![]() ![]() , which allows to find the minimal cost perfect matching of a Theory of graphs: the Blossom algorithm, proposed by Edmonds in1965 The method we present here is an indirect approach to ReceivedCopyright c 2010 John Wiley & Sons, Ltd. Moresophisticated indirect methods use a mix of advancing front and Triangle-merge methods then use thetriangles of the initial meshĪnd recombine them to form quadrangles. In indirect methods, a triangular mesh is built first. Produce lowquality elements close to the boundaries of the domainĪnd are unable to fulfill general sizeconstraints (anisotropy, Quads are considered to be non robust and quadtree methods usually In direct methods, the quadrilaterals are constructed at once,Įither using some kind ofadvancing front technique or using There are essentially two categories of methods. To build non uniformquadrilateral meshes in an automatic manner. Let us first briefly recall which kinds of methods can be used Present a new way of generating such meshes. That quadrilateral meshes are indeed useful and in thispaper we Will not try to argue about thatthorny question herebut we assume Trianglesare usually passionate in the finite element community. Superior to triangular meshes forfinite element simulations.ĭiscussions about if and why quadrilaterals are better than Quadrilateral surface meshes are sometimes considered as ![]() Key words: quadrilateral meshing surface remeshing graph Terms ofelement shape and in terms of size field efficiency. Meshes produced by the new approach are better both in ![]() The newīlossom-Quad algorithm is comparedwith standard indirect Perfect matching in a graph in polynomial time. Theory, namely the Blossom algorithm that computes the minimumcost The method takes advantage of a wellknown algorithm of the graph Materials and Civil Engineering (iMMC),Batiment Euler, AvenueĢ Universite de Liege, Department of Electrical Engineering andĬomputer Science, Montefiore InstituteB28, Grande Traverse 10, 4000Ī new indirect way of producing all-quad meshes is presented. Marchandise1, A.ġ Universite catholique de Louvain, Institute of Mechanics, Engng 2010 00:16 Prepared using nmeauth.clsīlossom-Quad: a non-uniform quadrilateral mesh generator usinga INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERINGInt. * Correspondence to: Received Copyright c 2010 John Wiley & Sons, Ltd. Other more sophisticated indirect methods use a mix of advancing front and triangle merge. Triangle-merge methods then use the triangles of the initial mesh and recombine them to form quadrangles. In indirect methods, a triangular mesh is built first. Advancing front methods for quads are considered to be non robust and quadtree methods usually produce low quality elements close to the boundaries of the domain and are unable to fulfill general size constraints (anisotropy, strong variations). In direct methods, the quadrilaterals are constructed at once, either using some kind of advancing front technique or using regular grid-based methods (quadtrees). Let us first briefly recall which kinds of methods can be used to build non uniform quadrilateral meshes in an automatic manner. We will not try to argue about that thorny question here-but we assume that quadrilateral meshes are indeed useful and in this paper we present a new way of generating such meshes. Discussions about if and why quadrilaterals are better than triangles are usually passionate in the finite element community. Introduction Quadrilateral surface meshes are sometimes considered as superior to triangular meshes for finite element simulations. key words: quadrilateral meshing surface remeshing graph theory optimization perfect matching 1. Meshes produced by the new approach are better both in terms of element shape and in terms of size field efficiency. The new Blossom-Quad algorithm is compared with standard indirect procedures. The method takes advantage of a well known algorithm of the graph theory, namely the Blossom algorithm that computes the minimum cost perfect matching in a graph in polynomial time. ![]() Geuzaine 2 1 Universit´ e catholique de Louvain, Institute of Mechanics, Materials and Civil Engineering (iMMC), Bˆ atiment Euler, Avenue Georges Lemaˆ ıLouvain-la-Neuve, Belgium 2 Universit´ e de Li` ege, Department of Electrical Engineering and Computer Science, Montefiore Institute B28, Grande TraveLi` ege, Belgium SUMMARY A new indirect way of producing all-quad meshes is presented. Engng 2010 00 :1–6 Prepared using nmeauth.cls Blossom-Quad: a non-uniform quadrilateral mesh generator using a minimum cost perfect matching algorithm J.-F. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING Int. ![]()
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