September 26, 2024
16:15
Louvain-la-Neuve
Place Sainte Barbe, auditorium BARB 91
Mesh generation is the cornerstone of numerical simulation. Block-structured meshes, made of large quadrilateral or hexahedral blocks, are bound to dominate the scene as they allow to leverage hyper-efficient numerical methods (high-order finite elements, or GPU-ready finite differences). Yet, these block decompositions are still often manually created by engineers, as automatic meshers do not meet industrial requirements in terms of quality and robustness. This thesis proposes significant contributions that bring us closer to fully automatic, industrial-grade structured meshing.
A first contribution is a method to transform a quadrilateral quasi-structured mesh to a block-structured one, by expanding on ideas from the computer graphics works on quad layout optimization. This provides an end-to-end robust block-structured mesher, soon to be integrated in the open-source software Gmsh.
A popular approach to structured meshing is to rely on cross and frame fields, which give a local orientation and sizing of the quad/hex elements. Yet, most existing methods do not guarantee that a mesh exists exactly following the frame field; in some cases even the topology of the field is wrong. Turning to hexahedral meshing, efforts have been made to extend frame field methods to 3D, but it turns out they suffer even more from topological issues. This is due to the 
frame field not being integrable.
We have constructed an integrability measure for both 2D and 3D frame fields based on odeco tensors, a versatile frame representation that implicitly encodes the necessary frame symmetries. This result unlocks an optimization scheme that produces meshable frame fields in 2D and 3D, and guarantees that a corresponding structured quad and hex mesh can be subsequently computed.
These contributions solve a long-standing and difficult problem, and pave the way to a fully automatic all-hexahedral mesher which is the holy grail of numerical simulation.
Jury members :
- Prof. Jean-François Remacle (UCLouvain, Belgium), supervisor
- Prof. Renaud Ronsse (UCLouvain, Belgium), chairperson
- Dr. Alexandre Chemin (UCLouvain, Belgium)
- Prof. David Bommes (University of Bern, Switzerland)
- Prof. Edward Chien (Boston University, USA)
- Dr. Etienne Corman (LORIA, France)
- Prof. Christophe Geuzaine (ULiège, Belgium)