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Optimisation de maillages

Jane Tournois 1
1 GEOMETRICA - Geometric computing
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : In this thesis, a practical approach to isotropic triangle mesh generation is proposed. In 2D as in 3D, the goal is to mesh the interior of a domain that possibly has a complex geometry. The studied approach consists in interleaving Delaunay refinement steps and mesh optimization steps, in order to generate quality graded meshes that satisfy size, shape, topology and approximation user-defined criteria for simplices. Widely used for simulation, finite element methods need graded meshes composed of well-shaped simplices. Alternatives to usual Delaunay refinement methods are developed. New mesh optimization methods, able to optimize internal and boundary vertices locations and to preserve the input boundary features, including sharp creases, are studied. In 2D, the optimization method is based on the Lloyd iteration and centroidal Voronoi tessellations (CVT). In 3D, a natural extension to optimal Delaunay triangulations (ODT) introduced by Chen that is able to optimize boundary vertices locations, is proposed. Our tetrahedron meshing algorithm is completed with a post-processing step that significantly improves the quality of tetrahedra dihedral angles. We finally give some experimental evidence that interleaving refinement and optimization results in generating meshes of higher quality than usual methods, in terms of simplices angles and number of vertices.
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Contributor : Tournois Jane <>
Submitted on : Friday, January 29, 2010 - 2:54:58 PM
Last modification on : Saturday, January 27, 2018 - 1:30:47 AM
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  • HAL Id : tel-00451619, version 1



Jane Tournois. Optimisation de maillages. Modeling and Simulation. Université Nice Sophia Antipolis, 2009. English. ⟨tel-00451619⟩



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