Smoothing and cleaning up slivers

Anisotropic meshes are triangulations of a given domain in the plane or in higher dimensions, with elements elongated along prescribed directions. Anisotropic triangulations are known to be well suited for interpolation of functions or solving PDEs. Assuming that the anisotropic shape requirements for mesh elements are given through a metric field varying over the domain, we propose a new approach to anisotropic mesh generation, relying on the notion of anisotropic Delaunay meshes. An anisotropic Delaunay mesh is defined as a mesh in which the star of each vertex v consists of simplices that are Delaunay for the metric associated to vertex v. This definition works in any dimension and allows to define a simple refinement algorithm. The algorithm takes as input a domain and a metric field and provides, after completion, an anisotropic mesh whose elements are shaped according to the metric field.

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“…[19]. It has been extended to higher dimensions [23] and extends naturally to anisotropic metrics as proved in the appendix.…”

Section: Sliversmentioning

confidence: 99%

Anisotropic Delaunay Mesh Generation

Boissonnat¹,

Wormser²,

Yvinec³

2015

SIAM J. Comput.

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“…(see [81], [28] and [23]). The one chosen in this work considers the radius of the inscribed circle and the longest edge length.…”

Section: Chapter 6 Adaptive Mesh Refinementmentioning

confidence: 99%

3D ALE Finite-Element Method for Two-Phase Flows With Phase Change

Anjos

Mangiavacchi

Borhani

et al. 2013

Heat Transfer Engineering

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“…Li [21,14] proposes to explicitly perturb the vertices incident to a sliver in an almost-good mesh, by locally relocating them so as to remove the incident slivers. The idea is based on the fact that, for any triangle qrs, the region of locations of the vertex p such that the tetrahedron pqrs is a sliver, is very small.…”

Section: Vertex Perturbationmentioning

confidence: 99%

Perturbing Slivers in 3D Delaunay Meshes

Tournois

Srinivasan

Alliez

2009

Proceedings of the 18th International Meshing Roundtable

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Summary. Isotropic tetrahedron meshes generated by Delaunay triangulations are known to contain a majority of well-shaped tetrahedra, as well as spurious sliver tetrahedra. As the slivers hamper stability of numerical simulations we aim at removing them while keeping the triangulation Delaunay for simplicity. The solution which explicitly perturbs the slivers through random vertex relocation and Delaunay connectivity update is very effective but slow. In this paper we present a perturbation algorithm which favors deterministic over random perturbation. The added value is an improved efficiency and effectiveness. Our experimental study applies the proposed algorithm to meshes obtained by Delaunay refinement as well as to carefully optimized meshes.

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Smoothing and cleaning up slivers

Cited by 51 publications

References 13 publications

Anisotropic Delaunay Mesh Generation

Anisotropic Delaunay Mesh Generation

3D ALE Finite-Element Method for Two-Phase Flows With Phase Change

Perturbing Slivers in 3D Delaunay Meshes

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