DFG Forschungszentrum Matheon “Mathematik für Schlüsseltechnologien”
Project F13: Combinatorics and geometry restrictions on triangulations and meshes

      FU Berlin



FU Diskrete Geometrie



Head Günter M. Ziegler
Members Moritz Schmitt


Construction of efficient meshes is a core problem in Numerical Analysis. In this project we will focus on 3D and higher-dimensional meshes, where numerical analysis side constraints may ask for tetrahedral or cubical (quad) geometries, may ask for Delaunay or Voronoi meshes, may pose boundary or periodicity constraints, etc. This project will explore the geometry and combinatorics of meshes and mesh generation, thus enabling or smoothening access of methods from
  • topology and geometry of mesh generation
  • combinatorial theory of polytopes
  • theory of lattices and tilings
  • convexity theory (including volumes, angle, valuations)
  • metric geometry in the sense of Gromov
Its aims are:
  • to connect various notions of "complexity" for meshes,
  • to see explain how restrictions on complexity can be derived from constraints such as the Delaunay condition,
  • to explain situations where undesirable geometric substructures such as "slivers" necessarily occur, and
  • to make this understanding available for mesh generation algorithms.


Moritz Schmitt . 23-JUN-2011.

DFG Forschungszentrum Matheon "Mathematik für Schlüsseltechnologien"