Anisotropic Delaunay Mesh Generation

Jean-Daniel Boissonnat 1, 2 Camille Wormser 1 Mariette Yvinec 1
1 GEOMETRICA - Geometric computing
CRISAM - Inria Sophia Antipolis - Méditerranée , Inria Saclay - Ile de France
2 DATASHAPE - Understanding the Shape of Data
CRISAM - Inria Sophia Antipolis - Méditerranée , Inria Saclay - Ile de France
Abstract : Anisotropic meshes are triangulations of a given domain in the plane or in higher dimensions, with elements elongated along prescribed directions. Anisotropic trian-gulations 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 De-launay 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 sized and shaped according to the metric field.
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SIAM Journal on Computing, Society for Industrial and Applied Mathematics, 2015, 44 (2), pp.467-512. 〈SIAM〉. 〈10.1137/140955446〉
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Jean-Daniel Boissonnat, Camille Wormser, Mariette Yvinec. Anisotropic Delaunay Mesh Generation. SIAM Journal on Computing, Society for Industrial and Applied Mathematics, 2015, 44 (2), pp.467-512. 〈SIAM〉. 〈10.1137/140955446〉. 〈hal-01251628v2〉

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