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Center for Nonlinear Studies |
The development of three-dimensional numerical discretisation schemes based on unstructured polyhedral grids is an exciting area of research, with such formulations imbued with a range of advantageous numerical properties compared to more conventional tetrahedral-type schemes. The generation of such grids, however, remains a challenging task. In this talk, I present recent work on the development of polyhedral grid-generation techniques --- algorithms designed to produce high-quality polyhedral meshes that conform to complex three-dimensional geometries and user-defined constraints. The geometrical and topological duality between Delaunay tessellations and Voronoi complexes is explored, with such a framework exploited to construct staggered polyhedral/tetrahedral grids that satisfy local-orthogonality conditions. The impact of several additional concepts is also investigated --- using a `restricted' Delaunay tessellation framework to achieve `generalised' boundary conformance, and `weighted' Voronoi complexes to improve polyhedral cell shape. Lastly, a coupled geometrical/topological optimisation framework is discussed, facilitating the generation of generalised, locally-optimal structures that depart from a Delaunay-based hierarchy.
Host: Mikhail Shashkov