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Theses

Automatic isogeometric analysis suitable trivariate models generation : Application to reduced order modeling

Abstract : This thesis presents an effective method to automatically construct trivariate tensor-product spline models of complicated geometry and arbitrary topology. Our method takes as input a solid model defined by its triangulated boundary. Using cuboid decomposition, an initial polycube approximating the input boundary mesh is built. This polycube serves as the parametric domain of the tensor-product spline representation required for isogeometric analysis. The polycube's nodes and arcs decompose the input model locally into quadrangular patches, and globally into hexahedral domains. Using aligned global parameterization, the nodes are re-positioned and the arcs are re-routed across the surface in a way to achieve low overall patch distortion, and alignment to principal curvature directions and sharp features. The optimization process is based on one of the main contributions of this thesis: a novel way to design cross fields with topological (i.e., imposed singularities) and geometrical (i.e., imposed directions) constraints by solving only sparse linear systems. Based on the optimized polycube and parameterization, compatible B-spline boundary surfaces are reconstructed. Finally, the interior volumetric parameterization is computed using Coon's interpolation and the B-spline surfaces as boundary conditions. This method can be applied to reduced order modeling for parametric studies based on geometrical parameters. For models with the same topology but different geometries, this method allows to have the same representation: i.e., meshes (or parameterizations) with the same topology.
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Hassan Al Akhras. Automatic isogeometric analysis suitable trivariate models generation : Application to reduced order modeling. Numerical Analysis [math.NA]. Université de Lyon, 2016. English. ⟨NNT : 2016LYSEI047⟩. ⟨tel-01755493⟩

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