Geodesic
A refinement of unstructured quadrilateral and mixed meshes
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 4 (2013), pp. 62-78 Cet article a éte moissonné depuis la source Math-Net.Ru

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This paper studies the refinement of unstructured quadrilateral and mixed meshes. We propose the variations for the definition of refinement templates “in nine cells” for the case if there is an unstructured quadrilateral mesh, which ensures cell's convexity of the result mesh. To control the maximum permissible mesh angle, we use the templates of refining the cells of bad quality. In addition, this paper presents a new unstructured mixed mesh refinement algorithm; also, we give several demonstration examples of the algorithm that show the considerable improvement of mesh quality, as compared with the well-known methods.
Keywords: unstructured meshes, mixed meshes, meshes refinement, refinement templates, geometry adaptive meshes. 
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A. S. Karavaev; S. P. Kopysov. A refinement of unstructured quadrilateral and mixed meshes. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 4 (2013), pp. 62-78. http://geodesic.mathdoc.fr/item/VUU_2013_4_a6/

[1] Kopysov S. P., Novikov A. K., “Domain decomposition for parallel adaptive finite element algorithm”, Vestn. Udmurt. Univ. Mat. Mekh. Komp'yut. Nauki, 2010, no. 3, 141–154

[2] Kopysov S. P., Novikov A. K., “Parallel algorithms of adaptive refinement and partitioning of unstructured grids”, Matematicheskoe Modelirovanie, 14:9 (2002), 91–96 | Zbl

[3] Kopysov S. P., Novikov A. K., “The review of refinement of triangular meshes”, Numerical methods for solving linear and nonlinear boundary value problems, Tr. Mat. Tsentra im. N. I. Lobachevskogo, 20, Kazan, 2003, 170–180 | MR

[4] Schneiders R., “Refining quadrilateral and hexahedral element meshes”, 5th International Conference on Grid Generation in Computational Field Simulations, 1996, 679–688

[5] Garimella R., “Conformal refinement of unstructured quadrilateral meshes”, 18th International Meshing Roundtable, Springer-Verlag, 2009, 31–44 | DOI

[6] Ebeida M. S., Patney A., Owens J. D., Mestreau E., “Isotropic conforming refinement of quadrilateral and hexahedral meshes using two-refinement templates”, International Journal for Numerical Methods in Engineering, 88 (2011), 974–985 | DOI | MR | Zbl

[7] Knupp P., “Algebraic mesh quality metrics”, SIAM J. Sci. Comput., 23:1 (2001), 193–218 | DOI | MR | Zbl

[8] Karavaev A. S., Kopysov S. P., Ponomarev A. B., “Algorithms for construction and refinement of unstructured quadrangle meshes on multiconnected domain”, Computational Continuum Mechanics, 5:2 (2012), 144–150

[9] Joe B., Local refinement of quadrilateral meshes, Technical Report ZCS2008-05, URL: http://members.shaw.ca/bjoe/techrep/zcs08-05.pdf

[10] Kopysov S. P., Novikov A. K., Ponomarev A. B., Rychkov V. N., Sagdeeva Yu. A., “A program environment for construction of computational models for parallel distributed computing”, Informatsionnye Tekhnologii, 2008, no. 3, 75–82