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Curved Optimal Delaunay Triangulation
Abstract : Meshes with curvilinear elements hold the appealing promise of enhanced geometric flexibility and higher-order numerical accuracy compared to their commonly-used straight-edge counterparts. However, the generation of curved meshes remains a computationally expensive endeavor with current meshing approaches: high-order parametric elements are notoriously difficult to conform to a given boundary geometry, and enforcing a smooth and non-degenerate Jacobian everywhere brings additional numerical difficulties to the meshing of complex domains. In this paper, we propose an extension of Optimal Delaunay Triangulations (ODT) to curved and graded isotropic meshes. By exploiting a continuum mechanics interpretation of ODT instead of the usual approximation theoretical foundations, we formulate a very robust geometry and topology optimization of Bézier meshes based on a new simple functional promoting isotropic and uniform Jacobians throughout the domain. We demonstrate that our resulting curved meshes can adapt to complex domains with high precision even for a small count of elements thanks to the added flexibility afforded by more control points and higher order basis functions.
Keywords :
Optimal Delaunay Triangulations
Optimal Delau-nay Triangulations
Additional Key Words and Phrases: Higher-order meshing
CCS Concepts: • Mathematics of computing → Mesh generation
Bézier elements ACM Reference Format:
Mesh generation
Bézier elements
Higher-order meshing
higher order finite elements
Cited literature [49 references]
https://hal.inria.fr/hal-01826055
Contributor : Pierre Alliez <>
Submitted on : Thursday, October 18, 2018 - 8:40:19 AM
Last modification on : Wednesday, January 6, 2021 - 4:10:05 PM
Long-term archiving on: : Saturday, January 19, 2019 - 12:37:04 PM
Contributor : Pierre Alliez <>
Submitted on : Thursday, October 18, 2018 - 8:40:19 AM
Last modification on : Wednesday, January 6, 2021 - 4:10:05 PM
Long-term archiving on: : Saturday, January 19, 2019 - 12:37:04 PM
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CODT-preprint-final.pdf
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