Tree-based Control Space Structures for Discrete Metric Sources in 3D Meshing

Barbara Głut; Tomasz Jurczyk

doi:10.7494/csci.2019.20.4.3416

Authors

Barbara Głut Department of Computer Science, AGH https://orcid.org/0000-0003-1522-873X
Tomasz Jurczyk Department of Computer Science, AGH https://orcid.org/0000-0003-3557-6985

DOI:

https://doi.org/10.7494/csci.2019.20.4.3416

Keywords:

control space, kd-tree, octree, anisotropic metric, mesh generation and adaptation, discrete metric sources

Abstract

This article compares the different variations of the octree and kd-tree structures used to create a control space based on a set of discrete metric point-sources. The control space thus created supervises the generation of the mesh providing efficient access to the required information on the desired shape and size of the mesh elements at each point of the discretized domain. Structures are compared in terms of computational and memory complexity as well as regarding the accuracy of the approximation of the set of discrete metric sources in the created control space structure.

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References

Alauzet F.: Size Gradation Control of Anisotropic Meshes. In: Finite Elem. Anal. Des., vol. 46(1-2), pp. 181-202, 2010.

Alauzet F., Loseille A., Dervieux A., Frey P.: Multi-Dimensional Continuous Metric for Mesh Adaptation, pp. 191-214. Springer Berlin Heidelberg, Berlin, Heidelberg, 2006.

Aubry R., Karamete K., Mestreau E., Dey S., Löhner R.: Linear Sources for Mesh Generation. In: SIAM Journal on Scientific Computing, vol. 35(2), pp. A886-A907, 2013.

de Berg M., Cheong O., van Kreveld M., Overmars M.: Computational Geometry: Algorithms and Applications. Springer-Verlag, 2008.

Borouchaki H., George P.L., Hecht F., Laug P., Saltel E.: Delaunay mesh generation governed by metric specifications. Part I. Algorithms. In: Finite Elements in Analysis and Design, vol. 25, pp. 61-83, 1997.

Bottasso C.L.: Anisotropic mesh adaption by metric-driven optimization. In: International Journal for Numerical Methods in Engineering, vol. 60(3), pp. 597-639, 2004. ISSN 1097-0207. URL http://dx.doi.org/10.1002/nme.977.

Chen J., Xiao Z., Zheng Y., Zheng J., Li C., Liang K.: Automatic sizing functions for unstructured surface mesh generation. In: International Journal for Numerical Methods in Engineering, vol. 109(4), pp. 577-608, 2017. ISSN 1097-0207.

URL http://dx.doi.org/10.1002/nme.5298. Nme.5298.

Cunha A., Canann S., Saigal S.: Automatic Boundary Sizing For 2D And 3D Meshes. In: In Trends in unstructured mesh generation, volume AMD-220, pp. 65-72. 1997.

Frey P.J.: About Surface Remeshing. In: Proc. 9th Int. Meshing Roundtable, pp. 123-136. Sandia National Laboratories, 2000.

Głut B., Jurczyk T.: Preparation of the Sizing Field for Volume Mesh Generation. In: Proc. 13th Int. Conf. on Civil, Structural and Environmental Engineering Computing. Chania, Crete, Greece, 2011. Paper 115.

Jurczyk T.: Efficient Algorithms of Automatic Discretization of Non-Trivial Three-Dimensional Geometries and its Object-Oriented Implementation. Ph.D. thesis, AGH University of Science and Technology, Kraków, Poland, 2007.

Jurczyk T., Głut B.: Adaptive Control Space Structure for Anisotropic Mesh Generation. In: Proc. of ECCOMAS CFD 2006 European Conference on Computational Fluid Dynamics. Egmond aan Zee, The Netherlands, 2006.

Jurczyk T., Głut B.: Metric 3D Surface Mesh Generation Using Delaunay Criteria. In: Lecture Notes in Computer Science, vol. 3992, pp. 302-309, 2006.

Jurczyk T., Głut B.: The Insertion of Metric Sources for Three-dimensional Mesh Generation. In: Proc. 13th Int. Conf. on Civil, Structural and Environmental Engineering Computing. Chania, Crete, Greece, 2011. Paper 116.

Jurczyk T., Głut B.: Tree Structures for Adaptive Control Space in 3D Meshing. In: Computer Science, vol. 17(4), p. 541, 2017. ISSN 2300-7036. URL https://journals.agh.edu.pl/csci/article/view/2126.

Labbé P., Dompierre J., Vallet M.G., Guibault F., Trépanier J.Y.: A universal measure of the conformity of a mesh with respect to an anisotropic metric field. In: Int. J. Numer. Meth. Engng, vol. 61, pp. 2675-2695, 2004.

Miranda A.C.O., Martha L.F.: Mesh generation on high-curvature surfaces based on a background quadtree structure. In: Proceedings, 11th International Meshing Roundtable, pp. 333-342. 2002.

Owen S.J., Saigal S.: Surface mesh sizing control. In: International Journal for Numerical Methods in Engineering, vol. 47(1-3), pp. 497-511, 2000.

Persson P.O., Staten M.L., Xiao Z., Chen J., Zheng Y., Zeng L., Zheng J.: 23rd International Meshing Roundtable (IMR23) Automatic Unstructured Elementsizing Specification Algorithm for Surface Mesh Generation. In: Procedia Engineering, vol. 82, pp. 240-252, 2014.

Pippa S., Caligiana G.: GradH-Correction: guaranteed sizing gradation in multipatch parametric surface meshing. In: International Journal for Numerical Methods in Engineering, vol. 62(4), pp. 495-515, 2005. ISSN 1097-0207. URL http://dx.doi.org/10.1002/nme.1177.

Pirzadeh S.Z.: Structured Background Grids for Generation of Unstructured Grids by Advancing-Front Method. In: AIAA Journal, vol. 31(2), pp. 257-265, 1993.

Quadros W.R., Vyas V., Brewer M., Owen S.J., Shimada K.: A computational framework for automating generation of sizing function in assembly meshing via disconnected skeletons. In: Engineering with Computers, vol. 26(3), pp. 231-247, 2010.

Xiao Z., Chen J., Zheng Y., Zeng L., Zheng J.: Automatic Unstructured Element-sizing Specification Algorithm for Surface Mesh Generation. In: Procedia Engineering, vol. 82, pp. 240-252, 2014. ISSN 1877-7058. URL

http://dx.doi.org/http://dx.doi.org/10.1016/j.proeng.2014.10.387.