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Theses

Génération de Maillages Quadrangulaires

Bertrand Pellenard 1
1 GEOMETRICA - Geometric computing
CRISAM - Inria Sophia Antipolis - Méditerranée , Inria Saclay - Ile de France
Abstract : The goal of this thesis is to devise methods and algorithms for the automatic generation of isotropic and anisotropic quadrilateral meshes. The first contribution is a method for isotropic quadrangular meshing of 2D domains, with control upon both element sizing and orientation. At the heart of our algorithm is an optimization procedure which uses several successive steps to improve the mesh quality criteria for size, shape, orientation and regularity. This methodology allows the simultaneous control of element sizing and orientation. The second contribution is an automatic method for computing an anisotropic rectangular metric on piecewise smooth surfaces approximated by triangle meshes. This metric is derived from a user-specified maximum tolerance error, and is expressed in angular deviation of the normal to the surface. It only depends on a single intuitive tolerance parameter and is shown particularly well suited to preserve boundaries and sharp features. The third contribution is a method for anisotropic polygonal remeshing of surfaces. The algorithm uses a greedy optimization procedure which adds, removes and relocates generators on the surface to satisfy two criteria related to partitioning and mesh conformity. These generators induce first a surface decomposition from their associated metrics during the optimization step, then a surface partitioning during the final meshing step. This methodology provides a good fit between the metric and the mesh elements during the optimization step.
Keywords : Mesh Generation
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Theses
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https://hal.inria.fr/tel-01098029
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Bertrand Pellenard. Génération de Maillages Quadrangulaires. Géométrie algorithmique [cs.CG]. UNSA, Polytech'Nice Sophia, 2012. Français. ⟨tel-01098029⟩

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