Quadrilateral mesh create from a given cross field
Kokou Dotse  1@  , Vincent Mouysset  1  , Sébastien Pernet  1  

Many high precision schemes with excellent quality and efficiency properties are built on quadrilateral meshes. However, automatic generation of quadrilateral meshes with good quality elements remains a challenge. The method proposed in the paper is of great interest with a final block structured mesh, respecting the geometry and with good quality elements. However, it has some limitations, such as its inability to produce on very stretched geometries or on some domains without corners (e.g., a 2D ring), a valid cross-field which is the main notion on which the method is based. On the other hand, the variant of the Ginzburg-landau theory does not allow to treat domains which are not simply related. In our work, we propose a new point of view allowing to solve the above mentioned limitations while keeping the structured aspect of the mesh and opening other possibilities on the generation of the cross field. To do so, our idea is to abstract, within the method, the generation of the cross fields from the rest of the partitioning process. We give ourselves a representation field which we then process in order to obtain a partitioning in blocks of 4 sides. We thus obtain different meshes depending on the initial representation field.

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