such as the finite element method (FEM) and computational fluid dynamics (CFD), higher mesh density generally increases accuracy but also raises computational cost in time and memory. Lower density reduces cost but may compromise results. Consequently, mesh density is chosen to balance precision with available resources, and it is often adapted to local solution behavior or geometry.

Factors affecting density include geometry complexity, boundary layers or regions with steep gradients, curvature, and material properties. Regions with large solution changes or near singularities typically require finer density, while smooth regions can use coarser meshes. Anisotropic density, where element shapes are elongated in certain directions, can efficiently capture directional features without uniformly increasing element counts.

Control methods involve specifying global or local target element sizes, using graded or adaptive meshing, and applying refinement criteria based on error indicators. Adaptive mesh refinement (AMR) and size fields allow automatic adjustment of density during solving. Meshing tools implement density control through background meshes, refinement markers, or size functions to produce appropriate density distributions.

Quality assessment includes metrics such as average element size, density variation, aspect ratio, and skewness. Diagnostics and error estimates guide density adjustments. Common mesh generators and environments support MeshDichte concepts, including tetrahedral or hexahedral meshes and methods like Delaunay-based or advancing-front approaches. See also mesh generation, adaptive meshing, and finite element analysis.