| |
Matheon
FU Diskrete Geometrie
|
|
|
People
Research
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.
|
References
-
Optimal elliptic Sobolev regularity near three--dimensional,
multi-material Neumann vertices,
Robert Haller-Dintelmann, Wolfgang Höppner, Hans-Christoph Kaiser, Joachim Rehberg and Günter M. Ziegler,
Matheon Preprint 808, April 2011, 27 pages.
-
On locally constructible spheres and balls,
Bruno Benedetti and Günter M. Ziegler,
Acta Mathematica 206 (2011), 205-243.
(arXiv:0902.0436)
-
Construction techniques for cubical complexes, odd cubical 4-polytopes,
and prescribed dual manifolds,
Alexander Schwartz and Günter M. Ziegler,
Experimental Mathematics 13 (2004), 385-413 (arXiv:0310269)
|
|
