Generalized Two-Dimensional Delaunay Mesh Refinement. Andrey Chernikov and Nikos Chrisochoides. SIAM Journal on Scientific Computing (Vol. 31, No. 5, pp. 3387-3403), 2009.

Abstract

Delaunay refinement is a popular mesh generation method which makes it possible to derive mathematical guarantees with respect to the quality of the elements. Traditional Delaunay refinement algorithms insert Steiner points in a small enumerable number (one or two) of specific positions inside circumscribed circles of poor quality triangles and on encroached segments. In this paper we prove that there exist entire two-dimensional and one-dimensional regions that can be used for the insertion of Steiner points (innumerable number of choices) while the guarantees on mesh quality can be preserved. This result opens up the possibility to use multiple point placement strategies, all covered by a single proof. In addition, the parallelization of this generalized algorithm immediately implies the parallelization for each individual point placement method.

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BibTex

@article{sisc09,
    author = "Andrey Chernikov and Nikos Chrisochoides",
    title = "Generalized Two-Dimensional Delaunay Mesh Refinement",
    journal = "SIAM Journal on Scientific Computing",
    year = "2009",
    volume = "31",
    issue = "5",
    pages = "3387--3403",
}