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Accreditation To Supervise Research Year : 2021

Mesh Generation

Génération de maillages

Abstract

Meshes are ubiquitous in computer science, they define the geometry of the virtual representations of objects and permit to study the physical properties of their real world counterparts. In engineering, meshes have a key role in most scientific computation methods and are a prerequisite to reliable and efficient numerical simulations. Unstructured meshes allow size, orientation and shape variations, that are necessary for some numerical methods. The objective of my research work is to develop algorithms to generate unstructured meshes in three dimensions, a topic that combine computational geometry, computational physics and computer science challenges. In a first part, I describe my contribution to the pre-processing of surface meshes in the 3D space as well as a remeshing method based on the Voronoi diagram. The second part focuses on 3D mesh generation. Algorithms to generate two types of meshes are described: tetrahedral meshes using a Delaunay based approach and hybrid mesh generation using an indirect approach. This work in 3D led me to study on the underlying theoretical questions of computational geometry which are presented in the third part where my contributions to the enumeration of the combinatorial subdivisions of polyhedra into tetrahedra or hexahedra are described. The final chapter draws some conclusions and presents perspectives of this research work in combining a practical and theoretical approaches in mesh generation
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Dates and versions

tel-03249549 , version 1 (04-06-2021)
tel-03249549 , version 2 (23-06-2021)

Identifiers

  • HAL Id : tel-03249549 , version 2

Cite

Jeanne Pellerin. Mesh Generation. Computer Science [cs]. Université de Lorraine, 2021. ⟨tel-03249549v2⟩
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