Mesh generation is considered as a hard problem. Surprisingly, only about 20 research teams are actively working on the subject (we are clearly one of those). Fundamental work is performed by MEMA on different topics related to mesh generation: quad/hex meshing, parallel meshing, curvilinear meshing, computational geometry. Moreover, the team is largely involved in the most important open source project devoted to mesh generation.
Gmsh鈥檚 developers have recently received a free software award (Les troph茅es du Libre). The team is presently trying to address several issues related to mesh generation. Among those are curvilinear meshing and hex meshing.
Mesh
A novel algorithm that produces a quad layout based on an imposed set of singularities is proposed. In this paper, we either use singularities that appear naturally, e.g., by minimizing Ginzburg-Landau energy, or use as an input user-defined singularity pattern, possibly with high valence singularities that do not appear naturally in cross-field computations. The first contribution of the paper is the development of a formulation that allows computing a cross-field from a given set of singularities through the resolution of two linear PDEs. Specific mesh refinement is applied at the vicinity of singularities to accommodate the large gradients of cross directions that appear in the vicinity of singularities of high valence. The paper鈥檚 second contribution is a correction scheme that repairs limit cycles and/or non-quadrilateral patches. Finally, a high-quality block-structured quad mesh is generated from the quad layout and per-partition parametrization.