Hybrid remeshing using metrics and frame field

Advisors: A. Loseille (INRIA Saclay) and F. Ledoux

Team: LIHPC, Université Paris-Saclay

Phd thesis started January, 10, 2020

Subject

Subject

While hexahedral meshes are preferred for some type of simulation codes, tetrahedral meshes are easier to generate. More precisely, it is generally not possible to generate the expected hexahedral mesh for any 3D shape domains, while tetrahedral meshers are nowadays able to automatically mesh very complex industrilal-level 3D models.

In this PhD works, we consider an hybrid approach that consists in generating 3D meshes made of both tetrahedral and hexahedral 3D cells. But, unlike state-of-the-art approaches, we do not focus on getting the highest number of hexahedral cells. We want to control the generation process using both frame fields (used in hex meshing) and metric fields (used in tetrahedral mesh adaptation) to create and align hexahedral cells in some areas of interest only (along strong discontinuities in a gradient field for instance).

Our approach relies on three major components:

• First, an unique robust tetrahedral remeshing operator: the cavity operator. Mesh generation and adaptation processes of tetrahedral meshes usually require a large number of operators: Delaunay-driven point insertion, edge-face-element point insertion, edge collapse, point smoothing, face/edge swaps, etc. Independently of the complexity of the geometrical shape, the more operators are used in a remeshing process, the less robust the process may become. As a consequence, a unique cavity-based operator was introduced a few years ago to embed all aforementioned operators. In this work, we focus on the definition and a robust implementation of this operator for hybrid remeshing of CAD-like geometrical shapes. In particular, we explain how to implement such an operator in a constrained context where both geometrical features and topological features have to be preserved.
• Second, a process to generate points to insert in an existing tetrahedral meshes. Those points must be generated by considering both a size and direction constraint provided by respectively an input metric field and an input frame field.
• Third, with the two previously given component, we can build an iterative process to generate an hydrid mesh.