Anisotropic Delaunay Mesh Generation

Jean-Daniel Boissonnat (1, 2) , Camille Wormser (1) , Mariette Yvinec (1)

1 GEOMETRICA - Geometric computing
2 DATASHAPE - Understanding the Shape of Data

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.

Domaines: Géométrie algorithmique [cs.CG]

Jean-Daniel Boissonnat, Camille Wormser, Mariette Yvinec. Anisotropic Delaunay Mesh Generation. SIAM Journal on Computing, 2015, 44 (2), pp.467-512. ⟨10.1137/140955446⟩. ⟨hal-01251628v1⟩