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High order mesh untangling for complex curved geometries

Abstract : We propose a new approach for constructing and untangling curved simplicial meshes that fit exactly to a geometrical boundary defined using quadratic Bézier patches. The method comprises two main ingredients: a linear elasticity analogy for untangling volume elements on the one hand and a local topological optimization for resolving invalid surface elements on the other hand. Starting from a linear mesh with a quadratic curved boundary, the first step of the algorithm consists in untangling surface mesh elements. In this phase, the problem is cast as a constrained optimization one whereby the worst element’s quality is improved iteratively under the constraint of maintaining valid neighboring elements. The problem is then reformulated as an unconstrained optimization through the use of a log-barrier method. The second step of the algorithm involves propagating the curvature to the volume of the domain via a linear elasticity analogy resulting in a valid volume mesh. Finally, two and three dimensional numerical examples are provided to validate the proposed approach.
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https://hal.inria.fr/hal-01632388
Contributor : Cécile Dobrzynski <>
Submitted on : Monday, November 13, 2017 - 4:51:11 PM
Last modification on : Tuesday, December 8, 2020 - 9:52:12 AM
Long-term archiving on: : Wednesday, February 14, 2018 - 3:08:29 PM

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  • HAL Id : hal-01632388, version 2

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Cecile Dobrzynski, Ghina El Jannoun. High order mesh untangling for complex curved geometries. [Research Report] RR-9120, INRIA Bordeaux, équipe CARDAMOM. 2017. ⟨hal-01632388v2⟩

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