A frontal Delaunay quad mesh generator using the L ∞ norm

• Published in: International journal for numerical methods in engineering Vol. 94; no. 5; pp. 494 - 512
• Main Authors: Remacle, J.-F., Henrotte, F., Carrier-Baudouin, T., Béchet, E., Marchandise, E., Geuzaine, C., Mouton, T.
• Format: Journal Article Web Resource
• Language: English
• Published: Chichester Blackwell Publishing Ltd 04-05-2013; Wiley; Wiley Subscription Services, Inc
• Subjects: Algorithmics. Computability. Computer arithmetics; Applied sciences; Combinatorics; Combinatorics. Ordered structures; Computer science; Computer science; control theory; systems; Engineering, computing & technology; Exact sciences and technology; Graph theory; Information retrieval. Graph; Ingénierie, informatique & technologie; Mathematics; Methods of scientific computing (including symbolic computation, algebraic computation); Numerical analysis. Scientific computation; optimization; perfect matching; quadrilateral meshing; Sciences and techniques of general use; Sciences informatiques; surface remeshing; Theoretical computing; Costs; Quadrilateral finite element; Refinement method; Delaunay triangulation; Graph theory; quadrilateral meshing; surface remeshing; Automatic mesh generation; Optimization; Polynomial time; Finite element method; Computational geometry; Minimum time; Alignment; Indirect method; Frontal; perfect matching; Mesh generation; Graph matching
• ISSN: 0029-5981; 1097-0207; 1097-0207
• DOI: 10.1002/nme.4458

SUMMARYIn a recent work, a new indirect method to generate all‐quad meshes has been developed. It takes advantage of a well‐known algorithm of the graph theory, namely the Blossom algorithm, which computes in polynomial time the minimum cost perfect matching in a graph. In this paper, we describe a method that allows to build triangular meshes that are better suited for recombination into quadrangles. This is performed by using the infinity norm to compute distances in the meshing process. The alignment of the elements in the frontal Delaunay procedure is controlled by a cross field defined on the domain. Meshes constructed this way have their points aligned with the cross‐field directions, and their triangles are almost right everywhere. Then, recombination with the Blossom‐based approach yields quadrilateral meshes of excellent quality. Copyright © 2013 John Wiley & Sons, Ltd.