**Seminar Numerische Mathematik**

WIAS Berlin

#### Prof. N. Lei (Dalian University of Technology, China)

## Quadrilateral and hexahedral mesh generation based on surface foliation theory

**Programm / Abstract:**

For the purpose of isogeometric analysis, one of the most common ways is to construct structured hexahedral meshes, which have regular tensor product structure, and fit them by volumetric T-Splines. This theoretic work proposes a novel surface quadrilateral meshing method, colorable quad-mesh, which leads to the structured hexahedral mesh of the enclosed volume for high genus surfaces. The work proves the equivalence relations among colorable quad-meshes, finite measured foliations and Strebel differentials on surfaces. This trinity theorem lays down the theoretic foundation for quadrilateral/hexahedral mesh generation, and leads to practical, automatic algorithms. The work proposes the following algorithm: the user inputs a set of disjoint, simple loops on a high genus surface, and specifies a height parameter for each loop; a unique Strebel differential is computed with the combinatorial type and the heights prescribed by the user?s input; the Strebel differential assigns a flat metric on the surface and decomposes the surface into cylinders; a colorable quad-mesh is generated by splitting each cylinder into two quadrilaterals, followed by subdivision; the surface cylindrical decomposition is extended inward to produce a solid cylindrical decomposition of the volume; the hexahedral meshing is generated for each volumetric cylinder and then glued together to form a globally consistent hex-mesh.

**Zeit:**

am Donnerstag den 14. September 2017 um 15:00

**Ort:**

Weierstraß-Institut

Mohrenstr. 39

10117 Berlin

Raum: 405/406 4. Etage

*eingetragen von lawrenz(marion.lawrenz@wias-berlin.de, 030 20372566)*

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