Combinatorial Algorithms for Quadrilateral and Hexahedral Mesh
Generation in Finite Element Methods
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Hence, engineers need tools to facilitate the mesh generation process. Algorithms for the automated mesh generation would lead to important savings in time and cost in the development of new products, for example, in the car industry.
Our goals in this project comprise a systematic study of the combinatorial structure of quadrilateral and hexahedral meshes, the identification of relations between the structure of a mesh and its quality with respect to different criteria, the development and analysis of efficient algorithms for mesh generation, the implementation of prototypes for our algorithms, and their empirical evaluation together with engineers.
Our method is based on an abstraction from the concrete geometric mesh generation problem to a purely discrete, combinatorial model. Graph algorithmic techniques like network flows and matchings play a decisive role in the solution of these combinatorial problems.